EM 1110-2-6054 1 Dec 01 6-14 Figure 6-18. Relation between dimensions of a discontinuity and the parameter ā for surface discontinuities. (Extracts from British Standards Institution 1980. Complete copies of the standard can be obtained by post from BSI Publications, Linford Wood, Milton Keynes, MK14 6LE) c. All steels have microscopic discontinuities, and welded structures always contain larger discontinuities due to the welding process. Thus, the main concern in fatigue assessment of welded structures is to determine the crack-propagation life before the critical crack size is reached that results in brittle fracture. The life of a structural component that contains a crack is governed by the rate of subcritical crack propagation. d. Fatigue analysis methods described in paragraphs 6-7 and 6-8 are based on extensive analyses of test results from numerous specimens. Variation in test data is large, and inherent uncertainty exists in defining load and strength parameters. Therefore, fatigue life predictions should be used as a means to evaluate a reliable service life, not to actually predict when a structure will fail. Fatigue analysis is needed when the remaining structure life and the crack growth rate are necessary for developing the inspection and maintenance scheduling for a distressed structure as discussed in paragraph 6-11. An example of the estimation of fatigue life from S r -N curves for a gate with a vibration problem is given in Chapter 7. 6-7. Fatigue Crack-Propagation The fatigue crack-propagation behavior for metals is shown in Figure 6-21. Figure 6-21 is a plot (log 10 scale) of the rate of fatigue crack growth per cycle of load da/dN versus the variation of the stress-intensity factor ∆K I . The parameter a denotes crack length, N the number of cycles, and ∆K I the stress-intensity factor range, K Imax to K Imin . Based on Figure 6-21, fatigue-crack behavior for steel can be characterized by three regions. Barsom and Rolfe (1987) describe these regions in more detail. EM 1110-2-6054 1 Dec 01 6-15 Figure 6-19. Relation between dimensions of a discontinuity and the parameter ā for embedded discontinuities (Extracts from British Standards Institution 1980. Complete copies of the standard can be obtained by post from BSI Publications, Linford Wood, Milton Keynes, MK14 6LE) a. Region I. In Region I, for levels of ∆K I below a certain threshold, cracks do not propagate under cyclic stress fluctuations. Conservative estimates of fatigue threshold, ∆K th , can be determined by ∆K th = 7 (1 - 0.85R) MPa- m (6.4 (1 - 0.85R) ksi- .in ) for R > 0.1 ∆K th = 6 MPa- m (5.5 ksi- .in ) for R < 0.1 (6-6) where R is the stress ratio (i.e., fatigue ratio) expressed as R = σ min / σ max (6-7) Residual stress should be considered for a crack near a weld area. If ∆K I is less than ∆K th , cracks do not propagate. b. Region II. The fatigue crack-propagation behavior for ∆K I > ∆K th in Region II (i.e., linear portion of the plot in Figure 6-21) may be represented by Equations 6-8 and 6-9. These equations were based on analyses in air at room temperature. Extensive fatigue-crack growth rate data for weld metals and heat-affected zones show that the fatigue rate in weld metals and heat-affected zones is equal to or less than that in the base metals. Thus, Equations 6-8 and 6-9 can also be used for conservative estimates of fatigue-crack growth rates in base metals, weld metals, and heat-affected zones. EM 1110-2-6054 1 Dec 01 6-16 Figure 6-20. Values of constant C for different loading conditions (Extracts from British Standards Institution 1980. Complete copies of the standard can be obtained by post from BSI Publications, Linford Wood, Milton Keynes, MK14 6LE) Figure 6-21. Fatigue-crack growth in steel EM 1110-2-6054 1 Dec 01 6-17 (1) Ferrite-pearlite steels. ASTM A36M-97 and ASTM A572/572M Grade 50 steels are classified as ferrite-pearlite steels: da/dN = 6.9 × 10 -9 (∆K I ) 3 (6-8) where a = mm ∆K I = MPa- m (For non-SI units, da/dN = 3.6 × 10 -10 (∆K I ) 3 where a = in. and ∆K I = ksi- .in ) (2) Martensitic steels. ASTM A514/A514M and ASTM A517/517M steels are martensitic steels: da/dN = 1.35 × 10 -7 (∆K I ) 2.25 (6-9) where a = mm ∆K I = MPa- m (For non-SI units, da/dN = 0.66 × 10 -8 (∆K I ) 2.25 where a = in. and ∆K I = ksi- .in ) c. Region III. Region III is characterized by a significant increase in the fatigue-crack growth rate per cycle over that predicted for Region II. At a certain value of ∆K I , the crack growth rate accelerates dramatically. For materials of high fracture toughness, the stress-intensity factor range value corresponding to acceleration in the fatigue-crack growth rate (i.e., transition from Region II to Region III) for zero to tension loading can be determined by Equation 6-10: K T = 0.0063 (E σ ys ) 1/2 (6-10) where K T = MPa- m E, σ ys = MPa (For non-SI units, K T = 0.04 (E σ ys ) 1/2 where K T = ksi- .in , and E and σ ys = ksi.) When the K Ic of the material is less than K T , acceleration in the fatigue rate occurs at a stress-intensity factor value slightly below K Ic . Due to the acceleration in crack growth rate, a significant increase in fracture tough- ness of a steel above K T may have a negligible effect on total fatigue life. Additionally, extrapolation of Region II behavior to Region III may overestimate the total fatigue life significantly. 