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Post-failure life evaluation: A corrosion-fatigue case history
Engineering Failure Analysis 105 (2019) 828–836
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Post-failure life evaluation: A corrosion-fatigue case history ⁎
E. Díaza, , L. Soriab, J.M. Gallardob
T
a
Asociación de Investigación y Cooperación Industrial de Andalucía, Av. Camino de los Descubrimientos s/n, 41092 Seville, Spain Department of Engineering and Materials Science and Transportation, University of Seville, Av. Camino de los Descubrimientos s/n, 41092 Seville, Spain
b
A R T IC LE I N F O
ABS TRA CT
Keywords: Steel rod Corrosion-fatigue Coastal environment
An AISI 1029 steel threaded rod belonging to a harbour crane fractured after ten years of service. Failure analysis, including metallography and both destructive and non-destructive testing, was carried out. Metallurgical properties and geometrical characteristics of the broken rod complied with the original design. The fractographic features were typical of fatigue fracture. Both a fracture mechanics approach and a conventional approach were employed to study the fatigue process. The real rate of crack growth was determined through scanning electron microscopy measurements. It is concluded that the failure was due to corrosion fatigue. An improved design is suggested.
1. Introduction Even though engineers and technicians are becoming progressively more aware regarding the role of fluctuating stresses in sudden and unpredicted fractures, fatigue processes remain a common failure mode in the case studies arriving at the offices of forensic engineers [1]. In determining the root cause of the failure, improper design along with service condition abuse are usually uncovered. Both of these causes could easily have been precluded by following the recommendations that should accompany the failure report. Nevertheless, hidden facts can sometimes ruin new designs. This is the case of cooperative failure mechanisms such as corrosion fatigue. It is sometimes difficult to distinguish between plain fatigue processes and corrosion-fatigue processes in the case when only visual or even SEM observations are carried out on the assessment of broken parts. It is well-known that a previous corrosion process can accelerate crack initiation thereby lowering the fatigue life of a component [2,3]. However, in addition, the crack propagation rate can increase by one or two orders of magnitude when the crack front is exposed to corrosion on every opening cycle [4]. Additional protective measures must be included in the final recommendations just in case corrosion fatigue is present. In this paper, a process for suspected corrosion fatigue is studied, where the effect of corrosion on predicted crack-growth rate is assessed through the measurement of the spacing of striation markings and simple calculations based on the load history of the components and the Paris fatigue crack-growth approach [5]. 2. Background A steel component, belonging to a harbour crane, broke after nearly 10,000 h of discontinuous service. This component was one of
⁎
Corresponding author. E-mail address: [email protected] (E. Díaz).
https://doi.org/10.1016/j.engfailanal.2019.07.022 Received 28 January 2019; Received in revised form 4 July 2019; Accepted 5 July 2019 Available online 09 July 2019 1350-6307/ © 2019 Elsevier Ltd. All rights reserved.
Engineering Failure Analysis 105 (2019) 828–836
E. Díaz, et al.
Fig. 1. A view of the ladle carrier showing the four anchorage tension rods.
a group of four parallel rods designed to work as anchoring and tensioning elements for traction ropes of the ladle-carrying car (Fig. 1). One half of the failed element was square in section, 75 × 75 mm; the other half was a square-threaded 70 mm-diameter rod (Fig. 2). The rod was specified to be made of normalised F1120 steel, in accordance with the Spanish UNE 36-011-075 standard. This steel is similar in composition and properties to SAE-AISI 1029. 3. Results and discussion 3.1. Visual inspection The fracture occurred at the beginning of the threaded region, far from the nut. The fracture origin was located at the root of the second thread lead, near the section change between the square and round parts of the rod (Fig. 3). Cracks were also detected at the root of the first lead (Fig. 4). The appearance of the fractured surfaces was characteristic of fatigue failure. Beach marks could be observed extending across nearly 90% of the surface. The remaining 10% (262 mm2) displayed the typical catastrophic fracture appearance. The classic interpretation of the appearance of a fatigue fracture [6] points towards a low-nominal-stress, mild-stress-concentration, tensiontension fatigue action. The clamshell markings become further apart, larger, and more distinct as the crack propagates (Fig. 5), and hence offer a clear indication of the location of the origin of the fracture. The fractured surfaces show signs of oxidation. Oxidation marks are present at irregular intervals. Oxidised zones are often coincident with crack arrest lines. This indicates the corrosive action of moisture and of a saline environment on the crack tip. Nevertheless, these arrest line marks are common in fatigue-fracture surfaces despite the environment corrosiveness, but they do depend on the periods of inactivity of the component [7]. 3.2. Chemical analysis and metallography Chemical analysis showed that the rod was produced from plain carbon steel of the following composition: 0.27C, 0.75Mn, 0.18Si, 0.011S, 0.023P. The metallographic structure was typical of hot-rolled steel, probably in the normalised temper. Bands of ferrite and pearlite could be observed in the direction of the working. Ferrite grain size was ASTM 8, that is, a grain diameter of 20 μm. Both chemical composition and microstructure conform to the requirements of the specified material. Microscopic examination also showed that the crack present at the first thread lead (Fig. 4) is mainly trans-granular and exhibits a minor amount of branching (Fig. 6). Secondary cracks on the fractured surface are also observed through scanning electron microscopy, as indicated below. Energy dispersive X-ray analysis detected chlorides in the corrosion products. Slight branching or secondary cracks are often associated with corrosion fatigue of carbon steel [8,9]. Cracks due to stress corrosion are normally heavily branched in contrast to environment-assisted fatigue cracking [10].
Fig. 2. Sketch of the rod. Dimensions given in mm. 829
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Fig. 3. Overall view of the broken rod.
Fig. 4. Longitudinal section of the broken rod (threaded round part) showing a 10 mm crack at the root of the first thread lead. Fracture occurred beginning at the second thread lead (right-hand-side of figure).
Fig. 5. Fractured surface showing beach marks and the final-fracture zone. The origin of the fracture is indicated by an arrow.
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Fig. 6. Micrograph exhibiting a crack, mainly transgranular, with a minor amount of branching. Etched with 2% nital.
3.3. Mechanical tests Steel hardness is 75.5 Rockwell B, equivalent to 138 Brinell. This hardness is in compliance with the specifications of the UNE standard. The ultimate tensile strength, σu, of this steel can be estimated [11] as 450 MPa. This value is also in compliance with the referred standard, which, for the diameter of the broken rod, specifies σu to be between 420 and 620 MPa. 3.4. Microfractography Examination of the fractured surface through scanning electron microscopy confirms that failure was caused by fatigue. Fig. 7, which corresponds to the region of crack growth, shows the characteristic striations of fatigue. A detailed examination of this region reveals secondary cracks and that the fracture, though mainly transgranular, is partly intercrystalline. The widths of the striations were measured at different points on the fracture surface. The measured values of the crack-length extension rate per cycle, da/dN, as a function of the distance to the crack origin, a, are plotted in Fig. 8. After a period of nearly
Fig. 7. Scanning electron microscopy fractograph showing fatigue striations. 831
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Fig. 8. Crack-growth rate as a function of crack length. Actual values measured through scanning electron microscopy.
constant growth rate, the crack propagates faster as it progresses. It must be stressed that the abscissa axis of Fig. 8 cannot be related to a timeline fracture progress. Indeed, it was learned from interviews with technicians that the crane used to unload ships twice a month, but experienced prolonged periods of inactivity. On the other hand, the zone corresponding to the last stage of sudden fracture exhibits a mixed ductile-brittle appearance. Both dimples and planar regions are detected. 3.5. Roughness measurements Surface roughness at the root of the threads has a mean value of 21.4 μm. This roughness corresponds approximately to an ISO N11 finishing. This is a coarse finishing. Surface roughness can be appreciated by the naked eye. Nevertheless, this is the degree of surface roughness specified by design. It is well-known that surface finishing plays a major role in how surface fatigue cracks nucleate [12]. 3.6. Non-destructive testing The critical crack depth, a0, that can trigger fatigue growth (see paragraph on fracture mechanics modelling) is estimated to be 1.6 mm. The probability of detecting such a crack is over 60% [13]. Non-destructive testing by magnetic particles detects no cracks in the three non-failed rods. The question remains why the failed rod presented larger cracks. This was probably caused by an uneven distribution of stress between the four rods, as explained in the following paragraph. 4. Analysis of fatigue stresses and fatigue life prediction 4.1. Stress state and real-life evaluation The stress state was calculated from the root mean square (rms) power diagram of the ladle-carrier gearbox, and from the geometry of the traction-rope catenary at rest. The failed rod has been considered to withstand a third of the force exerted by the electric motor, instead of a quarter of said force. To support this, the following facts have been taken into account: (a) only one out of four rods has broken; (b) no metallurgical defect has been detected in the failed part; (c) no cracks were observed in the unbroken rods; and (d) stress equilibria between the four ropes is carried out by watching the rope catenary with the naked eye. Stresses in the rod can be computed as the additive effect of two loading patterns: on one hand, forces applied during the emptyladle movement; and on the other hand, as the charged-ladle transfers. These two cycles were integrated by square mean treatment [14] into one sinusoidal-equivalent stress diagram. The difference between maximum (σmax) and minimum (σmin) tensile stresses in the cycle, Δσ, was calculated to be 27.3 MPa. This value equals twice the stress amplitude, σa (≡S). Average value (root mean square) of cycle stresses, σm, was estimated as 23.8 MPa. Stress ratio R (=σmin/σmax) resulted as 0.27. Load cycle frequency was 0.04 Hz. On the other hand, the number of working cycles, N, of the crane, during its 10 years of service, can be estimated, according to crane files, as N = 600,000. The computed value was obtained based on the total amount of material handled by the crane, and on ladle capacity. 4.2. Fatigue-life prediction based on calculated S–N curves In order to check the fatigue life of the rod, a Goodman diagram was constructed to account for the fluctuating (σa) plus mean832
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Fig. 9. Goodman diagram for the rod. Computed stress state is shown.
stress (σm) load profile. Fig. 9 shows the Goodman diagram drawn from data of the S–N diagram in Appendix A. The stress conditions for the rod (σa = 13.7 MPa and σm = 23.8 MPa) lie well within the infinite-life zone of the diagram. Safety factors are 1.5 for infinite life and 1.7 for a life of 600,000 cycles, that is, the rod should not have failed. Disagreement between theory and practice may come from: (a) Values of stresses, or fatigue factors (surface roughness, stress concentration, environment, etc.) have been under-estimated in the calculations of Appendix A. In this case, the remaining rods would also probably fail. (b) There is no fatigue limit for corrosion fatigue. Therefore, it is only a question of time for the failure of the remaining rods. (c) An undetected metallurgical or service fault has affected this rod. As a result, the remaining rods are of safe design. 4.3. Fatigue-fracture prediction based on fracture mechanics modelling Fatigue-life prediction based on Fracture Mechanics (Appendix B) indicates that the number of cycles necessary for crack growth, Nf, from the initial value of 1.5 mm to the final value of 57.2 mm, is 76,000 cycles. This number of cycles corresponds to 15 months of service life of the crane. The difference between real (600,000 cycles) and calculated service life is clearly spent in the nucleation of the first fatigue-crack from pits or other faults at the thread root. This crack propagated rapidly during the last 15 months of service. This usually occurs in a relatively brittle material, or in tough materials such as this steel, by a corrosion-fatigue process. In Fig. 10, in addition to the fatigue behaviour of the steel under study, the behaviour [14] of a low-carbon steel (0.18C, 0.75Mn) in air and an API X-65 steel (0.24C, 1.35Mn, > 0.02 V, and/or > 0.005Nb) in salt water, are displayed. Experimental crack-growth rate (this case history) is very high in comparison with crack propagation in air (low-carbon steel). Crack speed (this case history) is nearly as high as crack propagation rate in salt water (API X-65). Corrosive media may increase growth rate by a factor of 102–103, if the load cycle frequency is sufficiently low (lower than approximately 0.2 Hz) to permit corrosion at the crack tip between successive jumps [14]. Cycle frequency in the present case is only 0.04 Hz. This low cycle frequency, the marine environment, and the short fatigue life of the failed rod lead to the conclusion that the fracture occurred by corrosion fatigue. Furthermore, the chlorides inside cracks and the crack morphology also support this conclusion. 5. Considerations in design The screw design was inappropriate since it favours stress intensification at the first thread, as shown in Fig. 11a [15]. A large crack was observed at only this location (Fig. 4). The fracture, nevertheless, began at the second thread. With respect to screw design, in order to reduce stress concentration, it is recommended that a thread should run out gradually, as indicated in Fig. 11b. The runout angle θ should be made as gradual as possible and not > 15° [12,15]. In addition, the radius at the thread root is very acute; the measured values lie between 60 and 80 μm. This configuration produces a serious stress-raising effect. Ritchie [16] has demonstrated the harmful effect of an acute angle between the root and thread flank. The standard American thread (acute angle) has a stress concentration factor approximately 1.5 higher than the 833
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Fig. 10. Crack-growth rate versus stress-intensity factor range, for low-carbon steel in air, API X 65 steel in salt water (after [14]), and the present case history.
Fig. 11. (a) Stress concentration in a threaded rod. (b) Recommended machining to reduce the stress-raising effect.
Whitworth thread (rounded angle). Unfortunately, the square thread is not standardised [17], but for a trapezoidal thread of the same dimensions, with similar load-carrying capacity, a root radius of 0.15 mm is specified in ISO 2904. This radius is seven times higher than that of the failed rod. In general, trapezoidal threads should be preferred to square or rectangular threads [18]. These considerations regarding screw geometry and thread shape and the aforementioned coarse finishing, show that there is clearly room for improvement in the design. 6. Conclusions and corrective measures Although the rod failed in air and under cycle stresses, the fracture was not exclusively due to mechanical fatigue: the presence of a marine atmosphere and a low cycle frequency led to a failure by corrosion fatigue. The poor design, its coarse surface roughness, and the marine atmosphere all favoured fracture. A new design of the broken element is recommended. Root threads should have a generous radius (0.5 mm), be machined with diminishing flank height, and possess a fine finishing (surface roughness ISO N6/N7). In addition, steel elements should be protected against marine atmospheric corrosion by surface coatings or anti-rust grease. On the other hand, the non-failed rods should be inspected yearly by applying NDT testing to detect the presence of cracks.
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Appendix A The S–N curve for this steel was evaluated. This was carried out using a well-established approach [19]. Two (S–N) points are defined as follows:
• for 10
3
cycles, the fatigue or endurance strength, σn, is:
σn = σu / Kf
´
where K'f is the stress-concentration factor for limited life, and σu, is the ultimate tensile strength.
• for 10
6
cycles and beyond, the fatigue limit, σ'n, is:
σn = σn Kf /(Cs CL CD) ´
where, CS, CL, CD, and Kf, are factors defining the effect of surface condition, load mode, dimensions, and stress concentration on fatigue conditions, respectively. In addition, a complementary environmental factor Cen [20] could also be introduced. The surface factor (CS), when considering a machined surface with Ra = 21.4 μm and σu = 450 MPa, is 0.8 [19,21]. The load factor (CL) for the stress conditions of this case is 0.9 [19,22]. A rod with an outer diameter of 3 in. (nearest to the 62 mm real diameter), subjected to axial loads, is affected by a dimension factor (CD) of 0.85 [19,22]. The values of Kf and K'f are derived from the static stress concentration factor, Kt. The value of Kt for a square thread is difficult to ascertain from Neuber classic formulation. Two hypotheses have, therefore, been considered: (i) a 4 mm-deep notch with root radius of 80 μm (i.e., equal to the real value); and (ii) a 4 mm-deep notch with a root radius of 1 mm (minimum value that complies with theoretical requirements [23] for the forthcoming calculations of Kf). The values of Kt are: (i) 13.1 and (ii) 4.1 [23]. The stress concentration factor for fatigue loading is usually lower than that for static stress. In order to obtain the Kf value, the notch sensibility factor for fatigue, q, was previously calculated. In agreement with Peterson's model [23], q has a value, depending on the root radius of either 80 μ or 1 mm, of 0.2 or 0.76, respectively. This, in turn, gives a Kf value of 2.9, regardless of the notch radius considered. On the other hand, a stress concentration factor for limited fatigue life, K'f = 2.27, can be obtained from the ultimate tensile strength and the stress concentration factor for fatigue loading Kf [19]. Finally, the environmental factor, Cen, remains unsatisfactorily defined in the literature. Nevertheless, for similar steels to that of the failed steel, in seawater, a decrease in the fatigue limit by a factor of 0.5 has been reported [24]. Calculations according to the previous paragraphs result in an endurance strength for 103 cycles of 149 MPa, with a fatigue limit of 47.5 MPa for dry atmosphere, and 23.7 MPa for a marine environment. Fig. 12, plotted as a log-log diagram, shows the hypothetical SeN behaviour of the steel, at the thread root. In fact, there is no true fatigue limit in corrosion fatigue. Appendix B The crack propagation period, expressed as number of cycles to failure during stage II of fatigue, is to be estimated from the Paris equation:
da = C (ΔK) n dN where the values of C and n depend on microstructure (albeit only slightly), the average applied stress, the environment, and on specimen thickness [22]. ΔK, represents the range of stress intensity factor; this range can be obtained from:
ΔK = YΔσ πa
Fig. 12. Theoretical S–N curve for the rod under study. 835
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Factor Y, for threaded rods, at the centre of the crack front, can be obtained, according to Toribio et al. [25], from the expression:
a a 2 Ym = 0.820 − 0.111 ⎛ ⎞ + 1.589 ⎛ ⎞ ⎝d⎠ ⎝d⎠ where d is the diameter of the rod. C and n are calculated from the experimental values of crack-growth rate measured through scanning electron microscopy (Fig. 8). The values of da/dN versus ΔK are plotted in Fig. 10. Two regimes of crack-growth rate can be observed. Up to ΔK = 9.5 MPa·m½, corresponding to a crack size a = 20.1 mm, the propagation speed is nearly independent of ΔK (n = 0.094), and C is equal to 3.9E-07. For cracks larger than 20.1 mm, n = 0.87 and C = 6.5E-08. Both crack-growth regimes (Fig. 10) were taken into account to integrate the Paris equation. The initial crack length, a0, was taken as equal to 1.5 mm, as calculated from a stress-intensity threshold value, ΔKth, equal to 1.86 MPa·m½. This value has been obtained from various experimental values [26] and from theoretical considerations [14]. The a0 value is also in agreement with scanning electron microscope experimental observations. The experimental value of the final crack length (before sudden overload fracture), af, is 57.2 mm. The integration provides a value of Nf = 76,000 cycles necessary for crack growth from 1.5 mm to 57.2 mm. This number of cycles corresponds to 15 months of service life of the crane. The difference between real (600,000 cycles) and calculated service life is clearly spent in the nucleation of the initial fatigue-crack from pits or other faults at the thread root. This initial crack propagated rapidly during the last 15 months of service.
References [1] L. Soria, J. Dominguez y, J.M. Gallardo, ¿Por qué siguen produciéndose fallos por fatiga? Descripción de 2 casos paradigmáticos, Anales de Mecánica de la Fractura 29–1 (2012) 707–712. [2] Adrien Laurino, Eric Andrieu, Jean-Paul Harouard, Grégory Odemer, Jean-Claude Salabura, et al., Effect of corrosion on the fatigue life and fracture mechanisms of 6101 aluminum alloy wires for car manufacturing applications, Mater. Des. Elsevier 53 (2014) 236–249. [3] Dr.-Ing. Andreas Neidel, Susanne Riesenbeck, Pitting Corrosion induced fatigue fracture on a gas turbine compressor blade, Pract. Metallogr. 