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Fatigue analysis of butt welded AH36 steel joints: Thermographic Method and design S–N curve
Marine Structures 22 (2009) 373–386
Contents lists available at ScienceDirect
Marine Structures journal homepage: www.elsevier.com/locate/ marstruc
Fatigue analysis of butt welded AH36 steel joints: Thermographic Method and design S–N curve V. Crupi a, *, E. Guglielmino a, M. Maestro b, A. Marino` b a
University of Messina, Department of Industrial Chemistry and Materials Engineering, Contrada di Dio, Sant’Agata (ME), 98166 Messina, Italy University of Trieste, Department of Naval Architecture, Ocean and Environmental Engineering, Trieste, Italy
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 July 2008 Received in revised form 15 December 2008 Accepted 27 March 2009
The traditional methods of fatigue assessment of welded joints have some limitations, and are extremely time consuming. In order to overcome these difficulties, the Thermographic Method (TM), based on thermographic analyses, has been applied to predict the fatigue behaviour of butt welded joints, made of AH36 steel, largely used in shipbuilding. Experimental tests have been carried out to assess the fatigue capability in terms of S–N curves and fatigue limits. The predictions of the fatigue capability obtained resorting to the Thermographic Method show a good agreement with those derived from the traditional procedure. Moreover, the fatigue design recommendations were compared to the experimental data in order to analyse the reliability of the codes. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Ship design Welded joints Thermographic Method Fatigue strength prediction Design codes
1. Introduction In recent years there has been a considerable interest in the use of higher strength steels for the construction of ships to obtain a substantial weight reduction. However, during the past decades a great number of fatigue failures occurred in welded ship structures made of higher strength steel [1], due to an insufficient knowledge of the complex relationship between fatigue and tensile strength, and also due to the fact that high stress ranges are involved. The fatigue strength assessment is an important step in the structural design of a ship. In particular, welds are often regions of weakness, due to the presence of possible crack-like defects along with high stress concentration effects and tensile residual stresses caused by the thermal welding process itself. * Corresponding author. Tel.: þ39 90 3977251. E-mail address: [email protected] (V. Crupi). 0951-8339/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.marstruc.2009.03.001
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Nomenclature f m EC FAT IIW N Nf R TM d% DT DTAS
Ds DseIIW DseSN DseTM DseFTM F
frequency (Hz) negative inverse slope of the S–N curve in bi-logarithmic scale energy to failure per unit volume (J m3) fatigue class as expected with the S–N curve at 2 106 cycles (N mm2) International Institute of Welding number of cycles number of cycles to failure stress ratio Thermographic Method percentage difference between DseSN and DseTM temperature increment at the hot-spot area ( C) asymptotic temperature increment ( C) stress range (N mm2) fatigue limit reported in the IIW Code (N mm2) fatigue limit determined by the Traditional Approach (N mm2) fatigue limit predicted by TM (N mm2) fatigue limit predicted by TM using Energy Approach (N mm2) thermal increment to failure per unit volume ( C m3)
Thus, clear design guidelines are needed to ensure that fatigue failures are avoided in welded structures. The design of welded structures is commonly carried out by means of rules which impose conservative values of the allowable stress or consider partial corrective factors to take into account possible defects, residual stresses, corrosion and so on. In order to increase the confidence in the design of a critical detail it is certainly useful to have a deeper knowledge of its actual behaviour in the presence of cyclic loads. The literature on fatigue analysis of welded joints during the past 10–15 years was reviewed by Fricke [2]. In the nominal stress approach, the S–N curves obtained from fatigue tests are used in conjunction with the cyclic load history expressed in terms of nominal stress ranges evaluated at the detail site and relevant number of cycles. Thus, for welded joints of various configurations it is possible to define the corresponding FAT (fatigue class), which is the fatigue strength at 2 106 cycles. However, in real structures with complex geometries, nominal stresses are not always easy to determine. The DNV fatigue analysis procedure [3], which is specifically oriented on ship structures, is based on the hot-spot stress approach. The S–N curves, obtained from tests on actual welded joints, refer to hotspot stresses [4] instead of considering nominal stresses. The two above-mentioned approaches are adopted by many important industries in accordance with the current guidelines of the International Institute of Welding (IIW) [5], Eurocode 3 [6] and Eurocode 9 [7], and are also accepted by some of the major ship classification societies. Nevertheless, they have some important limitations: the selection of the fatigue class can be very subjective, since the weld classification is based not only on the geometry of the joint, but depends also on the dominant loading mode. Moreover, when the hot-spot stresses are determined resorting to finite element models there is a further uncertainty, since the local stresses in front of the weld discontinuity strongly depend on the mesh size. The notch stress approach [8], unlike the nominal and hot-spot stress approaches, is based on the stresses at the weld toe, so all the stress concentration sources due to the geometry of the detail and of the weld profile are taken into account. Thus a single S–N curve is sufficient for a given type of material. A practical problem arises in defining the geometry of the weld toe (notch), which has a great influence on the local stress concentration. Therefore, the notch stresses have been evaluated by FEA (Finite Element Analysis) and parametric formulae have been derived for a range of joint geometries [8]. Another approach for determining the fatigue life of cracked components is based on the Linear Elastic Fracture Mechanics (LEFM) theory, which predicts the crack growth by means of the Paris law. LEFM methods are very sensitive to the initial crack size, and are therefore most suitable primarily for
