- Email: [email protected]
Structural integrity assessment of the cast steel upper anchorage elements used in a cable stayed bridge
Engineering Structures 81 (2014) 309–317
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Structural integrity assessment of the cast steel upper anchorage elements used in a cable stayed bridge J. Terán-Guillén a, S. Cicero b,⇑, T. García b, J.A. Alvarez b, M. Martínez-Madrid a, J.T. Pérez-Quiroz a a
Instituto Mexicano del Transporte, Km. 12 Carretera Querétaro-Galindo, Sanfandila, Querétaro CP 076700, Mexico Universidad de Cantabria, Dpto. Ciencia e Ingeniería del Terreno y de los Materiales, Universidad de Cantabria, Av Los Castros 44, ETS. Ingenieros de Caminos, 39005 Santander, Cantabria, Spain b
a r t i c l e
i n f o
Article history: Received 14 April 2014 Revised 27 August 2014 Accepted 8 October 2014 Available online 24 October 2014 Keywords: Cable-stayed bridge Anchorage Cast steel Notch Failure Assessment Diagrams
a b s t r a c t This paper presents the structural integrity assessment of the cast steel upper anchorage elements of a cable-stayed bridge, which presents numerous fabrication defects. One of the elements failed in 2000. The assessment is performed by using Failure Assessment Diagrams (FADs), includes the effect of residual stresses and considers three different types of defects: postulated surface semi-elliptical cracks (with three different aspect ratios), an existing elliptical embedded crack, and an existing surface semi-elliptical crack. These last two represent two actual defects found in the material. Moreover, two loading hypotheses are also considered: one caused by a 30 year prediction of the ordinary traffic conditions, with a 6% annual increment, and another one caused by the loads produced by the total weight of four heavy trucks crossing the cable-stayed bridge. Material tensile properties were obtained using the ASTM E-8 standard, whereas fracture properties were obtained using the ASTM 1820 standard for both cracked and notched conditions. The results reveal that the anchorage elements work under safe conditions only if the first hypothesis is considered and no residual stresses are taken into account. In case of the second hypothesis, the conditions are unsafe even for null residual stresses. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The use of cast steels in bridge construction is a common practice which on many occasions entails material heterogeneities derived from the fabrication process, given that if this process is not performed properly, defects such as pores, inclusions, cavities or microstructural deficiencies will appear in the material. This may jeopardise the structural integrity of the cast steel structural component and, eventually, the structural integrity of the whole bridge. In this context, some analyses performed in the Rio Papaloapan bridge, which is a cable-stayed bridge located in the Gulf of Mexico (see Fig. 1), have been a matter of scientific and engineering interest, given that one of its 112 upper anchorage elements, connecting the stays to the pillars, failed in 2000. The bridge has two pillars, a main span of 203 m, and 112 cables distributed in 8 semi-harps (14 cables each) (see Fig. 2). In [1] it was concluded that the above mentioned failure was caused by the material’s low fracture toughness, derived from an excessively large grain size. Since then, several reports have been completed in order to determine the ⇑ Corresponding author. Tel.: +34 942200917. E-mail address: [email protected] (S. Cicero). http://dx.doi.org/10.1016/j.engstruct.2014.10.018 0141-0296/Ó 2014 Elsevier Ltd. All rights reserved.
structural integrity conditions of the bridge. These studies have analysed the presence of defects in the material by using ultrasonic techniques [2], have simulated by finite elements the acting loads in the bridge [3], have applied new techniques for damage detection [4], and have applied probabilistic approaches for the structural integrity assessment of the bridge [5]. The analyses gathered in [2] reported the presence of numerous randomly distributed volumetric defects (pores) in the cast steel of the anchorage elements, which obliged those components presenting the largest defects to be replaced (20 out of 112). However, the cast steel of the remaining anchorage elements still presents significant fabrication defects that generate stress concentrations which may cause structural failures. These defects are non-sharp, so that their structural integrity assessment should consider that they may not behave as cracks (i.e., the material load-bearing capacity in notched conditions may be significantly higher than in cracked conditions, e.g., [6–10]). Moreover, when performing structural integrity assessments, Failure Assessment Diagrams (FADs) constitute one of the main engineering tools, as they allow fracture-plastic collapse analyses to be performed through the definition of two non-dimensional parameters (Kr and Lr) and the Failure Assessment Line (FAL) [11–16]. The FAD methodology also allows welded components
310
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
P being the applied load, PL being the plastic collapse load, KI being the stress intensity factor, and Kmat being the material fracture resistance measured by the stress intensity factor (e.g., KIC, KJC, KJIc, etc). Lr may also be expressed following Eq. (3), which is totally equivalent to Eq. (2) [14]:
Lr ¼
Fig. 1. Detail of the cable-stayed bridge being analysed, showing one of the (double) pillars and 56 of the stays (the half of them). The anchorage elements being analysed connect the stays to the pillars.
to be analysed and residual stresses to be included in the assessment. Given that the anchorage elements analysed here present defects that may cause fracture-plastic collapse processes, and given that the defects may appear in the vicinity of a welded area (as explained below), the FAD methodology will be used in this paper for the structural integrity assessment of the anchorage elements. Thus, it will be determined whether or not these components work under safe conditions when subjected to different loading hypotheses. With all this, Section 2 presents an overview of the FAD methodology, Section 3 gathers a description of materials and methods, Section 4 develops the results of the experimental programme and the structural integrity assessments, together with the corresponding discussion, and Section 5 summarises the conclusions.
K r ¼ f ðLr Þ
KI K mat P Lr ¼ PL
ð1Þ ð2Þ
ð4Þ
From an engineering point of view, and beyond the origins of the FAD based on the strip yield model, the f(Lr) functions are actually plasticity corrections to the linear-elastic fracture assessment (KI = Kmat), whose exact analytical solution is:
sffiffiffiffi Je f ðLr Þ ¼ J
ð5Þ
J being the applied J-integral and Je being its corresponding elastic component [13–15]:
Je ¼
Kr ¼
ð3Þ
rref being the reference stress [13,14] and rY being the material yield strength (yield stress or proof strength). Lr evaluates the structural component situation against plastic collapse, and Kr evaluates the component against fracture, the assessed component being represented by a point of coordinates (Kr, Lr). Once the component assessment point is defined through these coordinates, it is necessary to define the component limiting conditions (i.e., those leading to final failure). To this end, the Failure Assessment Line (FAL) is defined, so that if the assessment point is located between the FAL and the coordinate axes, the component is considered to be under safe conditions, whereas if the assessment point is located above the FAL, the component is considered to be under unsafe conditions. The critical situation (failure condition) is that in which the assessment point lies exactly on the FAL. Fig. 3 shows an example with the three different possible situations when performing fracture initiation analyses. In any case, the FAL follows expressions which are functions of Lr:
2. Failure Assessment Diagrams: an overview For a given structural component containing a crack (e.g., beam, plate, pipe, etc.), Failure Assessment Diagrams (FADs) present a simultaneous assessment of both fracture and plastic collapse processes using two normalised parameters, Kr and Lr, whose expressions are Eqs. (1) and (2), respectively, in those situations with primary loading only (e.g., [11–16]):
rref rY
K eI E0
ð6Þ
E0 is E (the Young modulus) in plane stress conditions and E/(1 m2) in plane strain conditions (t is the Poisson ratio). By combining Eqs. (1), (4), (5) and (6), it is straightforward to demonstrate that the FAD methodology is actually providing an elasto-plastic analysis:
J ¼ J mat
ð7Þ
Jmat being the material fracture toughness in elastic–plastic conditions, which extend from purely linear-elastic conditions to situations with noticeable plasticity phenomena. In this sense, the
Fig. 2. Schematic of the cable stayed bridge geometry.