6-8. Fatigue Assessment Procedures a. Region II fatigue analysis with known discontinuities. The procedure to analyze Region II crack growth behavior in steels and weld metals using fracture mechanics concepts as recommended by Barsom and Rolfe (1987) is as follows. EM 1110-2-6054 1 Dec 01 6-18 (1) On the basis of the inspection data, determine the maximum initial discontinuity size a o present in the member being analyzed and the associated K I . (2) Knowing K Ic and the nominal maximum design stress, calculate the critical discontinuity size a cr (Equation 6-2) that would cause failure by brittle fracture. (3) Determine fatigue crack growth rate for type of steel (Equations 6-8 and 6-9 for ferrite-pearlite or martensitic steel, respectively). (4) Determine ∆K I using the appropriate expression for K I , the estimated initial discontinuity size a o , and the range of live load stress S r (i.e., cyclic stress range). For cases of variable amplitude loading, an equivalent constant amplitude stress range, S re should be computed as described in paragraph 2-3e. A live load stress range S r , which is due to cyclic compression stresses, may be detrimental in regions where tensile residual stress exists. In these regions, cracks may propagate, since the addition of tensile residual stresses will result in an applied stress range of tension and compression. The stress range, S r , used to determine fatigue life should be calculated from the algebraic difference of the maximum and minimum stresses even when the minimum stress is compression and has a negative value, since any tensile residual stresses will be superimposed on the applied cyclic stress (American Association of State Highway and Transportation Officials 1996; American Institute of Steel Construction 1994; EM 1110-2-2105). (5) Integrate the crack growth rate expression (i.e., Equations 6-8 and 6-9) between the limits of a o (at the initial K I ) and a cr (at K Ic ) to obtain the life of the structure prior to failure. To identify inspection intervals, integration may be applied with the upper limit being tolerable discontinuity size a t . An arbitrary safety factor based on analysis uncertainties may be applied to a cr to obtain a t (a factor of safety of 2.0 is recommended). Another consideration for specifying a tolerable discontinuity size is crack growth rate. The a t should be chosen so that da/dN is relatively small and a reasonable length of time remains before the critical size is reached. (6) For a determination of a o : (a) See Figure 6-3a for through-thickness discontinuities. (b) For embedded discontinuities (Figure 6-3b), assume that the discontinuity grows until it reaches a circular shape (b = !/2). Subsequently, it grows radially and eventually protrudes through a surface at which time it should be treated as a surface discontinuity of length !. (c) See Figure 6-3c for surface discontinuities. Initial propagation will result in a semicircular shape. Further propagation will result in the discontinuity reaching the other surface at which time it should be treated as a through-thickness discontinuity. b. Fatigue strength evaluation without known discontinuities. (1) Welded details. The fatigue life of welded details that do not include known discontinuities shall be determined as described in Chapters 2 and 3. (2) Riveted details. The following fatigue strength criteria for undamaged and noncorroded riveted details are recommended: (a) When S rm ≤ 41.4 MPa (6 ksi), where S rm is the maximum stress range, the possibility of fatigue damage can be ignored. EM 1110-2-6054 1 Dec 01 6-19 (b) When S re < 68.9 MPa (10 ksi), where S re is the equivalent constant-amplitude stress range, use Category C and S re to characterize the fatigue strength and life of the riveted member detail. (c) When S re ≥ 68.9 MPa (10 ksi), use Category D and S re to characterize the fatigue strength and life of the riveted member detail. For constant-amplitude loading, both S rm and S re are equivalent to S r . This recommended S r -N curve is illustrated in Figure 6-22. Figure 6-22. Recommended S r -N curve for riveted gates For severely corroded members or members with corroded, loose, or missing rivets where the clamping force is reduced or lost, lower fatigue strength curves may be more appropriate. Specifically, it is suggested that the Category E or E' curves and the corresponding fatigue limits should be used if corrosion notches are present (Chapter 2). As shown by Figure 2-5, fatigue cracks may initiate at corrosion notches instead of from rivet holes. 6-9. Evaluation of Corrosion Damage Traditional member/frame structural analysis or even finite element methods can be used to evaluate the effect of reduction in sections from corrosion damage. To perform such an analysis, the extent of corrosion damage must be defined by reduction of appropriate section properties or thicknesses in the affected members. This should include consideration of the reduced thicknesses and change in relative proportions of the member. For example, depending on the location of the corrosion, the shear strength of a flexural member may be more affected than the flexural strength. Analysis of the complete structure incorporating the reduced sections may be warranted if the corrosion is severe and/or widespread. EM 1110-2-6054 1 Dec 01 6-20 6-10. Evaluation of Plastically Deformed Members The effect of buckled or plastically deformed members can be characterized by a reduction in strength and stiffness. To assess the damage, an analysis should be performed that models the damage condition. This may simply be a frame analysis that incorporates the out-of-straightness of a crooked member or a local reduction of cross-sectional properties to model a locally buckled flange. In more significant cases of damage, a two- or three-dimensional model with the damaged locations represented as a hinge or with a damaged member being considered removed may be more appropriate. 6-11. Development of Inspection Schedules Inspection schedules can be developed from crack length versus fatigue life curves. Figure 6-23 shows a typical crack length-fatigue life (a-N) curve, which can be obtained from Equation 6-8 or 6-9. Critical crack length is determined based on K Ic and maximum design stress as discussed in paragraph 6-8. The time when repair is needed can be determined considering an appropriate factor of safety (2.0 is recommended), i.e., a r = a cr /(FS). Remaining loading cycles before repair are then determined from a i and a r using an a-N curve as shown in Figure 6-23. Inspection intervals for a structure can be determined from the remaining fatigue life of the members (Pennsylvania Department of Transportation 1988). Figure 6-23. Development of maintenance schedule 6-12. Recommended Solutions for Distressed Structures a. If a thorough evaluation of the hydraulic steel structure reveals no evidence of distress, damage, or potential failure, it should be reinspected in accordance with the inspection intervals specified in ER 1110-2- 100. However, if significant deficient conditions exist (e.g., heavy corrosion, fatigue cracks, or deformations) or severe operations occur (e.g., persistent vibrations), it may be appropriate to repair and/or recommend a shorter inspection interval to ensure the structural and operational integrity of the structure. Solutions to the cracking problems can be addressed in short-term or long-term solutions. A quick solution might involve repair of fractured members using qualified welding procedures and improved fatigue details or bolted cover plates. A long-term solution would involve detailed inspection and evaluation of the critical members and connections EM 1110-2-6054 1 Dec 01 6-21 using procedures discussed in this EM to assist in determining a more permanent solution. Repair procedures are discussed in Chapter 8, and recommended inspection intervals may be computed using fatigue principles as described in paragraph 6-11. The inspection intervals shall correspond to a crack size less than one-half of the critical crack length (i.e., employ a factor of safety equal to at least 2.0). b. In determining the recommended action for a distressed hydraulic steel structure, the redundancy of the damaged members or connections should be considered. Obviously cracks or severe corrosion in nonredundant components should be more carefully considered. Because the conditions at each site are unique, proposing a general guideline for selecting shorter inspection intervals would be difficult. Detrimental conditions should be evaluated on a case-by-case basis using appropriate analytical tools. c. A comprehensive maintenance and inspection program can reduce the occurrence of significant structural distress. Through a regularly scheduled cleaning and painting program, the effects of corrosion can be controlled, and by removing debris and lubricating all mechanical components, the potential overloads from lifting operations can be minimized. . 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Transportation 1 988 ). Figure 6-23. Development of maintenance schedule 6-12. Recommended Solutions for Distressed Structures