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the evaluation of the residual life of components with known cracks, while for general fatigue life prediction the assumptions concerning the initial crack turns out to be a crucial issue. The LEFM as well as local stress based approaches are potentially accurate even for complex structures, but the computational effort involved is significantly greater than that required in the nominal stress approach. Recommendations reported in some current Codes are very conservative. This can be explained by the fact that the Codes do not mention weld quality, so that low admissible stresses are needed in order to be always on the safe side [9]. Indeed weld quality has a great influence on the fatigue performance of joints, since it affects a possible crack initiation at the weld toe. Fatigue strength is known to be closely related to the precise geometrical characteristics of the welded joint (i.e., weld toe radius, flank angle and weld size). The bead geometry depends on the welding parameters, the operating conditions and, in case, the skill of the welder. The bead shape (in particular the toe radius) varies from joint to joint even in well-controlled manufacturing operations. Further factors may affect the fatigue response of welded structures. Among them are the thickness of the joined elements, the type and strength of the base material, the welding process and the environment. Available recommendations for fatigue design do not explicitly take into account that there are so many factors affecting the phenomenon. The unavoidable consequence is the establishment of quite conservative recommendations. In order to overcome the above-mentioned problems, an innovative approach for fatigue assessment of welded joints has been proposed: the Thermographic Method (TM). The Thermographic Method, developed by the Risitano Research Group [10–14] and based on thermographic analyses, allows the rapid determination of the high-cycle fatigue limit and the whole fatigue curve of materials, mechanical components and structural details, using a very limited number of tests. The TM has been already used successfully in many fields and there are also applications for ship structures [13,14]. Moreover the method has been applied also to investigate on some special aspects of the structural analyses (e.g., notch sensitivity [11], internal damping of metals [12]). In this paper, an application of the TM for assessing the fatigue strength of butt welded AH36 steel joints (largely used in shipbuilding) is presented. Fatigue tests were carried out applying axial cyclic loads at a frequency of 20 Hz and with a stress ratio R ¼ 0.5. The temperature increment DT of the specimen surface in the course of the experiments was detected by an infrared scanner. The analysis of the thermographic images has allowed to predict the fatigue limit and the S–N curve of the welded joints. The experimental tests were carried out on a statistically meaningful number of specimens, with the aim of doing a comparison with the standard S–N curve (with a 95% survival probability associated with a two-sided 75% confidence level of the mean) as reported in the IIW recommendations. 2. Materials and methods 2.1. The Thermographic Method According to Risitano et al. [10], the fatigue limit can be evaluated as the highest stress value for which there is no temperature increase in any point of a cyclically loaded specimen. When a specimen is cyclically loaded above its fatigue limit, its superficial temperature usually rises quickly in the initial phase (phase 1), then reaches a stabilised asymptotic value DTAS (phase 2), and eventually this asymptote is left when plastic deformations become quite important, leading soon to failure after few cycles, with a very high further temperature increment (phase 3). With a set of specimens the procedure is applied on each of them at different stress range levels Ds. For each test the asymptotic temperature increment DTAS related to the applied Ds is detected by means of a thermographic technique, and then is plotted versus the stress range squared Ds2. Finally, a linear regression is performed. The fatigue limit Dse can be assessed by the intersection of the regression straight line with the abscissa axis: this intersection corresponds to the highest stress range for which there is no temperature variation. The ‘‘stepped loading procedure’’ or Rapid Thermographic Method allows to assess the fatigue limit using theoretically only one specimen. A succession of increasing loads, at the same frequency, is applied stepwise to the same specimen. All the experiments carried out in the past [10–14] have shown
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that the asymptotic temperature is reached in a short time compared to the failure time. Thus it is possible to consider the temperature increment DTAS reached at every loading step Ds. With reference to the set of couples (Ds2, DTAS) so obtained from a single specimen, the procedure for assessing the fatigue limit is then the same already outlined above. 2.2. Energy Approach The TM allows also the rapid determination of the entire S–N curve, considering the amount of energy involved in the fatigue crack growth. The basic assumption of the so-called ‘‘Energy Approach’’ is that the fatigue failure takes place when the absorbed energy reaches a certain threshold value EC characteristic for each structural detail. The limit energy EC is proportional to the integral F of the DT–N curve:
EC fF ¼
Z
Nf
DTðNÞdN
(1)
0
where Nf is the number of cycles to failure. When a single constant-amplitude stress range level Ds is applied, since the number of cycles of the phases 1 and 3 is negligible compared with that of phase 2, the integral F can be practically assumed to be:
FzDTAS Nf
(2)
It has been ascertained that the energy absorbed by a unit volume of material till failure is the same when load histories at different levels are applied. This ascertainment, even if the involved parameters are not the same, substantially confirms the well-known Miner’s rule. In particular, the characteristic value F can be evaluated through a stepwise load history according to the so-called Rapid Thermographic Method. In this way it is possible to obtain the stabilised temperature DTAS at each applied stress range level Ds, and then, resorting to Eq. (2), to determine the relevant Nf value. Thus, the fatigue S–N curve can be drawn on the basis of the pairs (Ds, Nf) so obtained. This procedure allows to rapidly derive the whole S–N curve with a small number of load steps carried out on the same specimen in a total time of a few hours. Obviously, in order to be confident about the result, it is better to use more than one specimen. Anyway, the time consumed for the experiments is definitely much lower than that needed with a Traditional Approach. 2.3. Welded joints analysed The test pieces analysed are butt welded AH36 steel joints, widely used for ship structures (Fig. 1). The specimens of the welded joints are about 50 mm wide, 5 mm thick and 300 mm long, and are made with full penetration welds without lack of fusion. 2.4. Experimental investigation Tests were performed using an MTS 810 System servo-hydraulic load machine with a 250 kN capacity (Fig. 2). Fatigue tests were carried out applying axial cyclic loads at a stress ratio R ¼ 0.5, as required by the International Institute of Welding (IIW) recommendations [5], and at a frequency of 20 Hz. Constantamplitude values of the stress range Ds till failure were applied. More specifically, the different levels Ds were: 100, 150, 175, 180, 200, 220, 225, 240, 250 MPa. If failure did not occur within 5 million cycles, the test was suspended (that happened generally for Ds lesser than 180 MPa). To take into account the scattering of the experimental response, and to attain reliable data for a statistical analysis, 29 constant-amplitude fatigue tests with six replications at three different stress levels (200, 220, 240 MPa) were carried out. Furthermore, according to the above-mentioned Rapid Thermographic Method, tests at increasing loads were carried out by a stepwise succession (applied to the same specimen), starting from 140 MPa with steps of 20 MPa every 30,000 cycles (Fig. 3). Three tests of this kind were performed.
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Fig. 1. Geometry of the analysed welded joints.