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
311
From an engineering point of view, a key point in the FAD methodology is that it is based on a linear-elastic parameter (KI), regardless of the plasticity level existing on the crack tip, on the plastic collapse load definition, and also on the FAL definition. Moreover, together with the equations defining the FAL, structural integrity assessment procedures provide KI and PL solutions for a wide variety of components (plates, pipes, spheres. . .) and crack geometries (surface cracks, through thickness crack, corner crack. . .), something that facilitates enormously the development of structural integrity assessments. 3. Materials and methods 3.1. Material
Fig. 3. FAD analysis (initiation), showing three possible situations: (A) safe conditions; (B) critical condition; (C) unsafe conditions.
analysis is limited by the cut-off, which corresponds to the load level causing the plastic collapse of the analysed component. This cut-off is defined by the maximum value of Lr (see Lmax in Fig. 3), r which depends on the material flow stress (usually the average value of the yield stress and the ultimate tensile strength). In practice, structural integrity assessment procedures (e.g., [13–16]) provide approximate solutions to Eq. (5), which are defined through the tensile properties of the material. These approximate solutions are generally provided hierarchically, defining different levels of accuracy depending on the available information about the material stress–strain curve. For instance, [13] defines an Option 0 (Basic) that only requires the yield or proof strength to define the FAL approximation, whereas Option 1 (Standard) requires both the yield or proof strength and the ultimate tensile strength, and Option 3 is defined through the full stress–strain curve (Option 2 in [13] is dedicated to mismatch analysis). As an example, Option 3 (which coincides with Level 2B in [14]) is defined by the following equations:
Kr ¼
0 @Eer
rr
10:5 L2r rY A þ 2 Ererr
K r ¼ 0 when Lr > Lrmax
when Lr 6 Lrmax Þ
One of the in-service anchorage elements of the bridge was taken out of service and used to machine the specimens composing the experimental programme, which comprises chemical and microstructural characterisation, tensile tests and fracture tests. The component is shown in Fig. 4. Here, it should be noted that the volumetric defects found in the anchorage elements are randomly distributed in the cast steel, but they are not present in the weld material. Therefore, the material characterisation and the structural integrity analyses performed here do not take into account the weld material. 3.1.1. Microstructural and chemical characterisation Material samples taken from different parts of the anchorage element were mounted in bakelite, subjected to specular polishing
ð8Þ
ð9Þ
where er is the material’s true strain obtained from the uniaxial stress–strain curve at a true stress rr of LrrY, where rY is the yield or proof strength of the material. Lrmax is defined by:
ru Lrmax ¼ 0:5 1 þ
rY
ð10Þ
where ru is the ultimate tensile strength. As can be seen above, this definition of the FAL does not depend on the component being analysed (it depends only on the material properties). All the above explained methodology corresponds to a fracture initiation analysis. However, there are many practical applications in which there is considerable stable crack growth before the final failure. In such cases, it is also possible to perform a ductile tearing analysis. The position of the assessment point provides information about the predominant fracture mechanism. Following FITNET FFS [13], failures represented by assessment points above the Kr/Lr = 1.1 line (or in the area defined by Kr/Lr > 1.1) are fracture dominated, whereas failures represented by points located below the Kr/Lr = 0.4 line (Kr/Lr < 0.4) are plastic collapse dominated. In intermediate situations (0.4 < Kr/Lr < 1.1) fracture and plastic collapse are competing failure mechanisms.
Fig. 4. (a) Schematic of the anchorage elements used in the bridge; (b) anchorage element put out of service in order to obtain the material testing specimens.
312
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
(using sandpaper grits from 120 up to 2000 and aluminium oxide from 1 lm up to 0.05 lm) and etched with nital 2% (firstly) and Marshall reactive (secondly) [17]. The samples were then studied in an optical microscope in order to analyse the material microstructure. Moreover, small pieces of material were cut and used to determine the chemical composition using optical emission spectroscopy. 3.1.2. Tensile tests 25 Tensile tests were performed following ASTM E8 [18] and using a 100 kN servo hydraulic testing machine. The tests were performed under load control conditions, the loading rate being 0.108 kN/s. The geometry of the specimens is shown in Fig. 5. 3.1.3. Fracture resistance tests 30 fracture resistance tests were performed using SENB specimens and following ASTM E1820 [19]. The geometry of the specimens is shown in Fig. 6: the thickness (B) was 15 mm in all cases, the width being 30 mm. As mentioned in the introduction, the defects detected in the anchorage elements were volumetric defects, that is, they were not planar defects (cracks). Thus, in order to determine whether or not there was a notch effect in the fracture resistance (as reported in the literature, e.g., [6–10]), the 30 specimens were grouped in 6 sets of 5 specimens. The specimens of each set had a particular notch radius, varying from 0 mm (cracked specimens) up to 2.5 mm (0, 0.5, 1.0, 1.5, 2.0 and 2.5 mm). In all cases the defect length a was 15 mm (a/W = 0.5). The cracked specimens were subjected to a precracking process following [19], whereas the defect in the notched specimens was machined. The specimens
were tested in displacement control, the displacement rate being 0.30 mm/min. 3.2. Structural integrity assessment methodology The structural integrity assessment of the anchorage elements analysed in this document was performed using the BS79102005 [14]. This includes the corresponding FAD methodology (FAL, Kr and Lr equations), the interaction rules between the existing defects and the treatment of residual stresses. Concerning the definition of the FAL, Level 2B (material specific curve) of BS7910 was chosen, given that the whole stress–strain curve was known. Its definition has been gathered above (Eqs. 8– 10). The anchorage elements are welded to the pillars of the bridge. The failure reported in 2000 [1] took place close to the weld material, in the smallest section of the anchorage (395 mm 60 mm, located in the upper part of the component in Fig. 4), and the analyses of the defects performed in the in-service components [2] revealed that such defects may be found in any part of the cast steel. Thus, here, the structural integrity assessment of the anchorages is focussed on their smallest section (close to the joint with the pillars) and should take into account the possible existence of secondary (residual) stresses caused by the weld. This makes it necessary to apply a more complex formulation than Eq. (1). When following [14], the precise expressions for Kr and Lr in the presence of secondary stresses are:
Kr ¼ Lr ¼
KI þq K mat
rref rY
Fig. 5. Geometry of the tensile specimens used in the analysis.
Fig. 6. Geometry of the fracture specimens used in the analysis: (a) cracked specimens; (b) notched specimens.
ð11Þ ð12Þ
313
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
where in a general situation without misalignment or local discontinuities, KI is defined as:
pffiffiffiffiffiffi K I ¼ K pI þ K sI ¼ ðY rÞp þ ðY rÞs pa
ð13Þ
ðY rÞp ¼ Mfw ðM m P m þ Mb Pb Þ
ð14Þ
ðY rÞs ¼ M m Q m þ Mb Q b
ð15Þ
where a is the crack size, Y is the stress intensity correction factor, M is the bulging correction factor, fw is a correction term in stress intensity factor for elliptical flaws, Mm is the stress intensity magnification factor for membrane stresses, Mb is the stress magnification factor for bending stresses (both M, fw, Mm and Mb are functions of the component and crack geometry, as defined in BS7910 Annex M), Pm is the primary membrane stress, Pb is the primary bending stress, and Qm and Qb are, respectively, the secondary membrane and bending stresses. Finally, q is a plasticity correction factor used when there are primary and secondary stresses acting simultaneously. When following the BS7910 simplified procedure (Annex R), q is defined by:
q ¼ q1 Lr 6 0:8 q ¼ 4q1 ð1:05 Lr Þ 0:8 6 Lr 6 1:05 q ¼ 0 1:05 6 Lr Finally:
q1 ¼ 0:1
K sI Lr K PI
!0:714 0:007
K sI Lr K PI
Surface (semi-elliptical) flaw in a plate with defined dimensions (Fig. 7a): this defect is a consequence of the interactions between two flaws found in one of the anchorages. The interaction rules considered were those gathered in [14], and the resulting dimensions of the equivalent flaw are a = 9 mm and c = 10.4 mm, respectively (a/2c ratio equal to 0.43). The defects being analysed (real or postulated) are those existing in the anchorage elements from their fabrication process, without any consideration of fatigue propagation. As shown in [20] the stress variations in this kind of anchorages are very limited and, therefore, fatigue processes are not likely to occur. Finally, the assessments have been performed to determine whether or not the anchorages will work under safe conditions in the following 30 years. Thus, two loading scenarios were considered:
Table 1 Chemical composition of the cast steel being analysed.
ð16Þ
!2 þ 0:00003
K sI Lr K PI
ð17Þ
Element
wt%
ð18Þ
C Si Mn P S Cr Mo Ni Cu
0.34 0.38 0.71 0.031 0.025 1.25 0.13 0.74 0.33
!5 ð19Þ
The analysed defects have been the following: Postulated surface (semi-elliptical) flaws in a plate: the considered a/2c ratios are 0.2, 0.5 and 1.0. This corresponds to the more general assessment of the anchorages, assuming the hypothesis that this kind of defects is the most representative in the structural components being analysed. A schematic of the geometry is shown in Fig. 7a. Embedded (elliptical) flaw in a plate with defined dimensions: this particular defect was found in the interior of one anchorage. Its semiaxes a and c are 4.5 mm and 7.6 mm, respectively (a/2c ratio is equal to 0.29). A schematic of the geometry is shown in Fig. 7b.