49 (1) (2012) 35–48. [4] R. Akid, I.M. Dmytrakh, J. Gonzalez-Sanchez, Fatigue damage accumulation: aspects of environmental interaction, Mater. Sci. 42 (1) (2006). [5] P.C. Paris, F. Erdogen, A critical analysis of crack propagation laws, J. Basic Eng. 85 (1963) 528–533. [6] Russel A. Lund, Fatigue fracture appearances, Metals Handbook, 10th ed., vol. 11: Failure Analysis Prevention, American Society for Metals, Materials Park, OH, 1990, p. 631. [7] Stephen D. Antolovich, Ashok Saxena, Fatigue failures, Metals Handbook, 9th ed., vol.11: Failure Analysis Prevention, American Society for Metals, Materials Park, OH, 1986, p. 104. [8] L. Engel, H. Klingele, An Atlas of Metal Damage, Wolfe Pub. Ltd., London, 1981, pp. 114–115. [9] Metals Handbook, 9th ed., vol.13: Corrosion, American Society for Metals, Metals Park, OH, 1987, p. 142. [10] G. Henry, D. Horstmann, De Ferri Metallographia, V. Fractography and Microfractography, Verlag Stahleisen, Düsseldorf, 1979, pp. 160–163. [11] Metals Handbook, 10th ed., vol.1: Properties and Selection: Irons, Steels and High-Performance Alloys, American Society for Metals, Materials Park, OH, 1990, p. 237. [12] J.H. Bickford, An Introduction to the Design and Behaviour of Bolted Joints, Marcel Dekker, New York, 1990, pp. 485–492. [13] F. Ramírez, et al., Ensayos no Destructivos, INTA, Madrid, 1977 pp. 927–629. [14] W.W. Gerberich, R.H. van Stone, A.W. Gunderson, Fracture properties of Carbon and Alloy Steels, in: J.E. Campbell, et al. (Ed.), Application of Fracture Mechanics for Selection of Metallic Structural Materials, American Society for Metals, Metals Park, OH, 1982, pp. 41–103. [15] G.A. Cottell, Some common stress raisers in engineering parts, in: F.R. Hutchings, P.M. Unterweiser (Eds.), Failure Analysis: The British Engine Technical Reports, American Society for Metals, Metals Park, OH, 1981, pp. 99–120. [16] J.G. Ritchie, Fatigue behaviour of bolted joints, Proc. Symposium on the Failure of Metals by Fatigue, 1946, p. 260 Melbourne. [17] J.E. Schigley, C.R. Mischke (Eds.), Mechanical Designers' Workbook: Gearing, Mc-Graw Hill, New York, 1986, p. 3. [18] A. Ferraresi, Disegno di Costruzioni Meccaniche e Studi di Fabbricazione, vol. I, Hoepli, Milano, 1991, pp. 108–109. [19] C. Juvinal, Stress, Strain and Strength, McGraw-Hill, New York, 1967. [20] S. Ranguenath, J.N. Kass, J.D. Heald, Fatigue Behaviour of Carbon Steel Components in High-Temperature Water Environments, in: C. Amzallag, et al. (Ed.), Low-Cycle Fatigue and Life Prediction, ASTM, Philadelphia, 1982, pp. 436–459. [21] R.L. Norton, Machine Design, An Integrated Aproach, Prentice-Hall, Upper Saddle River, 1996. [22] R.M. Caddell, Deformation and Fracture of Solids, Prentice-Hall, Englewood, 1980, p. 278. [23] R.E. Peterson, Stress Concentration Factors, John Willey & Sons, New York, 1974. [24] M. Kawahara, et al., Corrosion fatigue crack initiation of carbon steels in seawater, in: R.P. Wei, R.P. Gangloff (Eds.), Basic Questions in Fatigue, vol. II, ASTM, Philadelphia, 1988, pp. 145–163. [25] J. Toribio, et al., Stress intensity factor solutions for a cracked bolt under tension, bending and residual stress loading, Eng. Fract. Mech. 39 (1991) 359–371. [26] D. Taylor, A Compendium of Fatigue Thresholds and Growth Rates, EMAS, 1985.
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Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Post-failure life evaluation: A corrosion-fatigue case history ⁎
E. Díaza, , L. Soriab, J.M. Gallardob
T
a
Asociación de Investigación y Cooperación Industrial de Andalucía, Av. Camino de los Descubrimientos s/n, 41092 Seville, Spain Department of Engineering and Materials Science and Transportation, University of Seville, Av. Camino de los Descubrimientos s/n, 41092 Seville, Spain
b
A R T IC LE I N F O
ABS TRA CT
Keywords: Steel rod Corrosion-fatigue Coastal environment
An AISI 1029 steel threaded rod belonging to a harbour crane fractured after ten years of service. Failure analysis, including metallography and both destructive and non-destructive testing, was carried out. Metallurgical properties and geometrical characteristics of the broken rod complied with the original design. The fractographic features were typical of fatigue fracture. Both a fracture mechanics approach and a conventional approach were employed to study the fatigue process. The real rate of crack growth was determined through scanning electron microscopy measurements. It is concluded that the failure was due to corrosion fatigue. An improved design is suggested.
1. Introduction Even though engineers and technicians are becoming progressively more aware regarding the role of fluctuating stresses in sudden and unpredicted fractures, fatigue processes remain a common failure mode in the case studies arriving at the offices of forensic engineers [1]. In determining the root cause of the failure, improper design along with service condition abuse are usually uncovered. Both of these causes could easily have been precluded by following the recommendations that should accompany the failure report. Nevertheless, hidden facts can sometimes ruin new designs. This is the case of cooperative failure mechanisms such as corrosion fatigue. It is sometimes difficult to distinguish between plain fatigue processes and corrosion-fatigue processes in the case when only visual or even SEM observations are carried out on the assessment of broken parts. It is well-known that a previous corrosion process can accelerate crack initiation thereby lowering the fatigue life of a component [2,3]. However, in addition, the crack propagation rate can increase by one or two orders of magnitude when the crack front is exposed to corrosion on every opening cycle [4]. Additional protective measures must be included in the final recommendations just in case corrosion fatigue is present. In this paper, a process for suspected corrosion fatigue is studied, where the effect of corrosion on predicted crack-growth rate is assessed through the measurement of the spacing of striation markings and simple calculations based on the load history of the components and the Paris fatigue crack-growth approach [5]. 2. Background A steel component, belonging to a harbour crane, broke after nearly 10,000 h of discontinuous service. This component was one of
⁎
Corresponding author. E-mail address: [email protected] (E. Díaz).
https://doi.org/10.1016/j.engfailanal.2019.07.022 Received 28 January 2019; Received in revised form 4 July 2019; Accepted 5 July 2019 Available online 09 July 2019 1350-6307/ © 2019 Elsevier Ltd. All rights reserved.