The surfaces of the specimens were painted black (in order to get a greater thermal contrast), and thermographic images were acquired in general every 25 s by means of an infrared scanner (Flyr System A40M with a thermal resolution lower than 0.08 C) located at 0.5 m in front of the specimen (Fig. 4). Only for very long tests, the interval between the infrared scanner acquisitions was changed from 25 s to 2 min. ThermaCAM Researcher software was used to analyse the thermographic images (Fig. 5). Digitized images contained 320 240 pixels. During the tests, in order to consider the sole effect due to the cyclic stresses, both the temperatures of the specimen surface and of the environment were simultaneously measured with the thermocamera scanner. The correct temperature increase of the specimen was then determined subtracting the environmental temperature variation.
Fig. 2. Experimental set-up.
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Fig. 3. Stepwise succession of stress ranges and temperature increments.
3. Results and discussion The experimental tests have allowed to obtain the following results. S–N curves at different survival probabilities; fatigue limit DseSN as drawn from the traditional experimental S–N curves at 5 106 cycles;
Fig. 4. Infrared scanner in front of a specimen.
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Fig. 5. Thermographic images of a welded joint (Ds ¼ 250 MPa) in the initial (left) and final (right) phases.
fatigue limit DseTM as obtained resorting to the TM; comparison between DseSN and DseTM values; comparison between DseSN and the fatigue limit DseIIW as reported in the IIW Code; S–N curve obtained through the Energy Approach.
In all the cyclically loaded specimens failure took place in the weld zone with the crack initiating in proximity of the weld toe, where there are high stress concentrations. All the fracture zones showed the typical fatigue fracture surface (Fig. 6).
3.1. S–N curves at different survival probabilities S–N curves at different survival probabilities PS were obtained according to the ASTM E 739-91 Standard [15], which gives the following guidelines. the minimum number of specimens required in S–N testing for reliability data is from 12 to 24; the minimum value of percent replication for reliability data is from 75% to 88% (replication % ¼ 100 [1 (total number of different stress levels used in testing/total number of specimen tested)]); the fatigue life N is assumed as the dependent variable in the S–N tests, whereas S (or Ds) is the independent variable.
Fig. 6. Specimen after fatigue fracture.
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Table 1 Experimental test results. Stress range Ds [MPa]
Number of cycles to failure (N)
250 250
124,420 363,618
240 240 240 240 240 240
492,729 427,376 476,481 730,875 613,610 351,971
225
793,298
220 220 220 220 220 220 220 220
459,470 863,865 1,491,155 1,115,057 1,195,378 742,846 823,872 No failure
200 200 200 200 200 200 200 200
1,452,716 1,160,783 817,756 975,414 958,043 1,354,914 No failure No failure
180
No failure
175
No failure
150
No failure
100
No failure
Fig. 7. S–N curves in bi-logarithmic scale.
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Fig. 8. DT–N curves obtained by constant-amplitude fatigue tests.
The S–N curves are obtained from constant-amplitude fatigue tests, using least-squares fitting of experimental data and the standard equation:
Dsm N ¼ C
(3)
where m and C are the fitting constants. Of course, the regression line given by Eq. (3) represents the S–N curve at 50% survival probability (median line). Experimental fatigue test results have always a certain degree of scattering, and consequently a statistical evaluation must be performed. All data are expressed in terms of log N and log Ds, and then the fitting parameters m and log C of the following linear regression equation are determined:
log N ¼ m log Ds þ log C
(4)
From the median S–N curve so obtained it is possible to determine a design S–N curve with an adequate probability of survival (normally PS ¼ 97.7% is taken). For this purpose a Gaussian log-normal
Fig. 9. DT–N curve obtained by stepwise load (test no. 1).
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Fig. 10. DT–N curve obtained by stepwise load (test no. 2).
distribution of the dependent variable log N is assumed, and the median curve (PS ¼ 50%) is parallelly shifted by two standard deviations of log N, so drawing a design S–N curve with PS ¼ 97.7%. Table 1 reports the values of the applied stress ranges Ds and the relevant number of cycles to failure N obtained from the 29 constant-amplitude fatigue tests. When failure did not occur within 5 million cycles, the test was suspended. In Fig. 7 the S–N curves at different survival probabilities (PS ¼ 50% and 97.7%) are plotted in bilogarithmic scale. The values of the negative inverse slope m, the stress range at 2 106 cycles (fatigue class FAT) and the stress range at 5 106 cycles (fatigue limit DseSN) are also reported. The confidence intervals for the parameters m and log C, reported in the legend of Fig. 7, were established using the tdistribution, in accordance with the ASTM E 739-91 Standards [15]. 3.2. Fatigue limit prediction by the Thermographic Method The basis of the TM is the assessment of the temperature increment DTAS caused by a given cyclically applied stress range Ds. The analyses of the DT–N curves, obtained by the experimental tests, show that in the presence of fatigue the temperature reaches an almost constant value before the first 30,000 cycles. The values of DTAS were assumed as the average temperature increments in the intermediate phase (phase 2). In Fig. 8 the DT–N curves corresponding to three specimens subjected to different stress range levels are plotted. In particular, the DT–N curve related to the highest Ds shows clearly also the phase 3 leading to the final failure. Figs. 9–11 show the DT–N curves obtained by three tests at increasing stepwise stress ranges. The specimens were subjected to increasing cyclic loads until failure, but only the stress range levels within the high-cycle fatigue field (that is to say with Ds lower than 250 MPa in the examined case) were considered in the thermographic analyses.
Fig. 11. DT–N curve obtained by stepwise load (test no. 3).
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Fig. 12. DTAS Ds2 curves obtained by the stepwise load fatigue tests.
Table 2 Percentage difference between DseTM and DseSN.
DseTM [MPa]
DseSN [MPa]
d%
155 (test no. 1) 148 (test no. 2) 159 (test no. 3)
157 157 157
1.3 5.7 1.3
In Fig. 12, for each test at increasing stress ranges, the asymptotic temperature increments DTAS are directly related to the stress range squared Ds2. The experimental data were interpolated with a linear function, and the fatigue limits DseTM were determined by the intersections of the straight lines with the abscissa axis, in accordance with the TM expounded above. The fatigue limits DseTM assessed resorting to the TM were compared with the fatigue limit DseSN drawn from the S–N curve of Fig. 7 (DseSN ¼ 157 MPa). Table 2 shows the results of this comparison in terms of percentage difference d% defined as:
d% ¼
DseTM DseSN 100 DseSN
(5)
The differences d are the consequence of the fact that the fatigue limit DseTM predicted by the Thermographic Method is related to the real physical phenomenon (i.e., no temperature increase when the stress range is below the fatigue limit), whereas the value of the fatigue limit DseSN obtained by the traditional procedure is the result of a generally accepted convention (i.e., the fatigue limit is assumed as the stress range at 5 106 cycles drawn from the S–N curve). The TM, indeed, defines the fatigue limit in a unique way in accordance with the physical phenomenon, and is not dependent on any conventional assumption.