Fig. 8. Ferritic–pearlitic microstructure with a 0.69 mm2 macro-grain.
Table 2 Average measured area of 7 macro-grains [21].
Fig. 7. Schematic of the crack geometries being analysed: (a) surface (semielliptical) flaw in a plate; (b) embedded (elliptical) flaw in a plate.
Macro-grain
Fraction area (%)
Area (mm2)
1 2 3 4 5 6 7 Mean grain size Std. deviation
0.27 2.95 1.99 1.14 1.42 0.75 0.82
0.69 7.66 5.18 2.96 3.69 1.94 2.12 3.46 2.33
314
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317 Table 3 Stress–strain curve of the material being analysed (average values). True strain
True stress (MPa)
0.00000 0.00022 0.00046 0.00069 0.00092 0.00119 0.00153 0.00237 0.00647 0.01255 0.01930 0.02758 0.03989
0.0 50.1 100.3 150.5 200.3 251.0 301.2 351.1 402.9 455.8 509.7 565.5 608.2
4. Results and discussion 4.1. Material
Table 4 Material tensile parameters.
Mean value Std. deviation
E (GPa)
rY (MPa)
ru (MPa)
% emax
213.0 7.89
366.0 12.74
584.9 32.72
7.21 0.59
30 year prediction (at 95% confidence level) of the ordinary traffic conditions, with a 6% annual increment. The corresponding maximum load supported by the anchorages is 337 tons, and the resulting stress in the analysed section is basically a constant tensile stress (Pm) of 139.5 MPa [4]. Maximum load in the anchorages produced by the total weight of four heavy trucks crossing the cable-stayed bridge by its middle section. This generates 974 tons in the most loaded anchorages, with a corresponding constant tensile stress (Pm) of 403.0 MPa [3].
Table 1 gathers the results of the chemical characterisation, revealing that it is a low alloy steel with a medium content of carbon. Fig. 8 shows the corresponding typical ferritic–pearlitic microstructure found in the different samples. This microstructure was found to be independent of the location of the samples within the anchorage. The grain size measurements were performed using Image J software, the results being gathered in Table 2. A wide variety of areas can be observed, corresponding to macro-grain sizes between M-11 and M-7.5 [21]. The tensile tests allowed the whole stress–strain curve of the material to be obtained. Table 3 presents this curve in true variables. Each value has been obtained by considering the average values generated in the 25 tests. Moreover, Table 4 presents the corresponding average values and standard deviation for the elastic modulus, the yield stress, the ultimate tensile strength and the strain under maximum load, expressed in engineering values. It can be observed that the material presents normal resistant parameters and low ductility. Concerning the fracture resistance of the cast steel, Table 5 and Fig. 9 gather the results of both the cracked and the notched specimens in terms of the apparent fracture toughness (KJN), which is obtained by using ASTM E1820 formulation for both the cracked and notched specimens. It can be observed that, although the general trend is an increase in the apparent fracture toughness with the notch radius, there is a high scatter all along the different notch radii, with test results at high notch radii providing low values of fracture resistance, very similar to those obtained in cracked conditions. These results justify that the structural integrity assessments performed in this paper do not consider any notch effect (i.e., it is assumed that notches behave as cracks). The high scatter
Table 5 Results of apparent fracture toughness tests. Notch radius (mm)
Pmax (kN)
KJN (MPa m1/2)
1 2 3 4 5
0.0
11.07 10.05 12.64 10.98 15.02
68.93 49.62 63.48 74.99 99.28
71.26
18.26
6 7 8 9 10
0.5
23.44 10.20 11.25 10.15 13.17
98.77 51.56 143.43 86.576 192.37
114.54
54.52
11 12 13 14 15
1.0
11.57 11.47 11.24 10.62 15.74
74.80 76.13 56.40 58.49 98.77
72.92
17.05
16 17 18 19 20
1.5
12.48 12.72 15.25 13.45 14.30
87.95 98.55 164.53 97.50 206.54
131.02
52.11
21 22 23 24 25
2.0
12.90 14.27 12.80 13.06 11.16
99.19 122.77 95.26 91.67 56.66
93.11
21.49
25 27 28 29 39
2.5
13.34 15.58 13.27 12.94 13.45
101.38 141.73 101.06 88.67 87.30
104.03
22.10
Specimen
KJN, mean (MPa m1/2)
Standard deviation (MPa m1/2)
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
315
4.2. Structural integrity assessment
Fig. 9. Apparent fracture toughness results.
observed in the results may be related to the presence of numerous defects in the material and their random distribution: those specimens with significant defects in the fracture process zone will provide the lower fracture resistance values, whereas those specimens without important defects in the fracture process zone will provide the higher values of the fracture resistance. Fig. 10 shows the fracture surfaces in a cracked and a notched specimen. In both cases the fracture micromechanisms are very similar, presenting brittle aspect and cleavages.
The structural integrity assessments were performed following the procedure outlined in Section 3.2. M, fw, Mm and rref values have been taken from [14]. In the case of the semi-elliptical cracks, the stress intensity factor (KI) was measured at the point of the crack front providing the maximum value. This corresponds to the surface points for aspect ratios (a/2c) of 0.5 and 1.0, and the deepest point for aspect ratio of 0.2. Mb is not necessary, given that the bending stresses (Pb and Qb) are negligible. Concerning Kmat, the equivalent to the minimum of three tests was used, following the indications of [14]. This, for the number of tests performed in cracked conditions (5 tests), corresponds to the minimum value shown in Table 5 (Kmat = 49.62 MPa m1/2). Concerning the yield stress, the average value was considered (rY = 366 MPa, see Table 4). Also, three types of defects and two loading hypotheses were considered. Fig. 11 gathers the results for postulated surface (semi-elliptical) flaws and three different aspect ratios. The effect of the residual stresses is not considered. An initial defect length (a) of 2.0 mm has been considered as a representative value of the capability of the ultrasonic NDT [13], whereas the discontinuous lines show the corresponding situation of the component when increasing the defect size and fixing the applied load.
Fracture surface
Crack front
Fig. 11. Assessment of postulated surface (semi-elliptical) flaws. Residual stresses are not considered.
Fatigue precrack
(a)
Fracture surface
Notch front
(b)
Notch
Fig. 10. Fracture surfaces: (a) specimen 3 (cracked conditions, notch radius = 0 mm); (b) specimen 8 (notched conditions, notch radius = 0.5 mm).
Fig. 12. Assessment of postulated surface (semi-elliptical) flaws. Residual stresses are considered.
316
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
Fig. 13. Assessment of an embedded (elliptical) defect found in the anchorages.
Fig. 14. Assessment of an equivalent surface (semi-elliptical) defect found in the anchorages.
For the 30 year prediction of the ordinary traffic (337 tons, Pm = 139.5 MPa), it can be observed how the lowest a/2c ratio provides the smallest critical defect (ac = 31 mm), whereas this critical size is 56 mm for an aspect ratio of 0.5. In the case of a/2c = 1.0, the critical size is larger than the thickness. This means that the crack should be re-characterised as a through-thickness crack, and the analysis should continue using the corresponding solutions for KI and PL (such an analysis has not been performed here given that the presence of through-thickness defects is highly unlikely). If the maximum load hypothesis is considered (974 tons, Pm = 403.0 MPa), a 2 mm defect length is critical for an aspect ratio of 0.2 (the assessment point is located above the FAL), whereas the situation is already safe for aspect ratios of 0.5 and 1.0. Thus, the aspect ratio is a determining factor in the assessment of the anchorages.
Fig. 12 analyses the same postulated defects subjected to the same loading hypotheses, but on this occasion the residual stresses are considered. The analyses are performed following Level 1 of FITNET FFS Procedure Annex C (Residual Stress Profiles), which considers that both the longitudinal and transverse components of residual stresses are tensile and uniformly distributed in both the through-thickness and transverse directions, with a magnitude equal to the material yield stress at room temperature [22] (Qm = rY). The fracture toughness of the material in the areas subjected to the residual stresses has been considered to be equal to the one in the base material, given that no substantial changes have been found in the corresponding microstructures. It can be observed how the critical size (ac) of the postulated defects for the 30th year traffic prediction is 3 mm, 6 mm and 14 mm for aspect ratios (a/2c) of 0.2, 0.5 and 1.0, respectively. Thus, the consideration of residual stress has a great impact on the structural integrity of the anchorages, with a significant reduction in the critical defect sizes. Moreover, for the maximum load hypothesis, the three considered aspect ratios provide critical (unsafe) situations for an initial defect length of 2 mm. Fig. 13 presents the structural integrity assessment of the anchorages considering the above mentioned embedded (elliptical) flaw, which represents an example of the defects found in the components. When the residual stresses are not considered, the component works under safe conditions for the 30th year load prediction, whereas the situation is unsafe for the maximum load hypothesis; when the residual stresses are considered, the situation is not acceptable (unsafe) for both loading hypotheses. Thus, the analysed defect is a serious threat in the analysed bridge. Moreover, the discontinuous assessment lines shown in the FAD have been obtained by fixing the crack dimensions and increasing the applied load. The resulting critical loads (corresponding to the assessment points located over the FAL) are 878 tons without residual stresses and 247 tons with residual stresses. Fig. 14 presents the assessment of the third analysed defect: an equivalent surface (semi-elliptical) flaw with defined dimensions arising from the interactions between two flaws found in one of the anchorages. The results are very similar to those obtained for the embedded defect: the component works under safe conditions for the 30th year load prediction when the residual stresses are not considered, whereas the situation is unsafe when the residual stresses are considered. For the maximum load hypothesis, the situation is not acceptable regardless of the residual stresses. Again, the discontinuous assessment lines shown in the FAD have been obtained by fixing the crack dimensions and increasing the applied load. The resulting critical loads are 757 tons without residual stresses and 58 tons with residual stresses. Here, it should be noted that the residual stresses generate a significant increase in the Kr coordinate at failure, and also of the Kr/Lr ratio. This causes more brittle failures, which are more dangerous as they have associated lower strains. Finally, Table 6 gathers a summary of the structural integrity situation of the two real defects analysed here. The table shows the corresponding critical loads and reserve factors (load factors, FL) [14] for the different defect and loading combinations. Reserve factors lower than 1.0 are associated to unsafe situations, whereas reserve factors higher than 1.0 correspond to safe situations.
Table 6 Obtained critical loads and reserve factors (load factor, FL) for the different combinations of defect geometry, residual stress level and loading scenario. Flaw type
Crack geometry (a/2c)
FL (30 year prediction)
FL (maximum load)
Pcritical (tons)
Embedded elliptical crack Embedded elliptical crack + residual stress Surface semi-elliptical crack Surface semi-elliptical crack + residual stress
4.5/15.2 4.5/15.2 9.0/20.8 9.0/20.8
2.61 0.72 2.25 0.18
0.90 0.25 0.81 0.06
878.4 247.8 757.6 58.0
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
317
5. Conclusions
References
The cast steel anchorages of the Rio Papaloapan cable stayed bridge present numerous non-sharp fabrication defects. In 2000 one of the anchorages failed and since then several analyses have been performed. Here, the structural integrity assessment of 112 anchorages has been performed using the Failure Assessment Diagram (FAD) methodology (FITNET FFS and BS7910 procedures). The assessments have required the material characterisation and the analysis of the notch effect in the cast steel. Tensile and fracture properties have been obtained, and the test results show that, from a structural integrity point of view, there is an insignificant effect of the notches on fracture resistance. The analysed defects have been postulated surface defects with different aspect ratios, and two specific defects found in some of the anchorages (an embedded defect and an equivalent surface defect that arises from the interaction of two smaller defects). Finally, the assessments have been performed considering two loading hypotheses (30th year traffic prediction and maximum load corresponding to 4 heavy trucks), and two scenarios of residual stresses: non-existent residual stresses and residual stresses equal to the material yield stress. For the 30th year loading prediction and the postulated surface defects, the results provide critical defect depths higher than 31 mm when the residual stresses are not considered, and between 3 mm and 14 mm (depending on the aspect ratio) when such stresses are considered; for the maximum load hypothesis and the postulated surface defects the critical depths are around 2 mm without residual stresses and well below 2 mm with residual stresses. This implies that the critical defects may not be detectable. The analysis of the two real defects provide safe results for the 30th year loading prediction without residual stresses, whereas the situation is unsafe for such a loading hypothesis coupled with residual stresses and for the maximum loading hypothesis regardless of the level of residual stresses. With all this, the assessments performed here indicate that it is necessary to take remedial actions. If it is intended to avoid the substitution of the anchorages, the traffic loads on the bridge should be limited unless a better definition of the existing defects and residual stresses demonstrate the structural integrity of the anchorages.
[1] Aguirre A, Carbajal J. Análisis del tirante 11 del puente Papaloapan. Corporación Mexicana de Investigación de Materiales S.A. de C.V. Reporte Interno AF-IFT00087. Saltillo, Coahuila, México; 2000. [2] López JA, Carrion FJ, Quintana JA, Samayoa D, Orozco PR. Verification of the ultrasonic qualification for structural integrity of partially embedded steel elements. Adv Mater Res 2009;65:69–78. [3] Samayoa-Ochoa D. Análisis de confiabilidad y riesgo en puentes atirantados. México DF: ESIME-IPN (Tesis Doctoral); 2005. [4] Quintana-Rodríguez JA. Análisis del método de búsqueda global para la detección de daño y monitoreo estructural de puentes. México DF: ESIME-IPN (Tesis Doctoral); 2009. [5] Alcaraz-Caracheo LA. Análisis probabilístico de integridad de un anclaje de acero estructural. México DF: ESIME-IPN (Tesis Doctoral); 2012. [6] Taylor D. The theory of critical distances: a new perspective in fracture mechanics. Elsevier; 2007. [7] Cicero S, Madrazo V, García T. Analysis of notch effect in the apparent fracture toughness and the fracture micromechanisms of ferritic-pearlitic steels operating within their lower shelf. Eng Fail Anal 2014;36:322–42. [8] Cicero S, Madrazo V, García T, Cuervo J, Ruiz E. On the notch effect in load bearing capacity, apparent fracture toughness and fracture mechanisms of polymer PMMA, aluminium alloy Al7075-T651 and structural steels S275JR and S355J2. Eng Fail Anal 2013;29:108–21. [9] Madrazo V, Cicero S, Carrascal IA. On the point method and the line method notch effect predictions in Al7075-T651. Eng Fract Mech 2012;79:363–79. [10] Cicero S, Madrazo V, Carrascal IA. Analysis of notch effect in PMMA using the theory of critical distances. Eng Fract Mech 2012;86:56–72. [11] Milne I, Ainswoth RA, Dowling AR, Stewart AT. Assessment of the integrity of structures containing defects. Int J Pres Ves Pip 1988;32:3–104. [12] Anderson TL. Fracture mechanics: fundamentals and applications. Florida: CRC Press; 2005. [13] Kocak M, Webster S, Janosch JJ, Ainsworth RA, Koers R, editors. FITNET fitnessfor-service (FFS) procedure, vol. I. Geesthacht: GKSS; 2008. [14] BS 7910: 2005. Guide to methods for assessing the acceptability of flaws in metallic structures. London: British Standards Institution; 2005. [15] R6. Assessment of the integrity of structures containing defects. Revision 4. Gloucester: British Energy Generation Limited; 2001. [16] API 579-1/ASME FFS-1 Fitness-For-Service. New York: American Society of Mechanical Engineers; 2007. [17] Bramfitt BL, Benscoter OA. Metallographer’s guide. Materials Park, Ohio: ASM International; 2002. [18] ASTM E8/E8M-09. Standard test methods for tension testing of metallic materials. Philadelphia: ASTM; 2009. [19] ASTM E1820-11. Standard test method for measurement of fracture toughness. Philadelphia: ASTM; 2011. [20] Astiz MA, Composite construction in cable-stayed bridge towers. In: IABSE reports. vol. 999; 1997. p. 127–32. [21] ASTM E112-12. Standard test methods for determining average grain size. Philadelphia: ASTM; 2012. [22] Kocak M, Hadley I, Szavai S, Tkach Y, Taylor N, editors. FITNET fitness-forservice (FFS) procedure, vol. II. Geesthacht: GKSS; 2008.
Acknowledgements Jorge Terán Guillén would like to express his gratitude to the Consejo Nacional de Ciencia y Tecnología de México for the support of his research stay at the Universidad de Cantabria, Spain.