Engineering Failure Analysis 105 (2019) 828–836
E. Díaz, et al.
Fig. 1. A view of the ladle carrier showing the four anchorage tension rods.
a group of four parallel rods designed to work as anchoring and tensioning elements for traction ropes of the ladle-carrying car (Fig. 1). One half of the failed element was square in section, 75 × 75 mm; the other half was a square-threaded 70 mm-diameter rod (Fig. 2). The rod was specified to be made of normalised F1120 steel, in accordance with the Spanish UNE 36-011-075 standard. This steel is similar in composition and properties to SAE-AISI 1029. 3. Results and discussion 3.1. Visual inspection The fracture occurred at the beginning of the threaded region, far from the nut. The fracture origin was located at the root of the second thread lead, near the section change between the square and round parts of the rod (Fig. 3). Cracks were also detected at the root of the first lead (Fig. 4). The appearance of the fractured surfaces was characteristic of fatigue failure. Beach marks could be observed extending across nearly 90% of the surface. The remaining 10% (262 mm2) displayed the typical catastrophic fracture appearance. The classic interpretation of the appearance of a fatigue fracture [6] points towards a low-nominal-stress, mild-stress-concentration, tensiontension fatigue action. The clamshell markings become further apart, larger, and more distinct as the crack propagates (Fig. 5), and hence offer a clear indication of the location of the origin of the fracture. The fractured surfaces show signs of oxidation. Oxidation marks are present at irregular intervals. Oxidised zones are often coincident with crack arrest lines. This indicates the corrosive action of moisture and of a saline environment on the crack tip. Nevertheless, these arrest line marks are common in fatigue-fracture surfaces despite the environment corrosiveness, but they do depend on the periods of inactivity of the component [7]. 3.2. Chemical analysis and metallography Chemical analysis showed that the rod was produced from plain carbon steel of the following composition: 0.27C, 0.75Mn, 0.18Si, 0.011S, 0.023P. The metallographic structure was typical of hot-rolled steel, probably in the normalised temper. Bands of ferrite and pearlite could be observed in the direction of the working. Ferrite grain size was ASTM 8, that is, a grain diameter of 20 μm. Both chemical composition and microstructure conform to the requirements of the specified material. Microscopic examination also showed that the crack present at the first thread lead (Fig. 4) is mainly trans-granular and exhibits a minor amount of branching (Fig. 6). Secondary cracks on the fractured surface are also observed through scanning electron microscopy, as indicated below. Energy dispersive X-ray analysis detected chlorides in the corrosion products. Slight branching or secondary cracks are often associated with corrosion fatigue of carbon steel [8,9]. Cracks due to stress corrosion are normally heavily branched in contrast to environment-assisted fatigue cracking [10].
Fig. 2. Sketch of the rod. Dimensions given in mm. 829
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Fig. 3. Overall view of the broken rod.
Fig. 4. Longitudinal section of the broken rod (threaded round part) showing a 10 mm crack at the root of the first thread lead. Fracture occurred beginning at the second thread lead (right-hand-side of figure).
Fig. 5. Fractured surface showing beach marks and the final-fracture zone. The origin of the fracture is indicated by an arrow.
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Fig. 6. Micrograph exhibiting a crack, mainly transgranular, with a minor amount of branching. Etched with 2% nital.
3.3. Mechanical tests Steel hardness is 75.5 Rockwell B, equivalent to 138 Brinell. This hardness is in compliance with the specifications of the UNE standard. The ultimate tensile strength, σu, of this steel can be estimated [11] as 450 MPa. This value is also in compliance with the referred standard, which, for the diameter of the broken rod, specifies σu to be between 420 and 620 MPa. 3.4. Microfractography Examination of the fractured surface through scanning electron microscopy confirms that failure was caused by fatigue. Fig. 7, which corresponds to the region of crack growth, shows the characteristic striations of fatigue. A detailed examination of this region reveals secondary cracks and that the fracture, though mainly transgranular, is partly intercrystalline. The widths of the striations were measured at different points on the fracture surface. The measured values of the crack-length extension rate per cycle, da/dN, as a function of the distance to the crack origin, a, are plotted in Fig. 8. After a period of nearly
Fig. 7. Scanning electron microscopy fractograph showing fatigue striations. 831
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Fig. 8. Crack-growth rate as a function of crack length. Actual values measured through scanning electron microscopy.
constant growth rate, the crack propagates faster as it progresses. It must be stressed that the abscissa axis of Fig. 8 cannot be related to a timeline fracture progress. Indeed, it was learned from interviews with technicians that the crane used to unload ships twice a month, but experienced prolonged periods of inactivity. On the other hand, the zone corresponding to the last stage of sudden fracture exhibits a mixed ductile-brittle appearance. Both dimples and planar regions are detected. 3.5. Roughness measurements Surface roughness at the root of the threads has a mean value of 21.4 μm. This roughness corresponds approximately to an ISO N11 finishing. This is a coarse finishing. Surface roughness can be appreciated by the naked eye. Nevertheless, this is the degree of surface roughness specified by design. It is well-known that surface finishing plays a major role in how surface fatigue cracks nucleate [12]. 3.6. Non-destructive testing The critical crack depth, a0, that can trigger fatigue growth (see paragraph on fracture mechanics modelling) is estimated to be 1.6 mm. The probability of detecting such a crack is over 60% [13]. Non-destructive testing by magnetic particles detects no cracks in the three non-failed rods. The question remains why the failed rod presented larger cracks. This was probably caused by an uneven distribution of stress between the four rods, as explained in the following paragraph. 4. Analysis of fatigue stresses and fatigue life prediction 4.1. Stress state and real-life evaluation The stress state was calculated from the root mean square (rms) power diagram of the ladle-carrier gearbox, and from the geometry of the traction-rope catenary at rest. The failed rod has been considered to withstand a third of the force exerted by the electric motor, instead of a quarter of said force. To support this, the following facts have been taken into account: (a) only one out of four rods has broken; (b) no metallurgical defect has been detected in the failed part; (c) no cracks were observed in the unbroken rods; and (d) stress equilibria between the four ropes is carried out by watching the rope catenary with the naked eye. Stresses in the rod can be computed as the additive effect of two loading patterns: on one hand, forces applied during the emptyladle movement; and on the other hand, as the charged-ladle transfers. These two cycles were integrated by square mean treatment [14] into one sinusoidal-equivalent stress diagram. The difference between maximum (σmax) and minimum (σmin) tensile stresses in the cycle, Δσ, was calculated to be 27.3 MPa. This value equals twice the stress amplitude, σa (≡S). Average value (root mean square) of cycle stresses, σm, was estimated as 23.8 MPa. Stress ratio R (=σmin/σmax) resulted as 0.27. Load cycle frequency was 0.04 Hz. On the other hand, the number of working cycles, N, of the crane, during its 10 years of service, can be estimated, according to crane files, as N = 600,000. The computed value was obtained based on the total amount of material handled by the crane, and on ladle capacity. 4.2. Fatigue-life prediction based on calculated S–N curves In order to check the fatigue life of the rod, a Goodman diagram was constructed to account for the fluctuating (σa) plus mean832
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Fig. 9. Goodman diagram for the rod. Computed stress state is shown.
stress (σm) load profile. Fig. 9 shows the Goodman diagram drawn from data of the S–N diagram in Appendix A. The stress conditions for the rod (σa = 13.7 MPa and σm = 23.8 MPa) lie well within the infinite-life zone of the diagram. Safety factors are 1.5 for infinite life and 1.7 for a life of 600,000 cycles, that is, the rod should not have failed. Disagreement between theory and practice may come from: (a) Values of stresses, or fatigue factors (surface roughness, stress concentration, environment, etc.) have been under-estimated in the calculations of Appendix A. In this case, the remaining rods would also probably fail. (b) There is no fatigue limit for corrosion fatigue. Therefore, it is only a question of time for the failure of the remaining rods. (c) An undetected metallurgical or service fault has affected this rod. As a result, the remaining rods are of safe design. 4.3. Fatigue-fracture prediction based on fracture mechanics modelling Fatigue-life prediction based on Fracture Mechanics (Appendix B) indicates that the number of cycles necessary for crack growth, Nf, from the initial value of 1.5 mm to the final value of 57.2 mm, is 76,000 cycles. This number of cycles corresponds to 15 months of service life of the crane. The difference between real (600,000 cycles) and calculated service life is clearly spent in the nucleation of the first fatigue-crack from pits or other faults at the thread root. This crack propagated rapidly during the last 15 months of service. This usually occurs in a relatively brittle material, or in tough materials such as this steel, by a corrosion-fatigue process. In Fig. 10, in addition to the fatigue behaviour of the steel under study, the behaviour [14] of a low-carbon steel (0.18C, 0.75Mn) in air and an API X-65 steel (0.24C, 1.35Mn, > 0.02 V, and/or > 0.005Nb) in salt water, are displayed. Experimental crack-growth rate (this case history) is very high in comparison with crack propagation in air (low-carbon steel). Crack speed (this case history) is nearly as high as crack propagation rate in salt water (API X-65). Corrosive media may increase growth rate by a factor of 102–103, if the load cycle frequency is sufficiently low (lower than approximately 0.2 Hz) to permit corrosion at the crack tip between successive jumps [14]. Cycle frequency in the present case is only 0.04 Hz. This low cycle frequency, the marine environment, and the short fatigue life of the failed rod lead to the conclusion that the fracture occurred by corrosion fatigue. Furthermore, the chlorides inside cracks and the crack morphology also support this conclusion. 5. Considerations in design The screw design was inappropriate since it favours stress intensification at the first thread, as shown in Fig. 11a [15]. A large crack was observed at only this location (Fig. 4). The fracture, nevertheless, began at the second thread. With respect to screw design, in order to reduce stress concentration, it is recommended that a thread should run out gradually, as indicated in Fig. 11b. The runout angle θ should be made as gradual as possible and not > 15° [12,15]. In addition, the radius at the thread root is very acute; the measured values lie between 60 and 80 μm. This configuration produces a serious stress-raising effect. Ritchie [16] has demonstrated the harmful effect of an acute angle between the root and thread flank. The standard American thread (acute angle) has a stress concentration factor approximately 1.5 higher than the 833
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Fig. 10. Crack-growth rate versus stress-intensity factor range, for low-carbon steel in air, API X 65 steel in salt water (after [14]), and the present case history.
Fig. 11. (a) Stress concentration in a threaded rod. (b) Recommended machining to reduce the stress-raising effect.
Whitworth thread (rounded angle). Unfortunately, the square thread is not standardised [17], but for a trapezoidal thread of the same dimensions, with similar load-carrying capacity, a root radius of 0.15 mm is specified in ISO 2904. This radius is seven times higher than that of the failed rod. In general, trapezoidal threads should be preferred to square or rectangular threads [18]. These considerations regarding screw geometry and thread shape and the aforementioned coarse finishing, show that there is clearly room for improvement in the design. 6. Conclusions and corrective measures Although the rod failed in air and under cycle stresses, the fracture was not exclusively due to mechanical fatigue: the presence of a marine atmosphere and a low cycle frequency led to a failure by corrosion fatigue. The poor design, its coarse surface roughness, and the marine atmosphere all favoured fracture. A new design of the broken element is recommended. Root threads should have a generous radius (0.5 mm), be machined with diminishing flank height, and possess a fine finishing (surface roughness ISO N6/N7). In addition, steel elements should be protected against marine atmospheric corrosion by surface coatings or anti-rust grease. On the other hand, the non-failed rods should be inspected yearly by applying NDT testing to detect the presence of cracks.
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Appendix A The S–N curve for this steel was evaluated. This was carried out using a well-established approach [19]. Two (S–N) points are defined as follows:
• for 10
3
cycles, the fatigue or endurance strength, σn, is:
σn = σu / Kf
´
where K'f is the stress-concentration factor for limited life, and σu, is the ultimate tensile strength.
• for 10
6
cycles and beyond, the fatigue limit, σ'n, is:
σn = σn Kf /(Cs CL CD) ´
where, CS, CL, CD, and Kf, are factors defining the effect of surface condition, load mode, dimensions, and stress concentration on fatigue conditions, respectively. In addition, a complementary environmental factor Cen [20] could also be introduced. The surface factor (CS), when considering a machined surface with Ra = 21.4 μm and σu = 450 MPa, is 0.8 [19,21]. The load factor (CL) for the stress conditions of this case is 0.9 [19,22]. A rod with an outer diameter of 3 in. (nearest to the 62 mm real diameter), subjected to axial loads, is affected by a dimension factor (CD) of 0.85 [19,22]. The values of Kf and K'f are derived from the static stress concentration factor, Kt. The value of Kt for a square thread is difficult to ascertain from Neuber classic formulation. Two hypotheses have, therefore, been considered: (i) a 4 mm-deep notch with root radius of 80 μm (i.e., equal to the real value); and (ii) a 4 mm-deep notch with a root radius of 1 mm (minimum value that complies with theoretical requirements [23] for the forthcoming calculations of Kf). The values of Kt are: (i) 13.1 and (ii) 4.1 [23]. The stress concentration factor for fatigue loading is usually lower than that for static stress. In order to obtain the Kf value, the notch sensibility factor for fatigue, q, was previously calculated. In agreement with Peterson's model [23], q has a value, depending on the root radius of either 80 μ or 1 mm, of 0.2 or 0.76, respectively. This, in turn, gives a Kf value of 2.9, regardless of the notch radius considered. On the other hand, a stress concentration factor for limited fatigue life, K'f = 2.27, can be obtained from the ultimate tensile strength and the stress concentration factor for fatigue loading Kf [19]. Finally, the environmental factor, Cen, remains unsatisfactorily defined in the literature. Nevertheless, for similar steels to that of the failed steel, in seawater, a decrease in the fatigue limit by a factor of 0.5 has been reported [24]. Calculations according to the previous paragraphs result in an endurance strength for 103 cycles of 149 MPa, with a fatigue limit of 47.5 MPa for dry atmosphere, and 23.7 MPa for a marine environment. Fig. 12, plotted as a log-log diagram, shows the hypothetical SeN behaviour of the steel, at the thread root. In fact, there is no true fatigue limit in corrosion fatigue. Appendix B The crack propagation period, expressed as number of cycles to failure during stage II of fatigue, is to be estimated from the Paris equation:
da = C (ΔK) n dN where the values of C and n depend on microstructure (albeit only slightly), the average applied stress, the environment, and on specimen thickness [22]. ΔK, represents the range of stress intensity factor; this range can be obtained from:
ΔK = YΔσ πa
Fig. 12. Theoretical S–N curve for the rod under study. 835
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Factor Y, for threaded rods, at the centre of the crack front, can be obtained, according to Toribio et al. [25], from the expression:
a a 2 Ym = 0.820 − 0.111 ⎛ ⎞ + 1.589 ⎛ ⎞ ⎝d⎠ ⎝d⎠ where d is the diameter of the rod. C and n are calculated from the experimental values of crack-growth rate measured through scanning electron microscopy (Fig. 8). The values of da/dN versus ΔK are plotted in Fig. 10. Two regimes of crack-growth rate can be observed. Up to ΔK = 9.5 MPa·m½, corresponding to a crack size a = 20.1 mm, the propagation speed is nearly independent of ΔK (n = 0.094), and C is equal to 3.9E-07. For cracks larger than 20.1 mm, n = 0.87 and C = 6.5E-08. Both crack-growth regimes (Fig. 10) were taken into account to integrate the Paris equation. The initial crack length, a0, was taken as equal to 1.5 mm, as calculated from a stress-intensity threshold value, ΔKth, equal to 1.86 MPa·m½. This value has been obtained from various experimental values [26] and from theoretical considerations [14]. The a0 value is also in agreement with scanning electron microscope experimental observations. The experimental value of the final crack length (before sudden overload fracture), af, is 57.2 mm. The integration provides a value of Nf = 76,000 cycles necessary for crack growth from 1.5 mm to 57.2 mm. This number of cycles corresponds to 15 months of service life of the crane. The difference between real (600,000 cycles) and calculated service life is clearly spent in the nucleation of the initial fatigue-crack from pits or other faults at the thread root. This initial crack propagated rapidly during the last 15 months of service.
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