Fig. 13. Structural detail from IIW Code.
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Table 3 IIW Code and experimental design S–N curve (PS ¼ 97.7%).
IIW Code Experiment
m
FAT [MPa]
DseSN [MPa]
3 5.6
80 161
59 137
3.3. Comparison with the values reported in the IIW Code The fatigue class FAT (i.e. the fatigue strength at 2 106 cycles) of the steel joint type that has been analysed, according to the International Institute of Welding (IIW) Code [5] (Fig. 13), is equal to 80 MPa. It is worth to note that the IIW considers m constant and equal to 3 for all welds. The higher value of m obtained from the test data indicates that the analysed detail is one in which the fatigue crack initiation occupies a significant proportion of the total fatigue life, while IIW with m ¼ 3 clearly refers to cases where the crack initiation phase is relatively short [16]. If the fatigue parameters (FAT, fatigue limit, slope of the S–N curve) reported in the IIW are compared with the values obtained by the experimental tests (Table 3 and Fig. 14) the high conservativeness of the recommendations appears evident. This is obviously justified by the many uncertainties involved when no information about the quality control of the manufacturer was available. Conversely, if it is possible to rely on a proper manufacturing quality control, a more realistic fatigue capability assessment is certainly desirable, and to this end the TM can be a suitable tool.
Fig. 14. Experimental and design S–N curves.
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Fig. 15. S–N curves as predicted by the Energy Approach.
Table 4 Scattering of the S–N curve parameters by Traditional and Energy approaches.
Traditional Approach Energy Approach
Number of tests
m
log C
29 3
5.6 2.3 5.6 0.2
19.1 5.3 18.9 0.3
3.4. S–N curve obtained through the Energy Approach As already mentioned, the Rapid Thermographic Method allows also the straightforward determination of the whole S–N curve applying the Energy Approach. This method was applied with reference to the tests carried out at increasing stepwise stress ranges. In Fig. 15 the S–N curves (PS ¼ 50%) obtained in accordance with the Energy Approach and with the Traditional Approach are plotted together for a direct comparison. The good agreement is evident. The Rapid Thermographic Method for fatigue analyses is much faster than the traditional procedure and requires less tests to draw the S–N curve. Moreover, the scattering of the S–N curve parameters (m, log C) predicted by the Energy Approach is lower than that of the traditional S–N curves (Table 4).
4. Conclusions The Rapid Thermographic Method allows the assessment of the fatigue limit of steel welded joints and of the entire S–N curve, resorting to a limited number of tests that can be performed in a very short time. The design S–N curve directly obtained by the traditional procedure has been compared to the design S–N curve as reported in the IIW Code, and the conservativeness of the latter has emerged. The actual strength of welded structures is affected by different parameters (weld quality, material, thickness, stress ratio, welding technique) that are not well considered by the current Codes and Standards. In order to consider the above-mentioned parameters also, ad hoc investigations are needed. However, traditional fatigue tests are extremely time consuming, so that, alternatively, innovative tests based on the Thermographic Method turn out to be very useful, due to its flexibility and rapidity in giving reliable results.
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Acknowledgments The authors are grateful to Fincantieri – Cantieri Navali Italiani SpA of Trieste for the technical support and the efficient cooperation. References [1] Fricke W, Cui W, Kierkgaard H, Kihl D, Koval M, Mikkola T, et al. Comparative fatigue strength assessment of a structural detail in a containership using various approaches of classification societies. Mar Struct 2002;15:1–13. [2] Fricke W. Fatigue analysis of welded joints: state of development. Mar Struct 2003;16:185–200. [3] DNV. Fatigue assessment of ship structure. Det Norske Veritas Classification Note 30.7. Oslo: DNV; 2001. [4] Niemi E, Fricke W, Maddox SJ. Fatigue analysis of welded components – designer’s guide to the hot-spot stress approach. Cambridge: Whoodhead Publishing Ltd.; 2006. [5] International Institute of Welding. Fatigue design of welded joints and components. Abington, Cambridge, UK: Abington Publishing; 1996. [6] Eurocode 3. Design of steel structures: part 1-1: general rules and rules for building. European Committee for Standardisation; 1993. [7] Eurocode 9. Design of aluminium structures, part 2: structures susceptible to fatigue. Brussels, Belgium: European Committee for Standardisation; 1999. [8] Radaj D. Design and analysis of fatigue-resistant welded structures. Cambridge, UK: Abington Publishing; 1990. [9] Huther I, Primot L, Lieurade HP, Janosh JJ, Colchen D, Debiez S. Weld quality and the cyclic fatigue strength of steel welded joints. Welding World/Le Soudage dans le Monde 1995;35(2):118–33. [10] La Rosa G, Risitano A. Thermographic methodology for the rapid determination of fatigue limit of materials and mechanical components. Int J Fatigue 2000;22(1):65–73. [11] Geraci AL, Guglielmino E, La Rosa G, Roccati G. Notch sensitivity in specimens with a blind hole under fatigue loading. Exp Tech 1995;19(1):17–20. [12] Audenino AL, Crupi V, Zanetti EM. Correlation between thermography and internal damping in metals. Int J Fatigue 2003; 25(4):343–51. [13] Crupi V, Guglielmino E, Risitano A, Taylor D. Different methods for fatigue assessment of T welded joints used in ship structures. J Ship Res 2007;51(2):150–9. [14] Crupi V, Marino` A, Biot M, Risitano G. Fatigue Prediction by thermographic method of aluminum alloy 6082 panels: comparison between FSW and MIG welding. J Ship Prod 2007;23(4):215–22. [15] ASTM E 739–91. Standard practice for statistical analysis of linear or linearized stress-life (S–N) and strain-life (e–N) fatigue data. ASTM; 2004. [16] Maddox SJ. Fatigue design rules for welded structures. Prog Struct Eng Mater 2000;2:102–9.