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Structural integrity assessment of the cast steel upper anchorage elements used in a cable stayed bridge J. Terán-Guillén a, S. Cicero b,⇑, T. García b, J.A. Alvarez b, M. Martínez-Madrid a, J.T. Pérez-Quiroz a a
Instituto Mexicano del Transporte, Km. 12 Carretera Querétaro-Galindo, Sanfandila, Querétaro CP 076700, Mexico Universidad de Cantabria, Dpto. Ciencia e Ingeniería del Terreno y de los Materiales, Universidad de Cantabria, Av Los Castros 44, ETS. Ingenieros de Caminos, 39005 Santander, Cantabria, Spain b
a r t i c l e
i n f o
Article history: Received 14 April 2014 Revised 27 August 2014 Accepted 8 October 2014 Available online 24 October 2014 Keywords: Cable-stayed bridge Anchorage Cast steel Notch Failure Assessment Diagrams
a b s t r a c t This paper presents the structural integrity assessment of the cast steel upper anchorage elements of a cable-stayed bridge, which presents numerous fabrication defects. One of the elements failed in 2000. The assessment is performed by using Failure Assessment Diagrams (FADs), includes the effect of residual stresses and considers three different types of defects: postulated surface semi-elliptical cracks (with three different aspect ratios), an existing elliptical embedded crack, and an existing surface semi-elliptical crack. These last two represent two actual defects found in the material. Moreover, two loading hypotheses are also considered: one caused by a 30 year prediction of the ordinary traffic conditions, with a 6% annual increment, and another one caused by the loads produced by the total weight of four heavy trucks crossing the cable-stayed bridge. Material tensile properties were obtained using the ASTM E-8 standard, whereas fracture properties were obtained using the ASTM 1820 standard for both cracked and notched conditions. The results reveal that the anchorage elements work under safe conditions only if the first hypothesis is considered and no residual stresses are taken into account. In case of the second hypothesis, the conditions are unsafe even for null residual stresses. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The use of cast steels in bridge construction is a common practice which on many occasions entails material heterogeneities derived from the fabrication process, given that if this process is not performed properly, defects such as pores, inclusions, cavities or microstructural deficiencies will appear in the material. This may jeopardise the structural integrity of the cast steel structural component and, eventually, the structural integrity of the whole bridge. In this context, some analyses performed in the Rio Papaloapan bridge, which is a cable-stayed bridge located in the Gulf of Mexico (see Fig. 1), have been a matter of scientific and engineering interest, given that one of its 112 upper anchorage elements, connecting the stays to the pillars, failed in 2000. The bridge has two pillars, a main span of 203 m, and 112 cables distributed in 8 semi-harps (14 cables each) (see Fig. 2). In [1] it was concluded that the above mentioned failure was caused by the material’s low fracture toughness, derived from an excessively large grain size. Since then, several reports have been completed in order to determine the ⇑ Corresponding author. Tel.: +34 942200917. E-mail address: [email protected] (S. Cicero). http://dx.doi.org/10.1016/j.engstruct.2014.10.018 0141-0296/Ó 2014 Elsevier Ltd. All rights reserved.
structural integrity conditions of the bridge. These studies have analysed the presence of defects in the material by using ultrasonic techniques [2], have simulated by finite elements the acting loads in the bridge [3], have applied new techniques for damage detection [4], and have applied probabilistic approaches for the structural integrity assessment of the bridge [5]. The analyses gathered in [2] reported the presence of numerous randomly distributed volumetric defects (pores) in the cast steel of the anchorage elements, which obliged those components presenting the largest defects to be replaced (20 out of 112). However, the cast steel of the remaining anchorage elements still presents significant fabrication defects that generate stress concentrations which may cause structural failures. These defects are non-sharp, so that their structural integrity assessment should consider that they may not behave as cracks (i.e., the material load-bearing capacity in notched conditions may be significantly higher than in cracked conditions, e.g., [6–10]). Moreover, when performing structural integrity assessments, Failure Assessment Diagrams (FADs) constitute one of the main engineering tools, as they allow fracture-plastic collapse analyses to be performed through the definition of two non-dimensional parameters (Kr and Lr) and the Failure Assessment Line (FAL) [11–16]. The FAD methodology also allows welded components
310
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
P being the applied load, PL being the plastic collapse load, KI being the stress intensity factor, and Kmat being the material fracture resistance measured by the stress intensity factor (e.g., KIC, KJC, KJIc, etc). Lr may also be expressed following Eq. (3), which is totally equivalent to Eq. (2) [14]:
Lr ¼
Fig. 1. Detail of the cable-stayed bridge being analysed, showing one of the (double) pillars and 56 of the stays (the half of them). The anchorage elements being analysed connect the stays to the pillars.
to be analysed and residual stresses to be included in the assessment. Given that the anchorage elements analysed here present defects that may cause fracture-plastic collapse processes, and given that the defects may appear in the vicinity of a welded area (as explained below), the FAD methodology will be used in this paper for the structural integrity assessment of the anchorage elements. Thus, it will be determined whether or not these components work under safe conditions when subjected to different loading hypotheses. With all this, Section 2 presents an overview of the FAD methodology, Section 3 gathers a description of materials and methods, Section 4 develops the results of the experimental programme and the structural integrity assessments, together with the corresponding discussion, and Section 5 summarises the conclusions.
K r ¼ f ðLr Þ
KI K mat P Lr ¼ PL
ð1Þ ð2Þ
ð4Þ
From an engineering point of view, and beyond the origins of the FAD based on the strip yield model, the f(Lr) functions are actually plasticity corrections to the linear-elastic fracture assessment (KI = Kmat), whose exact analytical solution is:
sffiffiffiffi Je f ðLr Þ ¼ J
ð5Þ
J being the applied J-integral and Je being its corresponding elastic component [13–15]:
Je ¼
Kr ¼
ð3Þ
rref being the reference stress [13,14] and rY being the material yield strength (yield stress or proof strength). Lr evaluates the structural component situation against plastic collapse, and Kr evaluates the component against fracture, the assessed component being represented by a point of coordinates (Kr, Lr). Once the component assessment point is defined through these coordinates, it is necessary to define the component limiting conditions (i.e., those leading to final failure). To this end, the Failure Assessment Line (FAL) is defined, so that if the assessment point is located between the FAL and the coordinate axes, the component is considered to be under safe conditions, whereas if the assessment point is located above the FAL, the component is considered to be under unsafe conditions. The critical situation (failure condition) is that in which the assessment point lies exactly on the FAL. Fig. 3 shows an example with the three different possible situations when performing fracture initiation analyses. In any case, the FAL follows expressions which are functions of Lr:
2. Failure Assessment Diagrams: an overview For a given structural component containing a crack (e.g., beam, plate, pipe, etc.), Failure Assessment Diagrams (FADs) present a simultaneous assessment of both fracture and plastic collapse processes using two normalised parameters, Kr and Lr, whose expressions are Eqs. (1) and (2), respectively, in those situations with primary loading only (e.g., [11–16]):
rref rY
K eI E0
ð6Þ
E0 is E (the Young modulus) in plane stress conditions and E/(1 m2) in plane strain conditions (t is the Poisson ratio). By combining Eqs. (1), (4), (5) and (6), it is straightforward to demonstrate that the FAD methodology is actually providing an elasto-plastic analysis:
J ¼ J mat
ð7Þ
Jmat being the material fracture toughness in elastic–plastic conditions, which extend from purely linear-elastic conditions to situations with noticeable plasticity phenomena. In this sense, the
Fig. 2. Schematic of the cable stayed bridge geometry.
