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Copyright © 1990 ASM International® ASM Handbook, Volume 1: Properties and Selection: Irons, , and High-Performance Alloys All rights reserved. ASM Handbook Committee, p 673-688 www.asminternational.org

Fatigue Resistance of Steels

Bruce Boardman, Deere and Company, Technical Center

FATIGUE is the progressive, localized, generalization is not true, however, for high was commonly assumed that total fatigue and permanent structural change that oc- tensile strength values where and life consisted mainly of crack initiation curs in a material subjected to repeated or critical flaw size may govern ultimate load (stage I of fatigue crack development) and fluctuating strains at nominal stresses that carrying ability. Processing, fabrication, that the time required for a minute fatigue have maximum values less than (and often heat treatment, surface treatments, finish- crack to grow and produce failure was a much less than) the tensile strength of the ing, and service environments significantly minor portion of the total life. However, as material. Fatigue may culminate into cracks influence the ultimate behavior of a better methods of crack detection became and cause after a sufficient number subjected to cyclic stressing. available, it was discovered that cracks of fluctuations. The process of fatigue con- Predicting the fatigue life of a metal part often develop early in the fatigue life of the sists of three stages: is complicated because materials are sensi- material (after as little as 10% of total life- tive to small changes in loading conditions time) and grow continuously until cata- • Initial fatigue damage leading to crack and concentrations and to other fac- strophic failure occurs. This discovery has initiation tors. The resistance of a metal structural led to the use of crack growth rate, critical • Crack propagation to some critical size (a member to fatigue is also affected by man- crack size, and fracture for the size at which the remaining uncracked ufacturing procedures such as cold forming, prediction of total life in some applica- cross section of the part becomes too , brazing, and plating and by surface tions. Hertzberg's text (Ref 1) is a useful weak to carry the imposed loads) conditions such as surface roughness and primer for the use of • Final, sudden fracture of the remaining residual stresses. Fatigue tests performed methods. cross section on small specimens are not sufficient for Fatigue damage is caused by the simulta- precisely establishing the fatigue life of a Prevention of Fatigue Failure neous action of cyclic stress, tensile stress, part. These tests are useful for rating the and plastic strain. If any one of these three is relative resistance of a material and the A thorough understanding of the factors not present, a fatigue crack will not initiate baseline properties of the material to cyclic that can cause a component to fail is essen- and propagate. The plastic strain resulting stressing. The baseline properties must be tial before designing a part. Reference 2 from cyclic stress initiates the crack; the combined with the load history of the part in provides numerous examples of these fac- tensile stress promotes crack growth (propa- a design analysis before a component life tors that cause fracture (including fatigue) gation). Careful measurement of strain shows prediction can be made. and includes high-quality optical and elec- that microscopic plastic strains can be present In addition to material properties and tron micrographs to help explain factors. at low levels of stress where the strain might loads, the design analysis must take into con- The incidence of fatigue failure can be otherwise appear to be totally elastic. Al- sideration the type of applied loading (uniax- considerably reduced by careful attention to though compressive stresses will not cause ial, , or torsional), loading pattern design details and manufacturing processes. fatigue, compressive loads may result in local (either periodic loading at a constant or vari- As long as the metal is sound and free from tensile stresses. able amplitude or random loading), magni- major flaws, a change in material composi- In the early literature, fatigue tude of peak stresses, overall size of the part, tion is not as effective for achieving satis- were often attributed to crystallization be- fabrication method, surface roughness, pres- factory fatigue life as is care taken in design, cause of their crystalline appearance. Be- ence of or corroded surface, operating fabrication, and maintenance during ser- cause are crystalline solids, the use and environment, and occur- vice. The most effective and economical of the term crystallization in connection rence of service-induced imperfections. method of improving fatigue performance is with fatigue is incorrect and should be Traditionally, fatigue life has been ex- improvement in design to: avoided. pressed as the total number of stress cycles required for a fatigue crack to initiate and • Eliminate or reduce stress raisers by Fatigue Resistance grow large enough to produce catastrophic streamlining the part failure, that is, separation into two pieces. • Avoid sharp surface tears resulting from Variations in mechanical properties, In this article, fatigue data are expressed in punching, stamping, shearing, and so on composition, microstructure, and macro- terms of total life. For the small samples • Prevent the development of surface dis- structure, along with their subsequent ef- that are used in the laboratory to determine continuities or decarburizing during pro- fects on fatigue life, have been studied fatigue properties, this is generally the case; cessing or heat treatment extensively to aid in the appropriate selec- but, for real components, crack initiation • Reduce or eliminate tensile residual tion of to meet specific end-use re- may be as little as a few percent or the stresses caused by manufacturing, heat quirements. Studies have shown that the majority of the total component life. treating, and welding fatigue strength of steels is usually propor- Fatigue data can also be expressed in • Improve the details of fabrication and tional to and tensile strength; this terms of crack growth rate. In the past, it fastening procedures 674 / Service Characteristics of Carbon and Low- Steels

g ?- a) 207022,0 ~ssratio, T-R ~ 325300 t--- I F I I P I I I I ] P I • - 1.00 0) ._g 0 1900 ~ 0.05 P'~i,I I ~ .... I I I I o 0.20 ~2~0 E L/L/L/ 8 1725 i Time 1550 (a) 1380

CD :~ 1035 ~ 150 ~s. 860 ~ 125

Time (b) 520 103 104 105 10s 107 108 Fatigue life (transverse direction), cycles

I:|, Best-fit S-A/curves for unnotched 300M alloy forging with an ultimate tensile strength of 1930 MPa (280 "'b ° 2 ksi). Stresses are based on net section. Testing was performed in the transverse direction with a theoretical factor, Kt, of 1.0. Source: Ref 4 (I) sm either between a maximum and a minimum other combination is known as an alternat- tensile stress or between a maximum tensile ing stress, which may be an alternating Time stress and a specified level of compressive tensile stress (Fig. lc), an alternating com- stress. The latter of the two, considered a pressive stress, or a stress that alternates (c) negative tensile stress, is given an algebraic between a tensile and a compressive value minus sign and called the minimum stress. (Fig. ld). g Applied Stresses. The mean stress, Sin, is Nominal axial stresses can be calculated the algebraic average of the maximum on the net section of a part (S = per 0) I- stress and the minimum stress in one cycle: unit area) without consideration of varia- tions in stress conditions caused by holes, g (Smax + Stain) Sm- (Eq I) grooves, fillets, and so on. Nominal stresses o~ 2 are frequently used in these calculations, E The range of stress, St, is the algebraic although a closer estimate of actual stresses 8 difference between the maximum stress and through the use of a stress concentration the minimum stress in one cycle: factor might be preferred. Time Stress ratio is the algebraic ratio of two Sr = Sma x - Smin (Eq 2) (d) specified stress values in a stress cycle. Two commonly used stress ratios are A, the The stress amplitude, S,, is one-half the ""~1:|° 1 Types of fatigue test stress. (a) Alternating ratio of the alternating stress amplitude to range of stress: stress in which S~ = 0 and /? = -1. (b) the mean stress (A = S,/Sm) and R, the ratio Pulsating tensile stress in which S~ = S,, the minimum Sr (Smax -- Smin) of the minimum stress to the maximum stress is zero, and/? = 0. (c) Fluctuating tensile stress Sa- - (Eq 3) in which both the minimum and maximum stresses 2 2 stress (R = Smin/Smax).The five conditions are tensile stresses and R = a/3. (d) Fluctuating tensile- that R can take range from +I to -1: to-compressive stress in which the minimum stress is During a fatigue test, the stress cycle is a compressive stress, the maximum stress is a tensile • Stresses are fully reversed: R = -1 stress, and R = -~/g usually maintained constant so that the ap- plied stress conditions can be written Sm -+ • Stresses are partially reversed: R is be- Sa, where Sm is the static or mean stress and tween - I and zero Control of or protection against , Sa is the alternating stress equal to one-half • Stress is cycled between a maximum erosion, chemical attack, or service- the stress range. The positive sign is used to stress and no load: The stress ratio R induced nicks and other gouges is an impor- denote a tensile stress, and the negative sign becomes zero tant part of proper maintenance of fatigue denotes a compressive stress. Some of the • Stress is cycled between two tensile life during active service life. Reference 3 possible combinations of Sm and S, are stresses: The stress ratio R becomes a contains numerous papers pertaining to shown in Fig. 1. When Sm = 0 (Fig. la), the positive number less than 1 these subjects. maximum tensile stress is equal to the max- • An R stress ratio of 1 indicates no varia- imum compressive stress; this is called an tion in stress, and the test becomes a sustained-load test rather than a Symbols and Definitions alternating stress, or a completely reversed stress. When Sm= Sa (Fig. lb), the mini- fatigue test In most laboratory fatigue testing, the mum stress of the cycle is zero; this is called $-NCurves. The results of fatigue tests are specimen is loaded so that stress is cycled a pulsating, or repeated, tensile stress. Any usually plotted as the maximum stress or Fatigue Resistance of Steels / 675 stress amplitude versus the number of Minimum stress, ksi cycles, N, to fracture, using a logarithmic - 100 - 50 0 50 100 150 200 20O scale for the number of cycles. Stress may be plotted on either a linear or a logarith- mic scale. The resulting curve of data points is called an S-N curve. A family of S-N curves for a material tested at various 150 stress ratios is shown in Fig. 2. It should be noted that the fully reversed condition, R = -1, is the most severe, with the least fatigue life. For carbon and low-alloy "~ I00 "~ steels, S-N curves (plotted as linear stress versus log life) typically have a fairly straight slanting portion with a negative slope at low cycles, which changes with a sharp transition into a straight, horizontal 50 line at higher cycles. An S-N curve usually represents the me- dian, or Bso, life, which represents the num- ber of cycles when half the specimens fail at 0 a given stress level. The scatter of fatigue - 1000 - 800 600 - 400 200 0 200 400 600 800 1000 1200 1400 lives covers a very wide range and can Minimum stress, MPa occur for many reasons other than material Constant-lifetime fatigue diagram for AISI-SAE 4340 alloy steel bars, hardened and tempered to a tensile variability. Fig. 3 strength of 1035 MPa (150 ksi) and tested at various . Solid lines represent data obtained A constant-lifetime diagram (Fig. 3) is a from unnotched specimens; dashed lines represent data from specimens having notches with Kt = 3.3. All lines summary graph prepared from a group of represent lifetimes of ten million cycles. Source: Ref 5 S-N curves of a material; each S-N curve is obt~tined at a different stress ratio. The diagram shows the relationship between the 620 I I I 90 alte)'nating stress amplitude and the mean • Notched stress and the relationship between maxi- 550 O Unnotched 80 mum stress and minimum stress of the I Runout stress cycle for various constant lifetimes. 485 I 70 Although this technique has received con- o o siderable use, it is now out of date. Earlier ~. 415 60 .- editions of the Military Standardization Handbook (Ref 5) used constant lifetime 345 \ 5O diagrams extensively, but more recent edi- tions (Ref 4) no longer include them. E E 275 40 E Fatigue limit (or endurance limit) is the E \ value of the stress below which a material 210 30 } can presumably endure an infinite number of stress cycles, that is, the stress at which 140 the S-N diagram becomes and appears to 2O remain horizontal. The existence of a fa- tigue limit is typical for carbon and low- 7O 10 alloy steels. For many variable-amplitude loading conditions this is true; but for con- 0! 0 103 104 105 10s 107 10a ditions involving periodic overstrains, as is typical for many actual components, large Fatigue life, cycles changes in the long-life fatigue resistance r'.*, Room temperature S-Ncurves for notched and unnotched AISI 4340 alloy steel with a tensile strength can occur (see the discussion in the section HS" 4 of 860 MPa (125 ksi). Stress ratio, R, equals -1.0. Source: Ref 4 "Comparison of Fatigue Testing Tech- niques" in this article). Fatigue strength, which should not be con- such as inclusions and thermal heat affected Fatigue notch factor, K r, is the ratio of the fused with fatigue limit, is the stress to zones. The theoretical stress concentration fatigue strength of a smooth (unnotched) which the material can be subjected for a factor, Kt, is the ratio of the greatest elasti- specimen to the fatigue strength of a specified number of cycles. The term fa- cally calculated stress in the region of the notched specimen at the same number of tigue strength is used for materials, such as notch (or other stress concentrator) to the cycles. The fatigue notch factor will vary most nonferrous metals, that do not exhibit corresponding nominal stress. For the de- with the life on the S-N curve and with the well-defined fatigue limits. It is also used to termination of Kt, the greatest stress in the mean stress. At high stress levels and short describe the fatigue behavior of carbon and region of the notch is calculated from the cycles, the factor is usually less than at low-alloy steels at stresses greater than the theory of or by finite-element lower stress levels and longer cycles be- fatigue limit. analysis. Equivalent values may be derived cause of a reduction of the notch effect by Stress Concentration Factor. Concentrat- experimentally. An experimental stress plastic . ed stress in a metal is evidenced by surface concentration factor is a ratio of stress in a Fatigue notch sensitivity, q, is determined discontinuities such as notches, holes, and notched specimen to the stress in a smooth by comparing the fatigue notch factor, Kr, scratches and by changes in microstructure (unnotched) specimen. and the theoretical stress concentration fac- 676 / Service Characteristics of Carbon and Low-Alloy Steels

1240 180 assumptions imply that all the stresses will essentially be elastic. 1105 Tensile strengths 160 The S-N plot shown in Fig. 4 presents o 1836 MPa data for AISI-SAE 4340 steel, heat treated • 1435 MPa 965 1090 MPa 140 to a tensile strength of 1035 MPa (150 ksi) in • 860 MPa the notched and unnotched condition. Fig- • ~• 825 Runout 120 ure 5 shows the combinations of cyclic E \ E stresses that can be tolerated by the same 690 ..~ ~o "~¢ .~ 100 E steel when the specimens are heat treated to different tensile strengths ranging from 860 550 "~ ~"' o to 1790 MPa (125 to 260 ksi). O 80 ""-,- • .._ .~=. The effect of elevated temperature on the fatigue behavior of 4340 steel heat treated to 415 ...... 60 "*-..,,,., L, ..,i ...... 1035 MPa (150 ksi) is shown in Fig. 6. An ,°.. °°°° increase in temperature reduces the fatigue 275 40 103 104 10 5 10e 107 10 8 strength of the steel and is most deleterious Fatigue life, cycles for those applications in which the stress ratio, R, lies between 0.4 and 1.0 (Fig. 3). A I:|. 5 Room temperature S-Ncurves for AlSl 4340 alloy steel with various ultimate tensile strengths and with decrease in temperature may increase the "'b ° R = -1.0. Source: Ref 4 fatigue limit of steel; however, parts with preexisting cracks may also show decreased total life as temperature is lowered, because 760 110 of accompanying reductions in critical crack size and . 690 O Room temperature 100 • 315°C Figure 7 shows the effect of notches on A 427oc the fatigue behavior of the ultrahigh- • 538°C 90 620 strength 300M steel. A K t value of 2 is "-~ Runout obtained in a specimen having a notch radi- 55O 80 .- us of about ! mm (0.040 in.). For small ,,~ parts, such a radius is often considered 485 70 large enough to negate the stress concentra- tion associated with any change in section. E mOI b~q E = 415 "4 • 6O E The significant effect of notches, even those E ~OmgmD with low stress concentration factors, on '°e,,, • 345 ta~oi 5o the fatigue behavior of this steel is apparent. °OQIO O ~ I Ioo~ Data such as those presented in Fig. 3 to BQO0 QmA 7 may not be directly applicable to the 275 ~mO48~QD 4O &- design of structures because these graphs do not take into account the effect of the 210 3O specific stress concentration associated with reentrant corners, notches, holes, 150 20 joints, rough surfaces, and other similar 103 104 10s 10e 107 10s conditions present in fabricated parts. The Fatigue life, cycles localized high stresses induced in fabricated S-Ncurves at various temperatures for AIS14340 alloy steel with an ultimate tensile strength of 1090 MPa parts by stress raisers are of much greater Fig, 6 (158 ksi). Stress ratio, R, equals -1.0. Source: Ref 4 importance for cyclic loading than for static loading. Stress raisers reduce the fatigue life significantly below those predicted by the tor, K,, for a specimen of a given size cycles. Under these conditions, the actual direct comparison of the smooth specimen containing a stress concentrator of a given peak stress at the base of the notch is partly fatigue strength with the nominal calculated shape and size. A common definition of in the plastic strain condition. This results stresses for the parts in question. Fabricat- fatigue notch sensitivity is: in the actual peak stress being lower than ed parts in simulated service have been the theoretical peak elastic stress used in found to fail at less than 50 000 repetitions Kf-I the calculation of the theoretical stress con- q - (Eq 4) of load, even though the nominal stress was K t - 1 centration factor. far below that which could be repeated in which q may vary between 0 (where Kt- = many millions of times on a smooth, ma- 1, no effect) and ! (where K t. = Kt, full Stress-Based Approach To Fatigue chined specimen. effect). This value may be stated as a per- Correction Factors for Test Data. The centage. As the fatigue notch factor varies The design of a machine element that will available fatigue data normally are for a with the position on the S-N curve, so does be subjected to cyclic loading can be ap- specific type of loading, specimen size, notch sensitivity. Most metals tend to be- proached by adjusting the configuration of the and surface roughness. For instance, the come more notch sensitive at low stresses part so that the calculated stresses fall safely R.R. Moore rotating- fatigue test ma- and long cycles. If they do not, it may be below the required line on an S-N plot. In a chine uses a 7.5 mm (0.3 in.) diam speci- that the fatigue strengths for the smooth stress-based analysis, the material is assumed men that is free of any stress concentra- (unnotched) specimens are lower than they to deform in a nominally elastic manner, and tions (because of specimen shape and a could be because of surface imperfections. local plastic strains are neglected. To the surface that has been polished to a mirror Most metals are not fully notch sensitive extent that these approximations are valid, finish), and that is subjected to completely under high stresses and a low number of the stress-based approach is useful. These reversed bending stresses. For the fatigue Fatigue Resistance of Steels / 677

1380 200 Table 1 Correction factors for surface roughness (Ks), type of loading (K0, and 1240 c 180 part diameter (gd), for fatigue life of steel parts O Unnotched 1105 ~ • Kt=2 160 Factor ~- Value for loading in t~ Kt 3 Bending Torsion " • K, 5 --~ aunout 140 g I ...... 1.0 0.58 0.9(a) 965 o~ g, oo where d -< 10 mm 830 o~ I 120 (0.4 in.) ...... 1.0 1.0 1.0 ~ o where 10 mm (0.4 in.) < d ~ 50 mm (2 in.)... 0.9 0.9 1.0 ~60oE . ~ 100 E OC,.~ 3 See C K~ ...... Fig. 8. 0 E "~ 550 ~. 80 "'~ (a) A lower value (0.06 to 0.85) may be used to take into account known or suspected undetermined bending because of load ec- centricity. Source: Ref 6 415 "'~. ~'~

275 -.. the abscissa is the number of strain rever- ~.., ~.,~ ~ ""°-l sals (twice the number of cycles) to failure, 140 "''"" • ,L and the ordinate is the strain amplitude (half 0000; D the strain range). 0 During cyclic loading, the stress-strain 103 104 105 106 107 108 relationship can usually be described by a Fatigue life, cycles loop, such as that shown in Fig. 9. For Room-temperature S-A/curves for a 300M steel with an ultimate tensile strength of 2000 MPa (290 ksi) purely elastic loading, the loop becomes a Fig. 7 having various notch severities. Stress ratio, R, equals 1.0. Source: Ref 4 straight line whose slope is the elastic mod- ulus, E, of the material. The occurrence of a hysteresis loop is most common. The defi- limits used in design calculations, Juvinall Design fatigue limit = K] . Kd • Ks • Ni nitions of the plastic strain range, A%, the (Ref 6) suggests the correction of fatigue (Eq 5) elastic strain range, A%, the total strain life data by multiplying the fatigue limit where Kl is the correction factor for the range, AEt, and the stress range, A(r, are from testing, Ni, by three factors that take type of loading, K d for the part diameter, indicated in Fig. 9. A series of fatigue tests, into account the variation in the type of and K S for the surface roughness. Values of each having a different total strain range, loading, part diameter, and surface rough- these factors are given in Table I and Fig. 8. will generate a series of hysteresis loops. ness: For each set of conditions, a characteristic Strain-Based Approach To Fatigue number of strain reversals is necessary to Tensile strength, ksi cause failure. As shown in Fig. 10, a plot on logarithmic 50 75 100 125 150 175 200 225 A strain-based approach to fatigue, devel- 1.1 L L t l I I I I oped for the analysis of low-cycle fatigue coordinates of the plastic portion of the data, has proved to be useful for analyzing strain amplitude (half the plastic strain 1.0 J long-life fatigue data as well. The approach range) versus the fatigue life often yields a ~Mirror-p lished can take into account both elastic and plas- straight line, described by the equation: specimen tic responses to applied loadings. The data 0.9 A~p t c ~o ~ne-grouL"" are presented on a log-log plot similar in T = ef(2Nf) (Eq 6) or commercially 0.8 shape to an S-N curve; the value plotted on ~ polished part where e~. is the fatigue ductility coefficient, c =~ 07 \ is the fatigue ductility exponent, and Nf is the number of cycles to failure. o ~o Machinedpart ~ \X Because the conditions under which elas- tic strains have the greatest on fa- ~0.5~~ \N~ ~,~Hot-rolled )art tigue behavior are the long-life conditions where stress-based analysis of fatigue is appropriate, the effects of elastic strain on 0.4 ~ . ~ As-forged part fatigue are charted by plotting stress ampli- Ao tude (half the stress range) versus fatigue 03 ,, ~, ~-~ life on logarithmic coordinates. As shown in Part corroded ~ Fig. 11, the result is a straight line having 0.2 in tap water the equation: Act 0.1 --Part corroded in -~- = cr'f(2Nf)b (Eq 7) saltwater 0 I I where cr;- is the fatigue strength coefficient 300 500 700 900 1100 1300 1500 1700 and b is the fatigue strength exponent. Tensile strength, MPa i Aep Aee The elastic strain range is obtained by dividing Eq 7 by E: IZ;rl Q Surface roughness correction factors for stan- Ae "'8 "o dard rotating-beam fatigue life testing of Ae¢ (r'f steel parts. See Table I for correction factors from part - -~(2Nf)b (Eq 8) diameter and type of loading. Source: Ref 6 Fig. 9 Stress-strain hysteresis loop. Source: Ref 7 L 678 / Service Characteristics of Carbon and Low-Alloy Steels

I I fatigue life, regardless of their strength lev- e~ = ~f 0.58 = els. Heat treating a steel to different hard- ~= 0.1 ~coefficient ness levels does not appreciably change the fatigue life for this strain amplitude (Fig. 14). Fuchs and Stephens's text (Ref 9), Pro- E ceedings of the SAE Fatigue Conference (Ref 10), and the recently published update .E A%_ ei(2N0~ = 0.58(2Nf) o.~7 to the SAE Fatigue Design Handbook (Ref 0.01 / 2 .o_~ ~ / 11) provide much additional detail on the use of state-of-the-art fatigue analysis meth- ~- Fatigue ductility ods. In fact, the chapter outline for the exponent = slope = c = 0.57 latter work, shown in Fig. 15, provides an "all0 3 excellent checklist of factors to include in a fatigue analysis.

Metallurgical Variables of Fatigue Behavior 10-4 I0 I00 103 I04 I0 s I0 e 107 The metallurgical variables having the Reversals to failure, 2Nf most pronounced effects on the fatigue be- Fig. 1 0 Ductility versus fatigue life for annealed AISI-SAE 4340 steel. Source: Ref 8 havior of carbon and low-alloy steels are strength level, ductility, cleanliness of the 69 000 104 steel, residual stresses, surface conditions, and aggressive environments. At least part- ly because of the characteristic scatter of g_ fatigue testing data, it is difficult to distin- guish the direct effects of other variables " 6900 [ 103 ~..1 such as composition on fatigue from their ~r~ = ~rf = 1200 MPa effects on the strength level of steel. Refer- ~ Fatigue strength coefficient ence 3 addresses some excellent research in (~ ,.o.._.,_,.~~ ~'-'"~ ] / ~{r a = (r~(2Nf) b = 174(2Nf) 009 the area of microstructure and its effect on : 690 100 .~ fatigue. Strength Level. For most steels with hard- E Fatigue strength / ~ ~ ~E nesses below 400 HB (not including precip- exponent = slope = b = 0.09 itation steels), the fatigue limit is 69 10 --~ about half the ultimate tensile strength. Thus, any heat treatment or alloying addi- < < tion that increases the strength (or hard- ness) of a steel can be expected to increase its fatigue limit as shown in Fig. 5 for a 6.9 1 10 100 103 104 I0 S I0 ~ 107 low-alloy steel (AISI 4340) and in Fig. 16 for Reversals to failure, 2Nf various other low-alloy steels as a function of hardness. However, as shown in Fig. 14 Strength versus fatigue life for annealed AISI-SAE 4340 steel. The equation for the actual stress Fig. 11 amplitude, %, is shown in ksi units. Source: Ref 8 for medium-, a higher hardness (or strength) may not be associated with improved fatigue behavior in a low-cycle The total strain range is the sum of the ksi); the other steel is a proprietary grade regime (<10 3 cycles) because ductility may elastic and plastic components, obtained by hardened and tempered to a strength be a more important factor. adding Eq 6 and 8 (see Fig. 12): of about 750 MPa (110 ksi). Under long-life Ductility is generally important to fatigue Ae ~ri fatigue conditions, the higher-strength steel life only under low-cycle fatigue conditions. -~ = ~'r(2Nf)"+ ~-(2Nt-)t' (Eq 9) can accommodate higher strain amplitudes Exceptions to this include spectrum loading for any specified number of cycles; such where there is an occasional overload with For low-cycle fatigue conditions (frequently strains are elastic. Thus, stress and strain millions of smaller cycles, or extremely fewer than about 1000 cycles to failure), the are proportional, and it is apparent that the brittle materials where crack propagation first term of Eq 9 is much larger than the higher-strength steel has a higher fatigue dominates. The fatigue-ductility coefficient, second; thus, analysis and design under limit. With low-cycle fatigue conditions, ~;., can be estimated from the reduction in such conditions must use the strain-based however, the more ductile lower-strength area occurring in a tension test. approach. For long-life fatigue conditions steel can accommodate higher strain ampli- Cleanliness of a steel refers to its relative (frequently more than about 10 000 cycles tudes. For low-cycle fatigue conditions (in freedom from nonmetallic inclusions. These to failure), the second term dominates, and which the yield strength of the material is inclusions generally have a deleterious ef- the fatigue behavior is adequately described exceeded on every cycle), the lower- fect on the fatigue behavior of steels, par- by Eq 7. Thus, it becomes possible to use strength steel can accommodate more strain ticularly for long-life applications. The type, Eq 7 in stress-based analysis and design. reversals before failure for a specified strain number, size, and distribution of nonmetal- Figure 13 shows the fatigue life behavior amplitude. For strain amplitudes of 0.003 to lic inclusions may have a greater effect on of two high-strength plate steels for which 0.01, the two steels have the same fatigue the fatigue life of carbon and alloy steel than extensive fatigue data exist. ASTM A 440 life, 104 to 10s cycles. For this particular will differences in composition, microstruc- has a yield strength of about 345 MPa (50 strain amplitude, most steels have the same ture, or stress gradients. Nonmetallic inclu- Fatigue Resistance of Steels / 679

0.03

0.01 - + = .... + .... 0.1

E /~.' p c 2" (from Fig. 10) "/ "~ .= Proprietary HSLA~ 0.01 690 MPa (100 ksi) rain UTS 0.001

O-a AEe 0.0004 10 3 E - 2 (from Fig. 11) 102 103 104 105 106 107 Cycles to failure

r-'n Total strain versus fatigue life for two high- H~, 1 3 strength low-alloy (HSLA) steels. Steels are ASTM A 440 having a yield strength of about 345 MPa 10 4 (50 ksi) and a proprietary quenched and tempered 10 100 103 104 105 106 107 HSLA steel having a yield strength of about 750 MPa Reversals to failure, 2Nf (110 ksi). Source: Ref 7 Total strain versus fatigue life for annealed AISI-SAE 4340 steel. Data are same as in Fig. 10 and 11. Fig. Source: Ref 8 12 (0.005 in.) in diameter, were observed in the fracture surfaces of these specimens. The sions, however, are rarely the prime cause graphic examination to ensure that the lim- inclusions were identified as silicate parti- of the fatigue failure of production parts; if ited sample size (volume rated) is repre- cles. No spherical inclusions larger than the design fatigue properties were deter- sentative of the critical area in the final 0.02 mm (0.00075 in.) were detected in the mined using specimens containing inclu- component. other specimens. sions representative of those in the parts, Points on the lower curve in Fig. 17 Large nonmetallic inclusions can often be any effects of these inclusions would al- represent the cycles to failure for a few detected by nondestructive inspection; ready be incorporated in the test results. specimens from one bar selected from a lot steels can be selected on the basis of such Great care must be used when rating the consisting of several bars of 4340H steel. inspection. Vacuum melting, which reduces cleanliness of a steel based on metallo- Large spherical inclusions, about 0.13 mm the number and size of nonmetallic inclu- sions, increases the fatigue limit of 4340 steel, as can be seen in Table 2. Improve- ment in fatigue limit is especially evident in the transverse direction. Surface conditions of a metal part, partic- ularly surface imperfections and roughness, can reduce the fatigue limit of the part. This \\ effect is most apparent for high-strength steels. The interrelationship between sur- face roughness, method of producing the surface finish, strength level, and fatigue limit is shown in Fig. 8, in which the ordi- &' °1 ~e00~ nate represents the fraction of fatigue limit \ relative to a polished test specimen that could be anticipated for the combination of i oo \ strength level and surface finish. \ 200 --"6 ~N ~ Hardness' HB Fretting is a phenomenon that oc- curs between two mating surfaces. It is adhesive in nature, and vibration is its es- O 0.01 sential causative factor. Usually, fretting is accompanied by oxidation. Fretting usually occurs between two tight-fitting surfaces that are subjected to a cyclic, relative mo- tion of extremely small amplitude. Fretted regions are highly sensitive to fatigue crack- ing. Under fretting conditions, fatigue ~~ 200 cracks are initiated at very low stresses, well below the fatigue limit of nonfretted 10 3 specimens. 1 10 100 103 104 105 106 107 Decarburization is the depletion of car- Stress reversals to failure bon from the surface of a steel part. As indicated in Fig. 18, it significantly reduces r;n Effect of hardness level on plot of total strain versus fatigue life. These are predicted plots for typical H~, 1 4 medium-carbon steel at the indicated hardness levels. The prediction methodology is described the fatigue limits of steel. Decarburization under the heading "Notches" in this article. of from 0.08 to 0.75 mm (0.003 to 0.030 in.) 680 / