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Estimation of the maximum allowable lack of penetration defects in
circumferential butt welds of structural tubular towers
Article in Engineering Structures · September 2009
DOI: 10.1016/j.engstruct.2009.03.013
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Engineering Structures 31 (2009) 2123–2131
Contents lists available at ScienceDirect
Engineering Structures
journal homepage: www.elsevier.com/locate/engstruct
Estimation of the maximum allowable lack of penetration defects in
circumferential butt welds of structural tubular towers
S. Cicero ∗ , R. Lacalle, R. Cicero
Dpto. Ciencia e Ingeniería del Terreno y de los Materiales, Universidad de Cantabria, Santander, Cantabria, Spain
article
info
Article history:
Received 19 November 2008
Received in revised form
11 February 2009
Accepted 17 March 2009
Available online 7 April 2009
Keywords:
Tubular tower
Lack of penetration
Fracture
Fatigue
Sensitivity analysis
abstract
This paper analyses the structural integrity of structural tubular towers (i.e., towers of wind turbines and
floodlight towers) with lack of penetration defects on their circumferential butt welds. The methodology
presented is particularised to the analysis of the lack of penetration defects detected in certain sections of
several wind towers after the construction process. It is also analysed how such defects affect the fitness
for service of the towers during their theoretical lifespan (20 years). The methodology (based on the use of
Failure Assessment Diagrams, FAD) can easily be extrapolated to the assessment of other types of defects
or towers. Its main hypotheses consist of establishing that the defects behave as internal cracks with
certain geometries and also that fracture and fatigue are the key processes affecting the structural integrity
of the towers. Then, the resulting allowable crack size, corresponding to the lifespan of the tower, for the
different sections analysed and for the different crack geometries considered is determined.
© 2009 Elsevier Ltd. All rights reserved.
1. Introduction
This paper presents a methodology for the structural integrity
assessment of tubular towers containing lack of penetration
defects on the butt welds of their circumferential sections.
In most cases, when the towers have large dimensions, these
structures are made up of several stretches (manufactured in plant)
which are, simultaneously, composed of different rings. The joints
between the rings are generally made using butt welds, while the
joints between the stretches composing the tower are performed
through butt welds or, alternatively, through a system of flanges
and bolts. In any case, the welding process requires a strict and
exhaustive quality control in order to avoid any kind of defects
threatening the structural integrity of the tower, particularly in
those welds performed in situ when the stretches are joined
through welding processes.
Unfortunately there are situations where the defects are
not avoided. In such cases, the structural consequences of the
defects are not straightforward, making it necessary to perform
a structural integrity assessment of the towers considering the
presence of such defects.
There are some characteristic examples of structural tubular
towers. Perhaps the towers of wind turbines (wind towers) and
∗ Corresponding address: Departamento de Ciencia e Ingeniería de Materiales,
Universidad de Cantabria, Av/Los Castros s/n, ETS Ingenieros de Caminos, 39005,
Santander, Spain. Fax: +34 942201818.
E-mail address: ciceros@unican.es (S. Cicero).
0141-0296/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.engstruct.2009.03.013
flood light towers (see Fig. 1) are among the most representative.
Generally, these towers are made up of several stretches or
modules (cylinder or cone trunk shaped) which are individually
carried to the final location (i.e., wind farm, stadium . . . ) and then
joined.
Starting from the steel sheet reception in the production centre,
the whole manufacturing and construction process of the towers
consists (in many cases) of the following steps:
(1) Shaping: the sheets (usually from 20 to 40 mm thick) are
inserted in a machine that shapes the rings using a system
of rollers. In this case, only one sheet per section was used,
leading to just one longitudinal joint per ring.
(2) Welding: The longitudinal joints are welded (submerged arc
welding, SAW) through double V type butt welds, obtaining
the corresponding rings. Then, the rings are joined performing
circumferential welds (also using SAW techniques and double
V type butt welds). As a result, primary cylinder/cone trunk
shaped stretches of different lengths are obtained. The number
of rings joined depends on the length of the stretches
(generally varying from 10 to 30 m in the case of wind towers).
Fig. 2 shows a scheme of a double V type butt weld, before
and after the welding process. No defects were found on the
longitudinal welds, so the analysis performed here is only
referred to the circumferential ones.
(3) Surface treatments (i.e., shoot peening, painting . . . ), drying and
assembly of the auxiliary equipment (flanges, ladders . . . ).
(4) Transport from the centre of production to the final location
(i.e., wind farm).