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
311
From an engineering point of view, a key point in the FAD methodology is that it is based on a linear-elastic parameter (KI), regardless of the plasticity level existing on the crack tip, on the plastic collapse load definition, and also on the FAL definition. Moreover, together with the equations defining the FAL, structural integrity assessment procedures provide KI and PL solutions for a wide variety of components (plates, pipes, spheres. . .) and crack geometries (surface cracks, through thickness crack, corner crack. . .), something that facilitates enormously the development of structural integrity assessments. 3. Materials and methods 3.1. Material
Fig. 3. FAD analysis (initiation), showing three possible situations: (A) safe conditions; (B) critical condition; (C) unsafe conditions.
analysis is limited by the cut-off, which corresponds to the load level causing the plastic collapse of the analysed component. This cut-off is defined by the maximum value of Lr (see Lmax in Fig. 3), r which depends on the material flow stress (usually the average value of the yield stress and the ultimate tensile strength). In practice, structural integrity assessment procedures (e.g., [13–16]) provide approximate solutions to Eq. (5), which are defined through the tensile properties of the material. These approximate solutions are generally provided hierarchically, defining different levels of accuracy depending on the available information about the material stress–strain curve. For instance, [13] defines an Option 0 (Basic) that only requires the yield or proof strength to define the FAL approximation, whereas Option 1 (Standard) requires both the yield or proof strength and the ultimate tensile strength, and Option 3 is defined through the full stress–strain curve (Option 2 in [13] is dedicated to mismatch analysis). As an example, Option 3 (which coincides with Level 2B in [14]) is defined by the following equations:
Kr ¼
0 @Eer
rr
10:5 L2r rY A þ 2 Ererr
K r ¼ 0 when Lr > Lrmax
when Lr 6 Lrmax Þ
One of the in-service anchorage elements of the bridge was taken out of service and used to machine the specimens composing the experimental programme, which comprises chemical and microstructural characterisation, tensile tests and fracture tests. The component is shown in Fig. 4. Here, it should be noted that the volumetric defects found in the anchorage elements are randomly distributed in the cast steel, but they are not present in the weld material. Therefore, the material characterisation and the structural integrity analyses performed here do not take into account the weld material. 3.1.1. Microstructural and chemical characterisation Material samples taken from different parts of the anchorage element were mounted in bakelite, subjected to specular polishing
ð8Þ
ð9Þ
where er is the material’s true strain obtained from the uniaxial stress–strain curve at a true stress rr of LrrY, where rY is the yield or proof strength of the material. Lrmax is defined by:
ru Lrmax ¼ 0:5 1 þ
rY
ð10Þ
where ru is the ultimate tensile strength. As can be seen above, this definition of the FAL does not depend on the component being analysed (it depends only on the material properties). All the above explained methodology corresponds to a fracture initiation analysis. However, there are many practical applications in which there is considerable stable crack growth before the final failure. In such cases, it is also possible to perform a ductile tearing analysis. The position of the assessment point provides information about the predominant fracture mechanism. Following FITNET FFS [13], failures represented by assessment points above the Kr/Lr = 1.1 line (or in the area defined by Kr/Lr > 1.1) are fracture dominated, whereas failures represented by points located below the Kr/Lr = 0.4 line (Kr/Lr < 0.4) are plastic collapse dominated. In intermediate situations (0.4 < Kr/Lr < 1.1) fracture and plastic collapse are competing failure mechanisms.
Fig. 4. (a) Schematic of the anchorage elements used in the bridge; (b) anchorage element put out of service in order to obtain the material testing specimens.
312
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
(using sandpaper grits from 120 up to 2000 and aluminium oxide from 1 lm up to 0.05 lm) and etched with nital 2% (firstly) and Marshall reactive (secondly) [17]. The samples were then studied in an optical microscope in order to analyse the material microstructure. Moreover, small pieces of material were cut and used to determine the chemical composition using optical emission spectroscopy. 3.1.2. Tensile tests 25 Tensile tests were performed following ASTM E8 [18] and using a 100 kN servo hydraulic testing machine. The tests were performed under load control conditions, the loading rate being 0.108 kN/s. The geometry of the specimens is shown in Fig. 5. 3.1.3. Fracture resistance tests 30 fracture resistance tests were performed using SENB specimens and following ASTM E1820 [19]. The geometry of the specimens is shown in Fig. 6: the thickness (B) was 15 mm in all cases, the width being 30 mm. As mentioned in the introduction, the defects detected in the anchorage elements were volumetric defects, that is, they were not planar defects (cracks). Thus, in order to determine whether or not there was a notch effect in the fracture resistance (as reported in the literature, e.g., [6–10]), the 30 specimens were grouped in 6 sets of 5 specimens. The specimens of each set had a particular notch radius, varying from 0 mm (cracked specimens) up to 2.5 mm (0, 0.5, 1.0, 1.5, 2.0 and 2.5 mm). In all cases the defect length a was 15 mm (a/W = 0.5). The cracked specimens were subjected to a precracking process following [19], whereas the defect in the notched specimens was machined. The specimens
were tested in displacement control, the displacement rate being 0.30 mm/min. 3.2. Structural integrity assessment methodology The structural integrity assessment of the anchorage elements analysed in this document was performed using the BS79102005 [14]. This includes the corresponding FAD methodology (FAL, Kr and Lr equations), the interaction rules between the existing defects and the treatment of residual stresses. Concerning the definition of the FAL, Level 2B (material specific curve) of BS7910 was chosen, given that the whole stress–strain curve was known. Its definition has been gathered above (Eqs. 8– 10). The anchorage elements are welded to the pillars of the bridge. The failure reported in 2000 [1] took place close to the weld material, in the smallest section of the anchorage (395 mm 60 mm, located in the upper part of the component in Fig. 4), and the analyses of the defects performed in the in-service components [2] revealed that such defects may be found in any part of the cast steel. Thus, here, the structural integrity assessment of the anchorages is focussed on their smallest section (close to the joint with the pillars) and should take into account the possible existence of secondary (residual) stresses caused by the weld. This makes it necessary to apply a more complex formulation than Eq. (1). When following [14], the precise expressions for Kr and Lr in the presence of secondary stresses are:
Kr ¼ Lr ¼
KI þq K mat
rref rY
Fig. 5. Geometry of the tensile specimens used in the analysis.
Fig. 6. Geometry of the fracture specimens used in the analysis: (a) cracked specimens; (b) notched specimens.
ð11Þ ð12Þ
313
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
where in a general situation without misalignment or local discontinuities, KI is defined as:
pffiffiffiffiffiffi K I ¼ K pI þ K sI ¼ ðY rÞp þ ðY rÞs pa
ð13Þ
ðY rÞp ¼ Mfw ðM m P m þ Mb Pb Þ
ð14Þ
ðY rÞs ¼ M m Q m þ Mb Q b
ð15Þ
where a is the crack size, Y is the stress intensity correction factor, M is the bulging correction factor, fw is a correction term in stress intensity factor for elliptical flaws, Mm is the stress intensity magnification factor for membrane stresses, Mb is the stress magnification factor for bending stresses (both M, fw, Mm and Mb are functions of the component and crack geometry, as defined in BS7910 Annex M), Pm is the primary membrane stress, Pb is the primary bending stress, and Qm and Qb are, respectively, the secondary membrane and bending stresses. Finally, q is a plasticity correction factor used when there are primary and secondary stresses acting simultaneously. When following the BS7910 simplified procedure (Annex R), q is defined by:
q ¼ q1 Lr 6 0:8 q ¼ 4q1 ð1:05 Lr Þ 0:8 6 Lr 6 1:05 q ¼ 0 1:05 6 Lr Finally:
q1 ¼ 0:1
K sI Lr K PI
!0:714 0:007
K sI Lr K PI
Surface (semi-elliptical) flaw in a plate with defined dimensions (Fig. 7a): this defect is a consequence of the interactions between two flaws found in one of the anchorages. The interaction rules considered were those gathered in [14], and the resulting dimensions of the equivalent flaw are a = 9 mm and c = 10.4 mm, respectively (a/2c ratio equal to 0.43). The defects being analysed (real or postulated) are those existing in the anchorage elements from their fabrication process, without any consideration of fatigue propagation. As shown in [20] the stress variations in this kind of anchorages are very limited and, therefore, fatigue processes are not likely to occur. Finally, the assessments have been performed to determine whether or not the anchorages will work under safe conditions in the following 30 years. Thus, two loading scenarios were considered:
Table 1 Chemical composition of the cast steel being analysed.
ð16Þ
!2 þ 0:00003
K sI Lr K PI
ð17Þ
Element
wt%
ð18Þ
C Si Mn P S Cr Mo Ni Cu
0.34 0.38 0.71 0.031 0.025 1.25 0.13 0.74 0.33
!5 ð19Þ
The analysed defects have been the following: Postulated surface (semi-elliptical) flaws in a plate: the considered a/2c ratios are 0.2, 0.5 and 1.0. This corresponds to the more general assessment of the anchorages, assuming the hypothesis that this kind of defects is the most representative in the structural components being analysed. A schematic of the geometry is shown in Fig. 7a. Embedded (elliptical) flaw in a plate with defined dimensions: this particular defect was found in the interior of one anchorage. Its semiaxes a and c are 4.5 mm and 7.6 mm, respectively (a/2c ratio is equal to 0.29). A schematic of the geometry is shown in Fig. 7b.