Contents lists available at ScienceDirect
Marine Structures journal homepage: www.elsevier.com/locate/ marstruc
Fatigue analysis of butt welded AH36 steel joints: Thermographic Method and design S–N curve V. Crupi a, *, E. Guglielmino a, M. Maestro b, A. Marino` b a
University of Messina, Department of Industrial Chemistry and Materials Engineering, Contrada di Dio, Sant’Agata (ME), 98166 Messina, Italy University of Trieste, Department of Naval Architecture, Ocean and Environmental Engineering, Trieste, Italy
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 July 2008 Received in revised form 15 December 2008 Accepted 27 March 2009
The traditional methods of fatigue assessment of welded joints have some limitations, and are extremely time consuming. In order to overcome these difficulties, the Thermographic Method (TM), based on thermographic analyses, has been applied to predict the fatigue behaviour of butt welded joints, made of AH36 steel, largely used in shipbuilding. Experimental tests have been carried out to assess the fatigue capability in terms of S–N curves and fatigue limits. The predictions of the fatigue capability obtained resorting to the Thermographic Method show a good agreement with those derived from the traditional procedure. Moreover, the fatigue design recommendations were compared to the experimental data in order to analyse the reliability of the codes. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Ship design Welded joints Thermographic Method Fatigue strength prediction Design codes
1. Introduction In recent years there has been a considerable interest in the use of higher strength steels for the construction of ships to obtain a substantial weight reduction. However, during the past decades a great number of fatigue failures occurred in welded ship structures made of higher strength steel [1], due to an insufficient knowledge of the complex relationship between fatigue and tensile strength, and also due to the fact that high stress ranges are involved. The fatigue strength assessment is an important step in the structural design of a ship. In particular, welds are often regions of weakness, due to the presence of possible crack-like defects along with high stress concentration effects and tensile residual stresses caused by the thermal welding process itself. * Corresponding author. Tel.: þ39 90 3977251. E-mail address: [email protected] (V. Crupi). 0951-8339/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.marstruc.2009.03.001
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Nomenclature f m EC FAT IIW N Nf R TM d% DT DTAS
Ds DseIIW DseSN DseTM DseFTM F
frequency (Hz) negative inverse slope of the S–N curve in bi-logarithmic scale energy to failure per unit volume (J m3) fatigue class as expected with the S–N curve at 2 106 cycles (N mm2) International Institute of Welding number of cycles number of cycles to failure stress ratio Thermographic Method percentage difference between DseSN and DseTM temperature increment at the hot-spot area ( C) asymptotic temperature increment ( C) stress range (N mm2) fatigue limit reported in the IIW Code (N mm2) fatigue limit determined by the Traditional Approach (N mm2) fatigue limit predicted by TM (N mm2) fatigue limit predicted by TM using Energy Approach (N mm2) thermal increment to failure per unit volume ( C m3)
Thus, clear design guidelines are needed to ensure that fatigue failures are avoided in welded structures. The design of welded structures is commonly carried out by means of rules which impose conservative values of the allowable stress or consider partial corrective factors to take into account possible defects, residual stresses, corrosion and so on. In order to increase the confidence in the design of a critical detail it is certainly useful to have a deeper knowledge of its actual behaviour in the presence of cyclic loads. The literature on fatigue analysis of welded joints during the past 10–15 years was reviewed by Fricke [2]. In the nominal stress approach, the S–N curves obtained from fatigue tests are used in conjunction with the cyclic load history expressed in terms of nominal stress ranges evaluated at the detail site and relevant number of cycles. Thus, for welded joints of various configurations it is possible to define the corresponding FAT (fatigue class), which is the fatigue strength at 2 106 cycles. However, in real structures with complex geometries, nominal stresses are not always easy to determine. The DNV fatigue analysis procedure [3], which is specifically oriented on ship structures, is based on the hot-spot stress approach. The S–N curves, obtained from tests on actual welded joints, refer to hotspot stresses [4] instead of considering nominal stresses. The two above-mentioned approaches are adopted by many important industries in accordance with the current guidelines of the International Institute of Welding (IIW) [5], Eurocode 3 [6] and Eurocode 9 [7], and are also accepted by some of the major ship classification societies. Nevertheless, they have some important limitations: the selection of the fatigue class can be very subjective, since the weld classification is based not only on the geometry of the joint, but depends also on the dominant loading mode. Moreover, when the hot-spot stresses are determined resorting to finite element models there is a further uncertainty, since the local stresses in front of the weld discontinuity strongly depend on the mesh size. The notch stress approach [8], unlike the nominal and hot-spot stress approaches, is based on the stresses at the weld toe, so all the stress concentration sources due to the geometry of the detail and of the weld profile are taken into account. Thus a single S–N curve is sufficient for a given type of material. A practical problem arises in defining the geometry of the weld toe (notch), which has a great influence on the local stress concentration. Therefore, the notch stresses have been evaluated by FEA (Finite Element Analysis) and parametric formulae have been derived for a range of joint geometries [8]. Another approach for determining the fatigue life of cracked components is based on the Linear Elastic Fracture Mechanics (LEFM) theory, which predicts the crack growth by means of the Paris law. LEFM methods are very sensitive to the initial crack size, and are therefore most suitable primarily for
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the evaluation of the residual life of components with known cracks, while for general fatigue life prediction the assumptions concerning the initial crack turns out to be a crucial issue. The LEFM as well as local stress based approaches are potentially accurate even for complex structures, but the computational effort involved is significantly greater than that required in the nominal stress approach. Recommendations reported in some current Codes are very conservative. This can be explained by the fact that the Codes do not mention weld quality, so that low admissible stresses are needed in order to be always on the safe side [9]. Indeed weld quality has a great influence on the fatigue performance of joints, since it affects a possible crack initiation at the weld toe. Fatigue strength is known to be closely related to the precise geometrical characteristics of the welded joint (i.e., weld toe radius, flank angle and weld size). The bead geometry depends on the welding parameters, the operating conditions and, in case, the skill of the welder. The bead shape (in particular the toe radius) varies from joint to joint even in well-controlled manufacturing operations. Further factors may affect the fatigue response of welded structures. Among them are the thickness of the joined elements, the type and strength of the base material, the welding process and the environment. Available recommendations for fatigue design do not explicitly take into account that there are so many factors affecting the phenomenon. The unavoidable consequence is the establishment of quite conservative recommendations. In order to overcome the above-mentioned problems, an innovative approach for fatigue assessment of welded joints has been proposed: the Thermographic Method (TM). The Thermographic Method, developed by the Risitano Research Group [10–14] and based on thermographic analyses, allows the rapid determination of the high-cycle fatigue limit and the whole fatigue curve of materials, mechanical components and structural details, using a very limited number of tests. The TM has been already used successfully in many fields and there are also applications for ship structures [13,14]. Moreover the method has been applied also to investigate on some special aspects of the structural analyses (e.g., notch sensitivity [11], internal damping of metals [12]). In this paper, an application of the TM for assessing the fatigue strength of butt welded AH36 steel joints (largely used in shipbuilding) is presented. Fatigue tests were carried out applying axial cyclic loads at a frequency of 20 Hz and with a stress ratio R ¼ 0.5. The temperature increment DT of the specimen surface in the course of the experiments was detected by an infrared scanner. The analysis of the thermographic images has allowed to predict the fatigue limit and the S–N curve of the welded joints. The experimental tests were carried out on a statistically meaningful number of specimens, with the aim of doing a comparison with the standard S–N curve (with a 95% survival probability associated with a two-sided 75% confidence level of the mean) as reported in the IIW recommendations. 2. Materials and methods 2.1. The Thermographic Method According to Risitano et al. [10], the fatigue limit can be evaluated as the highest stress value for which there is no temperature increase in any point of a cyclically loaded specimen. When a specimen is cyclically loaded above its fatigue limit, its superficial temperature usually rises quickly in the initial phase (phase 1), then reaches a stabilised asymptotic value DTAS (phase 2), and eventually this asymptote is left when plastic deformations become quite important, leading soon to failure after few cycles, with a very high further temperature increment (phase 3). With a set of specimens the procedure is applied on each of them at different stress range levels Ds. For each test the asymptotic temperature increment DTAS related to the applied Ds is detected by means of a thermographic technique, and then is plotted versus the stress range squared Ds2. Finally, a linear regression is performed. The fatigue limit Dse can be assessed by the intersection of the regression straight line with the abscissa axis: this intersection corresponds to the highest stress range for which there is no temperature variation. The ‘‘stepped loading procedure’’ or Rapid Thermographic Method allows to assess the fatigue limit using theoretically only one specimen. A succession of increasing loads, at the same frequency, is applied stepwise to the same specimen. All the experiments carried out in the past [10–14] have shown
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that the asymptotic temperature is reached in a short time compared to the failure time. Thus it is possible to consider the temperature increment DTAS reached at every loading step Ds. With reference to the set of couples (Ds2, DTAS) so obtained from a single specimen, the procedure for assessing the fatigue limit is then the same already outlined above. 2.2. Energy Approach The TM allows also the rapid determination of the entire S–N curve, considering the amount of energy involved in the fatigue crack growth. The basic assumption of the so-called ‘‘Energy Approach’’ is that the fatigue failure takes place when the absorbed energy reaches a certain threshold value EC characteristic for each structural detail. The limit energy EC is proportional to the integral F of the DT–N curve:
EC fF ¼
Z
Nf
DTðNÞdN
(1)
0
where Nf is the number of cycles to failure. When a single constant-amplitude stress range level Ds is applied, since the number of cycles of the phases 1 and 3 is negligible compared with that of phase 2, the integral F can be practically assumed to be:
FzDTAS Nf
(2)
It has been ascertained that the energy absorbed by a unit volume of material till failure is the same when load histories at different levels are applied. This ascertainment, even if the involved parameters are not the same, substantially confirms the well-known Miner’s rule. In particular, the characteristic value F can be evaluated through a stepwise load history according to the so-called Rapid Thermographic Method. In this way it is possible to obtain the stabilised temperature DTAS at each applied stress range level Ds, and then, resorting to Eq. (2), to determine the relevant Nf value. Thus, the fatigue S–N curve can be drawn on the basis of the pairs (Ds, Nf) so obtained. This procedure allows to rapidly derive the whole S–N curve with a small number of load steps carried out on the same specimen in a total time of a few hours. Obviously, in order to be confident about the result, it is better to use more than one specimen. Anyway, the time consumed for the experiments is definitely much lower than that needed with a Traditional Approach. 2.3. Welded joints analysed The test pieces analysed are butt welded AH36 steel joints, widely used for ship structures (Fig. 1). The specimens of the welded joints are about 50 mm wide, 5 mm thick and 300 mm long, and are made with full penetration welds without lack of fusion. 2.4. Experimental investigation Tests were performed using an MTS 810 System servo-hydraulic load machine with a 250 kN capacity (Fig. 2). Fatigue tests were carried out applying axial cyclic loads at a stress ratio R ¼ 0.5, as required by the International Institute of Welding (IIW) recommendations [5], and at a frequency of 20 Hz. Constantamplitude values of the stress range Ds till failure were applied. More specifically, the different levels Ds were: 100, 150, 175, 180, 200, 220, 225, 240, 250 MPa. If failure did not occur within 5 million cycles, the test was suspended (that happened generally for Ds lesser than 180 MPa). To take into account the scattering of the experimental response, and to attain reliable data for a statistical analysis, 29 constant-amplitude fatigue tests with six replications at three different stress levels (200, 220, 240 MPa) were carried out. Furthermore, according to the above-mentioned Rapid Thermographic Method, tests at increasing loads were carried out by a stepwise succession (applied to the same specimen), starting from 140 MPa with steps of 20 MPa every 30,000 cycles (Fig. 3). Three tests of this kind were performed.
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Fig. 1. Geometry of the analysed welded joints.
The surfaces of the specimens were painted black (in order to get a greater thermal contrast), and thermographic images were acquired in general every 25 s by means of an infrared scanner (Flyr System A40M with a thermal resolution lower than 0.08 C) located at 0.5 m in front of the specimen (Fig. 4). Only for very long tests, the interval between the infrared scanner acquisitions was changed from 25 s to 2 min. ThermaCAM Researcher software was used to analyse the thermographic images (Fig. 5). Digitized images contained 320 240 pixels. During the tests, in order to consider the sole effect due to the cyclic stresses, both the temperatures of the specimen surface and of the environment were simultaneously measured with the thermocamera scanner. The correct temperature increase of the specimen was then determined subtracting the environmental temperature variation.
Fig. 2. Experimental set-up.
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Fig. 3. Stepwise succession of stress ranges and temperature increments.
3. Results and discussion The experimental tests have allowed to obtain the following results. S–N curves at different survival probabilities; fatigue limit DseSN as drawn from the traditional experimental S–N curves at 5 106 cycles;
Fig. 4. Infrared scanner in front of a specimen.
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Fig. 5. Thermographic images of a welded joint (Ds ¼ 250 MPa) in the initial (left) and final (right) phases.
fatigue limit DseTM as obtained resorting to the TM; comparison between DseSN and DseTM values; comparison between DseSN and the fatigue limit DseIIW as reported in the IIW Code; S–N curve obtained through the Energy Approach.
In all the cyclically loaded specimens failure took place in the weld zone with the crack initiating in proximity of the weld toe, where there are high stress concentrations. All the fracture zones showed the typical fatigue fracture surface (Fig. 6).
3.1. S–N curves at different survival probabilities S–N curves at different survival probabilities PS were obtained according to the ASTM E 739-91 Standard [15], which gives the following guidelines. the minimum number of specimens required in S–N testing for reliability data is from 12 to 24; the minimum value of percent replication for reliability data is from 75% to 88% (replication % ¼ 100 [1 (total number of different stress levels used in testing/total number of specimen tested)]); the fatigue life N is assumed as the dependent variable in the S–N tests, whereas S (or Ds) is the independent variable.
Fig. 6. Specimen after fatigue fracture.
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Table 1 Experimental test results. Stress range Ds [MPa]
Number of cycles to failure (N)
250 250
124,420 363,618
240 240 240 240 240 240
492,729 427,376 476,481 730,875 613,610 351,971
225
793,298
220 220 220 220 220 220 220 220
459,470 863,865 1,491,155 1,115,057 1,195,378 742,846 823,872 No failure
200 200 200 200 200 200 200 200
1,452,716 1,160,783 817,756 975,414 958,043 1,354,914 No failure No failure
180
No failure
175
No failure
150
No failure
100
No failure
Fig. 7. S–N curves in bi-logarithmic scale.
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Fig. 8. DT–N curves obtained by constant-amplitude fatigue tests.
The S–N curves are obtained from constant-amplitude fatigue tests, using least-squares fitting of experimental data and the standard equation:
Dsm N ¼ C
(3)
where m and C are the fitting constants. Of course, the regression line given by Eq. (3) represents the S–N curve at 50% survival probability (median line). Experimental fatigue test results have always a certain degree of scattering, and consequently a statistical evaluation must be performed. All data are expressed in terms of log N and log Ds, and then the fitting parameters m and log C of the following linear regression equation are determined:
log N ¼ m log Ds þ log C
(4)
From the median S–N curve so obtained it is possible to determine a design S–N curve with an adequate probability of survival (normally PS ¼ 97.7% is taken). For this purpose a Gaussian log-normal
Fig. 9. DT–N curve obtained by stepwise load (test no. 1).
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Fig. 10. DT–N curve obtained by stepwise load (test no. 2).
distribution of the dependent variable log N is assumed, and the median curve (PS ¼ 50%) is parallelly shifted by two standard deviations of log N, so drawing a design S–N curve with PS ¼ 97.7%. Table 1 reports the values of the applied stress ranges Ds and the relevant number of cycles to failure N obtained from the 29 constant-amplitude fatigue tests. When failure did not occur within 5 million cycles, the test was suspended. In Fig. 7 the S–N curves at different survival probabilities (PS ¼ 50% and 97.7%) are plotted in bilogarithmic scale. The values of the negative inverse slope m, the stress range at 2 106 cycles (fatigue class FAT) and the stress range at 5 106 cycles (fatigue limit DseSN) are also reported. The confidence intervals for the parameters m and log C, reported in the legend of Fig. 7, were established using the tdistribution, in accordance with the ASTM E 739-91 Standards [15]. 3.2. Fatigue limit prediction by the Thermographic Method The basis of the TM is the assessment of the temperature increment DTAS caused by a given cyclically applied stress range Ds. The analyses of the DT–N curves, obtained by the experimental tests, show that in the presence of fatigue the temperature reaches an almost constant value before the first 30,000 cycles. The values of DTAS were assumed as the average temperature increments in the intermediate phase (phase 2). In Fig. 8 the DT–N curves corresponding to three specimens subjected to different stress range levels are plotted. In particular, the DT–N curve related to the highest Ds shows clearly also the phase 3 leading to the final failure. Figs. 9–11 show the DT–N curves obtained by three tests at increasing stepwise stress ranges. The specimens were subjected to increasing cyclic loads until failure, but only the stress range levels within the high-cycle fatigue field (that is to say with Ds lower than 250 MPa in the examined case) were considered in the thermographic analyses.
Fig. 11. DT–N curve obtained by stepwise load (test no. 3).
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Fig. 12. DTAS Ds2 curves obtained by the stepwise load fatigue tests.
Table 2 Percentage difference between DseTM and DseSN.
DseTM [MPa]
DseSN [MPa]
d%
155 (test no. 1) 148 (test no. 2) 159 (test no. 3)
157 157 157
1.3 5.7 1.3
In Fig. 12, for each test at increasing stress ranges, the asymptotic temperature increments DTAS are directly related to the stress range squared Ds2. The experimental data were interpolated with a linear function, and the fatigue limits DseTM were determined by the intersections of the straight lines with the abscissa axis, in accordance with the TM expounded above. The fatigue limits DseTM assessed resorting to the TM were compared with the fatigue limit DseSN drawn from the S–N curve of Fig. 7 (DseSN ¼ 157 MPa). Table 2 shows the results of this comparison in terms of percentage difference d% defined as:
d% ¼
DseTM DseSN 100 DseSN
(5)
The differences d are the consequence of the fact that the fatigue limit DseTM predicted by the Thermographic Method is related to the real physical phenomenon (i.e., no temperature increase when the stress range is below the fatigue limit), whereas the value of the fatigue limit DseSN obtained by the traditional procedure is the result of a generally accepted convention (i.e., the fatigue limit is assumed as the stress range at 5 106 cycles drawn from the S–N curve). The TM, indeed, defines the fatigue limit in a unique way in accordance with the physical phenomenon, and is not dependent on any conventional assumption.
Fig. 13. Structural detail from IIW Code.
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Table 3 IIW Code and experimental design S–N curve (PS ¼ 97.7%).
IIW Code Experiment
m
FAT [MPa]
DseSN [MPa]
3 5.6
80 161
59 137
3.3. Comparison with the values reported in the IIW Code The fatigue class FAT (i.e. the fatigue strength at 2 106 cycles) of the steel joint type that has been analysed, according to the International Institute of Welding (IIW) Code [5] (Fig. 13), is equal to 80 MPa. It is worth to note that the IIW considers m constant and equal to 3 for all welds. The higher value of m obtained from the test data indicates that the analysed detail is one in which the fatigue crack initiation occupies a significant proportion of the total fatigue life, while IIW with m ¼ 3 clearly refers to cases where the crack initiation phase is relatively short [16]. If the fatigue parameters (FAT, fatigue limit, slope of the S–N curve) reported in the IIW are compared with the values obtained by the experimental tests (Table 3 and Fig. 14) the high conservativeness of the recommendations appears evident. This is obviously justified by the many uncertainties involved when no information about the quality control of the manufacturer was available. Conversely, if it is possible to rely on a proper manufacturing quality control, a more realistic fatigue capability assessment is certainly desirable, and to this end the TM can be a suitable tool.
Fig. 14. Experimental and design S–N curves.
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Fig. 15. S–N curves as predicted by the Energy Approach.
Table 4 Scattering of the S–N curve parameters by Traditional and Energy approaches.
Traditional Approach Energy Approach
Number of tests
m
log C
29 3
5.6 2.3 5.6 0.2
19.1 5.3 18.9 0.3
3.4. S–N curve obtained through the Energy Approach As already mentioned, the Rapid Thermographic Method allows also the straightforward determination of the whole S–N curve applying the Energy Approach. This method was applied with reference to the tests carried out at increasing stepwise stress ranges. In Fig. 15 the S–N curves (PS ¼ 50%) obtained in accordance with the Energy Approach and with the Traditional Approach are plotted together for a direct comparison. The good agreement is evident. The Rapid Thermographic Method for fatigue analyses is much faster than the traditional procedure and requires less tests to draw the S–N curve. Moreover, the scattering of the S–N curve parameters (m, log C) predicted by the Energy Approach is lower than that of the traditional S–N curves (Table 4).
4. Conclusions The Rapid Thermographic Method allows the assessment of the fatigue limit of steel welded joints and of the entire S–N curve, resorting to a limited number of tests that can be performed in a very short time. The design S–N curve directly obtained by the traditional procedure has been compared to the design S–N curve as reported in the IIW Code, and the conservativeness of the latter has emerged. The actual strength of welded structures is affected by different parameters (weld quality, material, thickness, stress ratio, welding technique) that are not well considered by the current Codes and Standards. In order to consider the above-mentioned parameters also, ad hoc investigations are needed. However, traditional fatigue tests are extremely time consuming, so that, alternatively, innovative tests based on the Thermographic Method turn out to be very useful, due to its flexibility and rapidity in giving reliable results.
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Acknowledgments The authors are grateful to Fincantieri – Cantieri Navali Italiani SpA of Trieste for the technical support and the efficient cooperation. References [1] Fricke W, Cui W, Kierkgaard H, Kihl D, Koval M, Mikkola T, et al. Comparative fatigue strength assessment of a structural detail in a containership using various approaches of classification societies. Mar Struct 2002;15:1–13. [2] Fricke W. Fatigue analysis of welded joints: state of development. Mar Struct 2003;16:185–200. [3] DNV. Fatigue assessment of ship structure. Det Norske Veritas Classification Note 30.7. Oslo: DNV; 2001. [4] Niemi E, Fricke W, Maddox SJ. Fatigue analysis of welded components – designer’s guide to the hot-spot stress approach. Cambridge: Whoodhead Publishing Ltd.; 2006. [5] International Institute of Welding. Fatigue design of welded joints and components. Abington, Cambridge, UK: Abington Publishing; 1996. [6] Eurocode 3. Design of steel structures: part 1-1: general rules and rules for building. European Committee for Standardisation; 1993. [7] Eurocode 9. Design of aluminium structures, part 2: structures susceptible to fatigue. Brussels, Belgium: European Committee for Standardisation; 1999. [8] Radaj D. Design and analysis of fatigue-resistant welded structures. Cambridge, UK: Abington Publishing; 1990. [9] Huther I, Primot L, Lieurade HP, Janosh JJ, Colchen D, Debiez S. Weld quality and the cyclic fatigue strength of steel welded joints. Welding World/Le Soudage dans le Monde 1995;35(2):118–33. [10] La Rosa G, Risitano A. Thermographic methodology for the rapid determination of fatigue limit of materials and mechanical components. Int J Fatigue 2000;22(1):65–73. [11] Geraci AL, Guglielmino E, La Rosa G, Roccati G. Notch sensitivity in specimens with a blind hole under fatigue loading. Exp Tech 1995;19(1):17–20. [12] Audenino AL, Crupi V, Zanetti EM. Correlation between thermography and internal damping in metals. Int J Fatigue 2003; 25(4):343–51. [13] Crupi V, Guglielmino E, Risitano A, Taylor D. Different methods for fatigue assessment of T welded joints used in ship structures. J Ship Res 2007;51(2):150–9. [14] Crupi V, Marino` A, Biot M, Risitano G. Fatigue Prediction by thermographic method of aluminum alloy 6082 panels: comparison between FSW and MIG welding. J Ship Prod 2007;23(4):215–22. [15] ASTM E 739–91. Standard practice for statistical analysis of linear or linearized stress-life (S–N) and strain-life (e–N) fatigue data. ASTM; 2004. [16] Maddox SJ. Fatigue design rules for welded structures. Prog Struct Eng Mater 2000;2:102–9.