2124
S. Cicero et al. / Engineering Structures 31 (2009) 2123–2131
to extremely demanding conditions. Also, they are generally
constructed following the steps mentioned above. All of this
means that these structures have specific circumstances and
characteristics (geometries, materials, loads . . . ) that allow a
common methodology to be established for their structural
integrity assessment. In a general case, the different steps proposed
here for this assessment are the following:
Fig. 1. Flood light tower used in a football stadium.
Fig. 2. Longitudinal section of double V butt welds performed in the joints between
rings and, occasionally, between stretches. (a) Extremes of the rings being joined
after their preparation and before the welding; (b) Final joint.
(5) Erection of the tower by joining the different stretches or
modules which are placed one on top of the other (using lattice
cranes).
As a consequence of this manufacturing and construction
process, a large amount of welds are generated on the towers
and, in spite of the quality controls that can be applied, different
types of defects may arise (lack of penetration, pores, inclusions,
misalignment . . . ). The special precautions taken during the SAW
process (in terms of heat input, speed, etc.), together with the
shoot peening post-treatment, ensure that the welds obtained
have negligible residual stresses for structural integrity assessment
purposes.
As mentioned above, a methodology is here proposed for
the structural integrity assessment of towers containing lack
of penetration defects, which can be easily extrapolated to
other types of defects (i.e., pores) or towers (non-tubular). The
methodology is applied to the analysis of a case study consisting
of the structural integrity assessment of several wind towers
containing lack of penetration defects that were detected after the
construction process and before entering in service.
2. Proposed methodology
The towers considered in this paper are generally tall (up
to 100 m) and, in many cases (i.e., wind farms) are exposed
(a) Definition of the geometry of the tower: Basically, the height
of the tower and the diameter and thickness of the different
sections.
(b) Material properties: Tensile properties and fracture toughness
of base material, Heat Affected Zone (HAZ) and weld material.
Special caution should be taken to prevent the mismatch
phenomenon (differences in yield strengths between the base
material and the weld metal greater than 10%). In such cases, a
specific mismatch analysis has to be considered [1–7].
(c) Structural and stress analysis, determining forces, moments and
stresses on the sections where the defects may appear.
(d) Welds inspection using adequate inspection techniques (i.e.,
ultrasonic, magnetic particles, eddy current . . . ).
(e) Definition of the defects in the different sections: Type (crack,
notch, pore . . . ) and dimensions.
(f) Definition of the different processes or mechanisms affecting the
structural integrity of the tower: Generally, random loads caused
by the wind or variable loading caused by the blades (in the
case of wind towers) generate stress variation on the different
sections of the tower. Therefore, fatigue and fracture are the
key processes in these types of structures, but under certain
circumstances, such as offshore wind towers, other processes
such as Stress Corrosion Cracking (SCC) should be considered.
Here it is stressed that, in a general case, the combination of
defects and loads of a structure made from a certain material
then determines the integrity of the structure.
(g) Fracture analysis: Once the material properties, the geometry
of the sections and the characteristics of the defects are
known, critical crack sizes (those causing the failure) can
be obtained using a Failure Assessment Diagram (FAD) [1–3,
8], that simultaneously analyses fracture and plastic collapse
processes. In the cases where the defects are considered
to behave as notches (and not cracks), different corrections
(i.e., [9,10]) can be applied in order to avoid the excessive
conservatism obtained when notches are analysed as cracks.
Also, in cases with mismatch condition, fracture analysis
requires a special treatment that can be performed using
specific methodologies proposed in some structural integrity
procedures [1–7,11,12].
For tubular towers (circumferential sections) the solutions
for the stress intensity factors and the limit loads are straightforward for many types of defects (i.e., through thickness crack,
internal circumferential crack, external circumferential crack,
embedded crack . . . ) in most of the different assessment procedures (i.e., [1–3,11]).
The critical sizes obtained are then compared to those
defined in step (e). If they are bigger than these, actions
(repair, substitution . . . ) are required. If not, the analysis has
to consider the possible subcritical crack propagation caused
by the variable stresses acting on the tower (step (h)) or other
mechanisms (step (i)).
(h) Fatigue analysis: Considering the initial defects defined in (e)
and the stress variations determined in (c), the evolution of
the crack sizes caused by the fatigue process is determined
using adequate tools (i.e., Paris law [13], Forman–Mettu
equation [14] . . . ). In order to ensure the structural integrity of
the towers, the resulting crack size at the end of their lifespan
should be lower than the critical sizes obtained in step (g).
S. Cicero et al. / Engineering Structures 31 (2009) 2123–2131
2125
Table 1
Dimensions of the analysed circumferential sections.
Section
Diameter (mm)
Thickness (mm)
S1
S2
S3
4000
3865
2630
36
35
21
3. Case study
A number of lack of penetration type defects were detected
on several (and identical) wind towers after the construction of
the towers and before entering in service, with the consequent
uncertainty for the owner, given that the defects could put at
risk the integrity of the structures during their expected lifespan
(20 years). Each tower is made up of four stretches or modules
(cone trunk shaped) which are individually carried to the wind
farm and then joined in situ by means of circumferential flanges
placed on the extremes of the modules and a numerous set of bolts.
The stretches were manufactured in plant from a number of plates
following the process explained in Section 1.
The analysis consists of the fracture and fatigue assessment of
three circumferential welded joints, which repeatedly presented
deficiencies, determining the maximum allowable lack of penetration defects in such a way that the structural integrity of the towers
is not jeopardized. For this purpose the methodology presented in
this paper has been used together with the newly developed FITNET FFS Procedure [1–3].
3.1. Geometry of the tower and material properties (Steps (a) and (b))
Fig. 3. Flowchart summarising the methodology proposed for the structural
integrity assessment of the towers with lack of penetration defects.
(i) Analysis of other failure mechanisms: Although fracture and
fatigue are the key mechanisms in these types of structures,
there are other processes or situations (SCC, Local Thin Areas,
buckling . . . ) that may be affected by the initial defects
generated in the construction of the towers. If so, specific
analysis would be required [1].
(j) Sensitivity analysis: Given that some of the inputs considered
in the analysis (loads, stresses, fracture toughness . . . ) are not
deterministic, sensitivity analyses may be required in order to
check how the variations in the inputs considered affect the
result obtained.
Once the allowable crack sizes are determined, two main
possibilities may occur:
- The allowable crack sizes are larger than those detected in the
structure. In such cases, there is no need to take any remedial
action.
- There are some allowable crack sizes that are smaller than
those detected in the structure. In such cases, remedial actions
(i.e., removal of the damaged welded zone and subsequent
rewelding) are required. The number and the size of the defects
determine the feasibility of the repair, both in economical and
technological terms.
This methodology (summarised in the flowchart shown in
Fig. 3) is applied below to a case study in order to illustrate more
clearly the different steps explained above.
Table 1 gathers the dimensions of the circumferential sections
(S1, S2 and S3) of the 80 m high towers analysed, placed
(respectively) on the first, second and third stretch, as shown in
Fig. 4. These sections were judged by the owner as the critical ones
in terms of the structural integrity of the towers. Section S1 is made
of S355J2 steel [15], S2 is made of S235J0 steel [15] and, finally, S3
is made of S235JR steel [15], all of them being non-alloy structural
steels. Table 2 shows the corresponding mechanical properties
(C and m are the material constants in the Paris law), that can
be considered applicable for both the base material and the weld
(no mismatch analysis is required). The Paris law provided is a
lower bound value of the actual ones, including the effect of the
R ratio. Therefore, the integration of this law is made by using the
stress variations without any consideration of the mean stress.
Before the welding process, the edges of the rings being joined
were machined and prepared as shown in Fig. 5, in order to perform
double V butt welds (Fig. 1). The welds were developed from both
the inner and the outer surface of the final tower.
3.2. Structural and stress analysis (Step (c))
The loads acting on the towers have an evident random
component which mainly arises from the random nature of wind
loads. Wind effects were determined following [16] and then
the corresponding loading conditions for the tower, designed
according to [17], can be inferred. The resulting acting loads
(caused by wind and the rotation of the rotor blades) were obtained
as a Markov matrix (supplied by the owner), distinguishing
bending moment range, mean bending moment and number of
cycles for each type of cycle. The compression arising from their
own weight is not considered. This constitutes a conservative
assumption, given that it provides higher tensile stresses than
the actual ones. As an example, Table 3 gathers part of the loads
in Section S1. It should be noted that these loads are defined as
operational stability loads, which represent operation of the wind
farm over a service life of 20 years.
2126
S. Cicero et al. / Engineering Structures 31 (2009) 2123–2131
Table 2
Mechanical properties of the different materials.
Section
Material [15]
Yield stress (σy , MPa)
Ultimate tensile stress (σu , MPa)
Charpy T27J (◦ C)
S1
S2
S3
S355J2
S235J0
S235JR
345
225
225
470
360
360
−20
0
20
∆Kth (MPa m1/2 )
C (da/dN in m/cycle)
m
8.8
6.89E−12
3
Table 3
Markov matrix gathering the load spectrum in Section S1.
Range (N m)
Mean (N m)
650 000
650 000
650 000
−21 450 004
−4 550 004
−3 250 004
...
1 950 000
1 950 000
1 950 000
...
4 550 001
4 550 001
4 550 001
...
11 050 001
11 050 001
11 050 001
...
16 250 001
16 250 001
16 250 001
...
55 250 004
56 550 004
56 550 004
Cycles
42
10
290
...
...
6 142 800
11 987 665
13 771 145
...
757 051
2 075 812
3 223 629
...
30
12
98 892
...
9
67 380
71 040
...
150
120
150
97 49 997
11 049 997
12 349 997
...
17 549 998
18 849 998
20 149 998
...
5 849 997
7 149 997
9 749 997
...
5 849 997
7 149 997
9 749 997
...
−1 950 004
−3 250 004
−1 950 004
Table 4
Maximum tensile stresses in the different sections analysed.
Section
Maximum tensile stress (MPa)
S1
S2
S3
175
177
161
Fig. 4. Sketch representing the structure of the case study.
Fig. 6. Scheme of lack of penetration defects found on the butt welds of the towers.
The maximum tensile stresses (pure bending) in the three
sections are shown in Table 4. These stresses arise from the socalled extreme loads, which correspond to the operation of the
wind farm over a service life of at least 50 years. It should be noted
that these maximum stresses are moderately higher than those
that would be obtained from Table 3 and were provided by the
owner.
3.3. Weld inspection and definition of defects (Steps (d) and (e))
Fig. 5. Geometry of the machined edges of the sections joined by circumferential
butt welds (dimensions in mm).
NDE techniques (ultrasonic inspection) were used by the owner
in order to detect possible defects on the different welds. The
lack of penetration defects was systematically detected in three
sections (S1, S2 and S3). Fig. 6 represents a scheme of this type of
defect.
S. Cicero et al. / Engineering Structures 31 (2009) 2123–2131
2127
Failure
Assesment
Line
1.0
C
B
A = Acceptable Condition
B = Limiting Condition
C = Unacceptable Condition
Kr
A
0
Fig. 7. Geometry of cracks analysed [2]. 2c = 5 mm, π R/2, π R y 2π R.
The definition of the geometry of the detected defects was not
straightforward and did not present any general characteristics
in terms of length or depth. Also, interactions between adjacent
defects were not ruled out. For these reasons, the defects were
idealised as embedded and circumferential (see Fig. 7) with
2c values of 5 mm, quarter, half and whole circumference, 2a
being the unknown value to be obtained in steps (g)–(i). These
assumptions cover the defect geometries detected in the welds.
Moreover, in most cases these kinds of defects are notches,
with lower stress concentrations than those in cracks [9,10,18–23],
but the uncertainty about the corresponding notch radius and
the possibility of microcracks arising from the notch tip after
the welding process make it advisable to consider that these
defects behave as cracks. This assumption is conservative for both
fracture [9,10,22,23] and fatigue (it does not consider possible
crack initiation times, just crack propagation) assessments, so the
results obtained correspond to lower bound estimations of the
performance of the towers.
The fracture analyses were made using the Failure Assessment
Diagram (FAD) methodology proposed in [1] and maximum
allowable crack sizes (2aall , see Fig. 7) were obtained for the
different hypotheses of crack geometry. Every cracked component
subjected to a certain load can fail due to a fracture mechanism, due
to a plastic collapse mechanism or, finally, due to a combination
of both mechanisms (fracture and plastic collapse). The FAD
methodology [1,8,24–26] allows all these three possible situations
to be assessed with a single comprehensive tool.
Once the tensile properties of the material are known, the
Failure Assessment Line (FAL) can be defined, which determines
the region corresponding to safe conditions in the component
(area within the FAL and the coordinate axes defined below). Here,
FAD Option 1 in FITNET FFS Procedure (Eq. (1)) for discontinuous
yielding material has been used (given that the materials used in
the towers usually show the Lüders strain during yielding), which
Lrmax
is defined from the proof stress (here Rp ), the ultimate tensile
strength (Rm ) and Young’s modulus (E):
−1/2
f (Lr ) = 1 + 0.5L2r
f (Lr ) = f (1)Lr(N −1)/2N
f (Lr ) = 0
Lr ≤ 1
1 ≤ Lr ≤ Lmax
r
Lr ≥ Lmax
r
S
(1)
where
µ = min 0.001
N = 0.3 1 −
E
Rp
Rp
; 0.6
(2)
(3)
Rm
Lmax
= 0.5 1 + Rm /Rp .
r
(4)
On the other hand, the situation of the component in the FAD is
defined by the coordinates Kr (relation between the applied stress
intensity factor, KI , and the material fracture resistance, Kmat ) and
Lr (relation between the applied load, F , and the plastic collapse
load, Fy ). Fig. 8 clarifies the FAD methodology (Eqs. (5) and (6)):
Kr =
3.5. Fracture analysis (Step (g))
1.0
Fig. 8. Scheme showing the FAD methodology [1]. F : applied load; Fy : plastic
collapse load; Lmax
: maximum permitted value of Lr ; Kr : fracture ratio of applied
r
elastic K value to Kmat (material toughness).
3.4. Mechanisms affecting structural integrity of the towers (Step (f))
Given the nature of the wind towers (which are mainly
subjected to variable loading) and the type of defects considered
(cracks), fracture and fatigue processes were identified as the
major causes of concern. It was also considered that other
mechanisms like SCC, corrosion or buckling, had no possible and
reasonable relation with the defects found in the welds.
Lr=F/Fy
Lr =
KI
(5)
Kmat
F
Fy
.
(6)
For KI calculations, the formulation proposed in the FITNET FFS
Procedure [1–3] (case A.4.2.3. in Annex A [2]) has been used. As
mentioned above, four circumferential crack extensions have been
considered in each section: 2c = 5 mm, quarter, half and whole
circumference (see Fig. 7).
The fracture toughness of the different materials at the most
severe working conditions (−40 ◦ C) has been estimated using the
Master Curve Approach [27] and the corresponding Charpy values
(in terms of T27J ) [1]. For this purpose, Eq. (7) (corresponding to
Eq. 5.43, chapter 5, in FITNET FFS Procedure) has been used, which
provides a conservative estimation of the fracture toughness,
Kmat , from the corresponding Charpy T27J . This equation provides
the fracture toughness of the material within the Transition
Zone (between Lower Shelf and Upper Shelf) in certain steels
(i.e., ferritic). The chosen failure probability was Pf = 1% and the
results are shown in Table 5.
Kmat = 20 + 11 + 77 exp 0.019 T − T27J + 3 ◦ C
×
25
B
0.25 ln
1
1 − Pf
0.25
.
(7)
The yield load considered (in this case the load is a bending
moment) for each of the three sections and for every crack size
2128
S. Cicero et al. / Engineering Structures 31 (2009) 2123–2131
1.2
Table 5
Estimation of fracture toughness from Charpy values.
Section Material [15] Charpy T 27J (◦ C) Thickness, B (mm) Kmat (MPa m1/2 ) [1]
S1
S2
S3
−20
S355J2
S235J0
S235JR
36
35
21
0
20
1
39.3
34.3
32.3
0.8
2c=5 mm
Kr
2c = 1/4 circumference
1.2
0.6
2c = 1/2 circumference
2c = whole circumference
0.4
1
2c=5 mm
0.8
0.2
2c = 1/4 circumference
2c = 1/2 circumference
Kr
2c = whole circumference
0
0.6
0
0.4
2a = 2 mm
0.4
0.6
0.8
Lr
1
1.2
1.4
1.6
Fig. 11. FAD analysis in section S3.
0.2
0
0.2
2a = 10 mm
2a = 5 mm
Table 6
Critical crack sizes (2ac ) in Sections S1, S2 and S3 for the four crack extension (2c)
hypotheses (mm).
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Section
Lr
S1
Thickness: 36 mm
S2
Thickness: 35 mm
S3
Thickness: 21 mm
Fig. 9. FAD analysis in section S1.
1.2
2c =
5 mm
2c =
1/4 circ.
2c =
1/2 circ.
2c =
whole circ.
17.5
17.5
17.5
13.2
7.4
7.4
7.4
7.4
5.9
5.9
5.9
5.9
1
Kr
0.8
Table 7
Crack sizes (2ath ), below which there is no fatigue propagation (mm).
2c=5 mm
0.6
Section
2c = 1/4 circumference
2c =
5 mm
2c =
1/4 circ.
2c =
1/2 circ.
2c =
whole circ.
4.3
3.0
3.0
2.9
4.0
2.9
2.9
2.8
7.3
4.2
4.1
3.8
2c = 1/2 circumference
S1
Thickness: 36 mm
S2
Thickness: 35 mm
S3
Thickness: 21 mm
2c = whole circumference
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Lr
produce the fracture–plastic collapse of the corresponding wind
tower for the maximum stresses foreseen during its lifespan.
Fig. 10. FAD analysis in section S2.
3.6. Fatigue analysis (Step (h))
hypothesis, has been the one that produces the beginning of
yielding in the net section (cracked area not considered). This
assumption is conservative, given that it considers the yielding in
the extreme ligament and not the yielding of the whole section.
Once the inputs (tensile properties, fracture toughness and
yield load) are defined, the FAD methodology can be applied. Four
FAD assessments were made for each section (corresponding to the
four crack geometry hypotheses), and three types of crack depth
(2a, see Fig. 7) were considered in each FAD: 2 mm, 5 mm and
10 mm (covering the size range of the defects found). Figs. 9–11
gather the FAD assessment in circumferential Sections S1, S2
and S3, respectively. Each of these figures shows the situation
of the corresponding section under 12 different crack geometry
hypotheses (4 values of crack extension (2c) × 3 values of crack
length (2a)) and for the bending moments corresponding to the
maximum stresses shown in Table 4.
Table 6 shows, for each combination of section and crack
extension hypothesis (2c), the corresponding critical crack size
(2ac ) obtained from Figs. 9–11 (intersection of the different 2c lines
with the FAL). Larger cracks than those gathered in Table 6 would
Once the critical crack sizes for the different hypotheses (and
for fracture–plastic collapse mechanisms) have been obtained,
it is necessary to obtain those initial cracks in the tower that
would propagate under fatigue processes during its lifespan.
Previous fracture–plastic collapse assessment is focussed on the
application of a certain load (bending moment) in the component
containing some specified defects. However, subcritical fatigue
crack propagation is produced when the stress intensity factor
variation, ∆KI , is higher than the material fatigue threshold, ∆Kth
(see Table 2). In such a case, the towers would not fail at the
initial stage, but critical conditions could be achieved during their
lifespan due to the fatigue crack propagation.
Table 7 gathers, for each section and crack extension (2c), the
crack size (2ath ) for which the stress intensity factor variation, ∆KI ,
reaches the material fatigue threshold, ∆Kth , when the section is
subjected to the corresponding maximum stress variation. Crack
sizes below these values would never produce fatigue propagation,
given that they would always produce stress intensity factor
variations lower than the fatigue threshold. Therefore, the values
S. Cicero et al. / Engineering Structures 31 (2009) 2123–2131
Table 8
Final crack sizes (2af ) at the end of the lifespan of the towers (mm). Bold characters
correspond to those situations where 2ath causes the structural failure before the
lifespan finishes.
Section
S1
Thickness: 36 mm
S2
Thickness: 35 mm
S3
Thickness: 21 mm
2c =
5 mm
2c =
1/4 circ.
2c =
1/2 circ.
2c =
whole circ.
5.9
13.3
15.5
>2ac
5.4
>2ac
>2ac
>2ac
>2ac
>2ac
>2ac
>2ac
da
dN
= C (∆K )m .
Table 9
Maximum tolerable lack of penetration defects (2amax ) in the wind towers (mm).
Bold characters correspond to situations conditioned by the fatigue threshold; those
in italics are limited by crack propagation; the underlined value is conditioned by
fracture–plastic collapse.
Section
S1
Thickness: 36 mm
S2
Thickness: 35 mm
S3
Thickness: 21 mm
in Table 7 can be considered as acceptable, as they are lower than
the critical ones (no fracture–plastic collapse failure) and also, they
would never cause subcritical fatigue crack propagation.
However, the values shown above are lower bound values of
the tolerable crack sizes ensuring the structural integrity of the
towers during their lifespan, as they have been obtained adding
different conservative assumptions (loads, material properties,
defect nature . . . ) and also because it is possible to have larger
cracks causing subcritical fatigue crack propagation that does not
reach the critical values during the 20 years of lifespan (failure
would occur from the 20th year onwards). This is the reason why
in the case where these crack sizes exist on the different sections,
it is necessary to analyse the crack propagation process during
the in-service life of the towers. With this goal, the Paris law
of the material (Eq. (8)) has been integrated (taking 2ath as the
initial crack size) introducing all the cycles considered in the design
(i.e., Table 3) and the corresponding final crack sizes (2af ) have
been obtained, as shown in Table 8.
(8)
As a conservative assumption, the integration has been performed
considering the most critical sequence of cycles, from lowest stress
variations to the largest stress ones. In fact this consideration is
highly conservative, given that only the highest stress variation
would produce crack propagation for the considered initial
crack sizes. However, it was decided to proceed thus given the
uncertainty concerning the dimensions of the existing lack of
penetration defects (the exhaustive detection of the defects and
the determination of their dimensions was performed after the
analysis presented here) and, in particular, given the critical
consequences (economic losses, safety risks . . . ) that premature
failures would have for the owner.
Then, there will be crack propagation if the initial crack sizes
(the lack of penetration defects) are larger than those values
shown in Table 7. Moreover, such a propagation will be critical
(fracture–plastic collapse failure before the expected lifespan) in
those cases shown in bold letters in Table 8 (2af > 2ac ). In
such cases, crack sizes above the corresponding 2ath would not
guarantee the structural integrity of the towers during the lifespan
(then, 2ath is the maximum tolerable lack of penetration defect). In
the other cases, the maximum tolerable defect would be the one
causing the failure at the end of the lifespan (at the end of the 20th
year) and can easily be calculated by the iterative integration of the
Paris law (until the initial crack, 2a0 , producing 2ac at the end of the
lifespan is obtained).
In summary, Table 9 gathers the maximum tolerable defects
(2amax ) for the different hypotheses. Smaller defects than these
would ensure the structural integrity of the towers during their
entire lifespan. The values in bold characters correspond to
situations in which the limiting conditions are provided by the
fatigue threshold (2amax = 2ath ); those in italics are limited
by crack propagation (where 2amax > 2ath ) and correspond
to situations in which there is propagation during the whole
2129
2c =
5 mm
2c =
1/4 circ.
2c =
1/2 circ.
2c =
whole circ.
4.9
3.1
3.1
2.9
4.8
2.9
2.9
2.8
5.9
4.2
4.1
3.8
lifespan (reaching the critical size at the end of the lifespan);
finally, the underlined value is a particular case in which the
limiting condition is the fracture–plastic collapse (no fatigue
influence). This singularity arises from the arbitrary increase
(additional safety margin) considered in the maximum stresses
shown in Table 4. These increased stresses were used to establish
the fracture–plastic collapse critical condition, while the fatigue
analysis was performed from the values gathered in Table 3
(without any additional safety margin).
3.7. Sensitivity analysis
The results obtained in the previous sections were obtained
after several conservative assumptions, so they can be considered
as conservative estimations of the maximum allowable lack of penetration defects. However, as mentioned above, the hypothetical
premature failure of the towers would cause critical economic consequences for the owner of the wind farm (and could also inflict
severe damage on people). This makes it advisable to analyse the
influence of the different inputs on the obtained results.
As seen in the Fracture Analysis of this paper, the failure in the
different sections would be mainly caused by a plastic collapse
mechanism, given that the lines representing the different crack
hypotheses intersect the right part of the FAL (which, in principle,
corresponds to such a mechanism [1]). Therefore, variations in the
considered fracture resistance of the materials would not have
relevant consequences on the results. Furthermore, the fracture
resistance values taken in the assessment correspond to a 1%
failure probability, something that adds an additional security
margin onto this consideration, given that higher Kmat values
would reduce the corresponding Kr value, Lr (and then plastic
collapse) being even more predominant.
Concerning the tensile properties, which determine the plastic
collapse load, in steel structures there is generally overmatching
(the yield stress of the weld is higher than the yield stress in
the base material), something that increases the yield load [1].
For the case analysed, there was negligible overmatching and,
as a conservative assumption of the tensile properties, this was
not considered (providing an additional safety margin). Moreover,
tensile properties are subjected to small scatter if compared to
fracture toughness [1] and the material was properly certified.
For all these reasons, it does not seem reasonable to assume
the existence of any great uncertainties regarding the tensile
properties, the values considered being sufficiently conservative.
Therefore, there are no major reasons to perform a sensitivity
analysis of the results regarding the mechanical properties of the
material, given that the fracture toughness values do not affect the
final results and given that both the fracture toughness and the
tensile properties have been demonstrated to be conservative (and,
in the case of tensile properties, affected by small scatter).
In contrast, the effect on the results caused by variations
in both the fatigue loads shown in Table 3 and the maximum
stresses shown in Table 4 (considered in the fracture–plastic
2130
S. Cicero et al. / Engineering Structures 31 (2009) 2123–2131
S3: 2c = whole circ.
S3: 2c = 1/2 circ.
S3: 2c = 1/4 circ.
S3: 2c = 5mm
S2: 2c = whole circ.
Loads 10% increased
S2: 2c = 1/2 circ.
Design loads
Loads 10% reduced
S2: 2c = 1/4 circ.
S2: 2c = 5mm
S1: 2c = whole circ.
S1: 2c = 1/2 circ.
S1: 2c = 1/4 circ.
S1: 2c = 5mm
2a max(mm)
Fig. 12. Maximum tolerable lack of penetration defects (2amax ) in the wind towers for the different hypotheses of applied loads (mm).
collapse analysis) is not so evident. Therefore, it is necessary to
establish some arbitrary variations in such loads and perform
the analysis shown above. To this end, all calculations were
repeated considering a 10% increase in the applied loads and also
a 10% reduction in them. Tables 10 and 11 show the maximum
tolerable defects obtained for the two new hypotheses of the
applied loads. Again, the values in bold characters correspond to
situations limited by the fatigue threshold (2amax = 2ath ), those
in italics are limited by crack propagation (being 2amax > 2ath )
and the underlined values are particular cases dominated by the
fracture–plastic collapse of the section.
Finally, Fig. 12 compares the maximum tolerable defects (2amax )
for the different loads considered (10% increased, design load and
10% reduced).
The sensitivity of the results can be appreciated. The 10% variations considered in the applied loads produce higher variations
in the tolerable defects, varying (approximately) between 15% and
30%. Generally, the 10% reductions in the considered loads produce higher variations in the resulting tolerable defects than those
obtained when the loads are increased by 10%. This analysis, together with the assumptions considered for obtaining the applied
loads, can be used by the owner-designer to take the corresponding
decisions.
4. Conclusions
Tubular towers constitute a singular structure typology and
their use is being more and more widespread, especially in the case
Table 10
Maximum tolerable lack of penetration defects (2amax ) in the wind towers (mm).
Loads 10% increased.
Section
S1
Thickness: 36 mm
S2
Thickness: 35 mm
S3
Thickness: 21 mm
2c =
5 mm
2c =
1/4 circ.
2c =
1/2 circ.
2c =
whole circ.
4.2
2.5
2.4
2.3
3.2
2.4
2.3
2.2
4.4
3.4
3.3
3.1
of wind towers given the great development of wind energy in the
last decade.
Despite the quality controls implemented during the manufacturing and construction processes, the existence of different types
of defects on these kinds of structures is quite likely. In such cases,
it is necessary to perform structural integrity analyses in order to
evaluate how the existing defects affect the integrity and the performance of the towers.
This paper proposes a general methodology for the structural
integrity assessment of tubular towers containing lack of penetration defects. The analysis has been particularised to the case
of a given set of wind towers with lack of penetration defects on
certain sections. Fracture and fatigue have been considered as the
major causes of concern and some conservative but reasonable hypotheses (i.e., defects behaving as cracks) have been established.
The structural integrity assessment has been performed using the
FITNET FFS procedure and the corresponding lack of penetration
S. Cicero et al. / Engineering Structures 31 (2009) 2123–2131
Table 11
Maximum tolerable lack of penetration defects (2amax ) in the wind towers (mm).
Loads 10% reduced.
Section
S1
Thickness: 36 mm
S2
Thickness: 35 mm
S3
Thickness: 21 mm
2c =
5 mm
2c =
1/4 circ.
2c =
1/2 circ.
2c =
whole circ.
6.1
3.8
3.8
3.5
6.0
3.7
3.7
3.4
7.4
5.1
5.0
4.6
tolerances have been determined for the different defect geometries considered. These values can be assumed to be conservative
and ensure the lifespan considered in the initial design.
Moreover, a sensitivity analysis has been performed, as the final
step in the structural integrity assessment, in order to determine
how variations in the different inputs can affect the final results.
All this analysis, together with precise measurements of
the existing defects, will allow the owner-designer to take the
corresponding decisions (basically, to repair or not to repair).
Given the accumulated conservatism caused by the different
assumptions considered in the analysis, and also considering that
the design loads are defined based on the site conditions (obtained
in situ using instrumentation devices and including extreme
events), the final recommendation to the owner, and for the case
study being analysed, is to compare the detected defects with those
equivalent values (in terms of crack extension hypothesis, (2c))
gathered in Table 9 (obtained prior to the sensitivity analysis). The
rest of the values gathered in Tables 10 and 11 (including those
obtained in the sensitivity analysis) can be taken as a reference,
also showing the coherence between the loads considered and the
allowable crack sizes obtained. If the detected defects are larger
than those gathered in Table 9, repairs are required if the structural
integrity of the towers has to be ensured.
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