Fig. 8. Ferritic–pearlitic microstructure with a 0.69 mm2 macro-grain.
Table 2 Average measured area of 7 macro-grains [21].
Fig. 7. Schematic of the crack geometries being analysed: (a) surface (semielliptical) flaw in a plate; (b) embedded (elliptical) flaw in a plate.
Macro-grain
Fraction area (%)
Area (mm2)
1 2 3 4 5 6 7 Mean grain size Std. deviation
0.27 2.95 1.99 1.14 1.42 0.75 0.82
0.69 7.66 5.18 2.96 3.69 1.94 2.12 3.46 2.33
314
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317 Table 3 Stress–strain curve of the material being analysed (average values). True strain
True stress (MPa)
0.00000 0.00022 0.00046 0.00069 0.00092 0.00119 0.00153 0.00237 0.00647 0.01255 0.01930 0.02758 0.03989
0.0 50.1 100.3 150.5 200.3 251.0 301.2 351.1 402.9 455.8 509.7 565.5 608.2
4. Results and discussion 4.1. Material
Table 4 Material tensile parameters.
Mean value Std. deviation
E (GPa)
rY (MPa)
ru (MPa)
% emax
213.0 7.89
366.0 12.74
584.9 32.72
7.21 0.59
30 year prediction (at 95% confidence level) of the ordinary traffic conditions, with a 6% annual increment. The corresponding maximum load supported by the anchorages is 337 tons, and the resulting stress in the analysed section is basically a constant tensile stress (Pm) of 139.5 MPa [4]. Maximum load in the anchorages produced by the total weight of four heavy trucks crossing the cable-stayed bridge by its middle section. This generates 974 tons in the most loaded anchorages, with a corresponding constant tensile stress (Pm) of 403.0 MPa [3].
Table 1 gathers the results of the chemical characterisation, revealing that it is a low alloy steel with a medium content of carbon. Fig. 8 shows the corresponding typical ferritic–pearlitic microstructure found in the different samples. This microstructure was found to be independent of the location of the samples within the anchorage. The grain size measurements were performed using Image J software, the results being gathered in Table 2. A wide variety of areas can be observed, corresponding to macro-grain sizes between M-11 and M-7.5 [21]. The tensile tests allowed the whole stress–strain curve of the material to be obtained. Table 3 presents this curve in true variables. Each value has been obtained by considering the average values generated in the 25 tests. Moreover, Table 4 presents the corresponding average values and standard deviation for the elastic modulus, the yield stress, the ultimate tensile strength and the strain under maximum load, expressed in engineering values. It can be observed that the material presents normal resistant parameters and low ductility. Concerning the fracture resistance of the cast steel, Table 5 and Fig. 9 gather the results of both the cracked and the notched specimens in terms of the apparent fracture toughness (KJN), which is obtained by using ASTM E1820 formulation for both the cracked and notched specimens. It can be observed that, although the general trend is an increase in the apparent fracture toughness with the notch radius, there is a high scatter all along the different notch radii, with test results at high notch radii providing low values of fracture resistance, very similar to those obtained in cracked conditions. These results justify that the structural integrity assessments performed in this paper do not consider any notch effect (i.e., it is assumed that notches behave as cracks). The high scatter
Table 5 Results of apparent fracture toughness tests. Notch radius (mm)
Pmax (kN)
KJN (MPa m1/2)
1 2 3 4 5
0.0
11.07 10.05 12.64 10.98 15.02
68.93 49.62 63.48 74.99 99.28
71.26
18.26
6 7 8 9 10
0.5
23.44 10.20 11.25 10.15 13.17
98.77 51.56 143.43 86.576 192.37
114.54
54.52
11 12 13 14 15
1.0
11.57 11.47 11.24 10.62 15.74
74.80 76.13 56.40 58.49 98.77
72.92
17.05
16 17 18 19 20
1.5
12.48 12.72 15.25 13.45 14.30
87.95 98.55 164.53 97.50 206.54
131.02
52.11
21 22 23 24 25
2.0
12.90 14.27 12.80 13.06 11.16
99.19 122.77 95.26 91.67 56.66
93.11
21.49
25 27 28 29 39
2.5
13.34 15.58 13.27 12.94 13.45
101.38 141.73 101.06 88.67 87.30
104.03
22.10
Specimen
KJN, mean (MPa m1/2)
Standard deviation (MPa m1/2)
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
315
4.2. Structural integrity assessment
Fig. 9. Apparent fracture toughness results.
observed in the results may be related to the presence of numerous defects in the material and their random distribution: those specimens with significant defects in the fracture process zone will provide the lower fracture resistance values, whereas those specimens without important defects in the fracture process zone will provide the higher values of the fracture resistance. Fig. 10 shows the fracture surfaces in a cracked and a notched specimen. In both cases the fracture micromechanisms are very similar, presenting brittle aspect and cleavages.
The structural integrity assessments were performed following the procedure outlined in Section 3.2. M, fw, Mm and rref values have been taken from [14]. In the case of the semi-elliptical cracks, the stress intensity factor (KI) was measured at the point of the crack front providing the maximum value. This corresponds to the surface points for aspect ratios (a/2c) of 0.5 and 1.0, and the deepest point for aspect ratio of 0.2. Mb is not necessary, given that the bending stresses (Pb and Qb) are negligible. Concerning Kmat, the equivalent to the minimum of three tests was used, following the indications of [14]. This, for the number of tests performed in cracked conditions (5 tests), corresponds to the minimum value shown in Table 5 (Kmat = 49.62 MPa m1/2). Concerning the yield stress, the average value was considered (rY = 366 MPa, see Table 4). Also, three types of defects and two loading hypotheses were considered. Fig. 11 gathers the results for postulated surface (semi-elliptical) flaws and three different aspect ratios. The effect of the residual stresses is not considered. An initial defect length (a) of 2.0 mm has been considered as a representative value of the capability of the ultrasonic NDT [13], whereas the discontinuous lines show the corresponding situation of the component when increasing the defect size and fixing the applied load.
Fracture surface
Crack front
Fig. 11. Assessment of postulated surface (semi-elliptical) flaws. Residual stresses are not considered.
Fatigue precrack
(a)
Fracture surface
Notch front
(b)
Notch
Fig. 10. Fracture surfaces: (a) specimen 3 (cracked conditions, notch radius = 0 mm); (b) specimen 8 (notched conditions, notch radius = 0.5 mm).
Fig. 12. Assessment of postulated surface (semi-elliptical) flaws. Residual stresses are considered.
316
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
Fig. 13. Assessment of an embedded (elliptical) defect found in the anchorages.
Fig. 14. Assessment of an equivalent surface (semi-elliptical) defect found in the anchorages.
For the 30 year prediction of the ordinary traffic (337 tons, Pm = 139.5 MPa), it can be observed how the lowest a/2c ratio provides the smallest critical defect (ac = 31 mm), whereas this critical size is 56 mm for an aspect ratio of 0.5. In the case of a/2c = 1.0, the critical size is larger than the thickness. This means that the crack should be re-characterised as a through-thickness crack, and the analysis should continue using the corresponding solutions for KI and PL (such an analysis has not been performed here given that the presence of through-thickness defects is highly unlikely). If the maximum load hypothesis is considered (974 tons, Pm = 403.0 MPa), a 2 mm defect length is critical for an aspect ratio of 0.2 (the assessment point is located above the FAL), whereas the situation is already safe for aspect ratios of 0.5 and 1.0. Thus, the aspect ratio is a determining factor in the assessment of the anchorages.
Fig. 12 analyses the same postulated defects subjected to the same loading hypotheses, but on this occasion the residual stresses are considered. The analyses are performed following Level 1 of FITNET FFS Procedure Annex C (Residual Stress Profiles), which considers that both the longitudinal and transverse components of residual stresses are tensile and uniformly distributed in both the through-thickness and transverse directions, with a magnitude equal to the material yield stress at room temperature [22] (Qm = rY). The fracture toughness of the material in the areas subjected to the residual stresses has been considered to be equal to the one in the base material, given that no substantial changes have been found in the corresponding microstructures. It can be observed how the critical size (ac) of the postulated defects for the 30th year traffic prediction is 3 mm, 6 mm and 14 mm for aspect ratios (a/2c) of 0.2, 0.5 and 1.0, respectively. Thus, the consideration of residual stress has a great impact on the structural integrity of the anchorages, with a significant reduction in the critical defect sizes. Moreover, for the maximum load hypothesis, the three considered aspect ratios provide critical (unsafe) situations for an initial defect length of 2 mm. Fig. 13 presents the structural integrity assessment of the anchorages considering the above mentioned embedded (elliptical) flaw, which represents an example of the defects found in the components. When the residual stresses are not considered, the component works under safe conditions for the 30th year load prediction, whereas the situation is unsafe for the maximum load hypothesis; when the residual stresses are considered, the situation is not acceptable (unsafe) for both loading hypotheses. Thus, the analysed defect is a serious threat in the analysed bridge. Moreover, the discontinuous assessment lines shown in the FAD have been obtained by fixing the crack dimensions and increasing the applied load. The resulting critical loads (corresponding to the assessment points located over the FAL) are 878 tons without residual stresses and 247 tons with residual stresses. Fig. 14 presents the assessment of the third analysed defect: an equivalent surface (semi-elliptical) flaw with defined dimensions arising from the interactions between two flaws found in one of the anchorages. The results are very similar to those obtained for the embedded defect: the component works under safe conditions for the 30th year load prediction when the residual stresses are not considered, whereas the situation is unsafe when the residual stresses are considered. For the maximum load hypothesis, the situation is not acceptable regardless of the residual stresses. Again, the discontinuous assessment lines shown in the FAD have been obtained by fixing the crack dimensions and increasing the applied load. The resulting critical loads are 757 tons without residual stresses and 58 tons with residual stresses. Here, it should be noted that the residual stresses generate a significant increase in the Kr coordinate at failure, and also of the Kr/Lr ratio. This causes more brittle failures, which are more dangerous as they have associated lower strains. Finally, Table 6 gathers a summary of the structural integrity situation of the two real defects analysed here. The table shows the corresponding critical loads and reserve factors (load factors, FL) [14] for the different defect and loading combinations. Reserve factors lower than 1.0 are associated to unsafe situations, whereas reserve factors higher than 1.0 correspond to safe situations.
Table 6 Obtained critical loads and reserve factors (load factor, FL) for the different combinations of defect geometry, residual stress level and loading scenario. Flaw type
Crack geometry (a/2c)
FL (30 year prediction)
FL (maximum load)
Pcritical (tons)
Embedded elliptical crack Embedded elliptical crack + residual stress Surface semi-elliptical crack Surface semi-elliptical crack + residual stress
4.5/15.2 4.5/15.2 9.0/20.8 9.0/20.8
2.61 0.72 2.25 0.18
0.90 0.25 0.81 0.06
878.4 247.8 757.6 58.0
J. Terán-Guillén et al. / Engineering Structures 81 (2014) 309–317
317
5. Conclusions
References
The cast steel anchorages of the Rio Papaloapan cable stayed bridge present numerous non-sharp fabrication defects. In 2000 one of the anchorages failed and since then several analyses have been performed. Here, the structural integrity assessment of 112 anchorages has been performed using the Failure Assessment Diagram (FAD) methodology (FITNET FFS and BS7910 procedures). The assessments have required the material characterisation and the analysis of the notch effect in the cast steel. Tensile and fracture properties have been obtained, and the test results show that, from a structural integrity point of view, there is an insignificant effect of the notches on fracture resistance. The analysed defects have been postulated surface defects with different aspect ratios, and two specific defects found in some of the anchorages (an embedded defect and an equivalent surface defect that arises from the interaction of two smaller defects). Finally, the assessments have been performed considering two loading hypotheses (30th year traffic prediction and maximum load corresponding to 4 heavy trucks), and two scenarios of residual stresses: non-existent residual stresses and residual stresses equal to the material yield stress. For the 30th year loading prediction and the postulated surface defects, the results provide critical defect depths higher than 31 mm when the residual stresses are not considered, and between 3 mm and 14 mm (depending on the aspect ratio) when such stresses are considered; for the maximum load hypothesis and the postulated surface defects the critical depths are around 2 mm without residual stresses and well below 2 mm with residual stresses. This implies that the critical defects may not be detectable. The analysis of the two real defects provide safe results for the 30th year loading prediction without residual stresses, whereas the situation is unsafe for such a loading hypothesis coupled with residual stresses and for the maximum loading hypothesis regardless of the level of residual stresses. With all this, the assessments performed here indicate that it is necessary to take remedial actions. If it is intended to avoid the substitution of the anchorages, the traffic loads on the bridge should be limited unless a better definition of the existing defects and residual stresses demonstrate the structural integrity of the anchorages.
[1] Aguirre A, Carbajal J. Análisis del tirante 11 del puente Papaloapan. Corporación Mexicana de Investigación de Materiales S.A. de C.V. Reporte Interno AF-IFT00087. Saltillo, Coahuila, México; 2000. [2] López JA, Carrion FJ, Quintana JA, Samayoa D, Orozco PR. Verification of the ultrasonic qualification for structural integrity of partially embedded steel elements. Adv Mater Res 2009;65:69–78. [3] Samayoa-Ochoa D. Análisis de confiabilidad y riesgo en puentes atirantados. México DF: ESIME-IPN (Tesis Doctoral); 2005. [4] Quintana-Rodríguez JA. Análisis del método de búsqueda global para la detección de daño y monitoreo estructural de puentes. México DF: ESIME-IPN (Tesis Doctoral); 2009. [5] Alcaraz-Caracheo LA. Análisis probabilístico de integridad de un anclaje de acero estructural. México DF: ESIME-IPN (Tesis Doctoral); 2012. [6] Taylor D. The theory of critical distances: a new perspective in fracture mechanics. Elsevier; 2007. [7] Cicero S, Madrazo V, García T. Analysis of notch effect in the apparent fracture toughness and the fracture micromechanisms of ferritic-pearlitic steels operating within their lower shelf. Eng Fail Anal 2014;36:322–42. [8] Cicero S, Madrazo V, García T, Cuervo J, Ruiz E. On the notch effect in load bearing capacity, apparent fracture toughness and fracture mechanisms of polymer PMMA, aluminium alloy Al7075-T651 and structural steels S275JR and S355J2. Eng Fail Anal 2013;29:108–21. [9] Madrazo V, Cicero S, Carrascal IA. On the point method and the line method notch effect predictions in Al7075-T651. Eng Fract Mech 2012;79:363–79. [10] Cicero S, Madrazo V, Carrascal IA. Analysis of notch effect in PMMA using the theory of critical distances. Eng Fract Mech 2012;86:56–72. [11] Milne I, Ainswoth RA, Dowling AR, Stewart AT. Assessment of the integrity of structures containing defects. Int J Pres Ves Pip 1988;32:3–104. [12] Anderson TL. Fracture mechanics: fundamentals and applications. Florida: CRC Press; 2005. [13] Kocak M, Webster S, Janosch JJ, Ainsworth RA, Koers R, editors. FITNET fitnessfor-service (FFS) procedure, vol. I. Geesthacht: GKSS; 2008. [14] BS 7910: 2005. Guide to methods for assessing the acceptability of flaws in metallic structures. London: British Standards Institution; 2005. [15] R6. Assessment of the integrity of structures containing defects. Revision 4. Gloucester: British Energy Generation Limited; 2001. [16] API 579-1/ASME FFS-1 Fitness-For-Service. New York: American Society of Mechanical Engineers; 2007. [17] Bramfitt BL, Benscoter OA. Metallographer’s guide. Materials Park, Ohio: ASM International; 2002. [18] ASTM E8/E8M-09. Standard test methods for tension testing of metallic materials. Philadelphia: ASTM; 2009. [19] ASTM E1820-11. Standard test method for measurement of fracture toughness. Philadelphia: ASTM; 2011. [20] Astiz MA, Composite construction in cable-stayed bridge towers. In: IABSE reports. vol. 999; 1997. p. 127–32. [21] ASTM E112-12. Standard test methods for determining average grain size. Philadelphia: ASTM; 2012. [22] Kocak M, Hadley I, Szavai S, Tkach Y, Taylor N, editors. FITNET fitness-forservice (FFS) procedure, vol. II. Geesthacht: GKSS; 2008.
Acknowledgements Jorge Terán Guillén would like to express his gratitude to the Consejo Nacional de Ciencia y Tecnología de México for the support of his research stay at the Universidad de Cantabria, Spain.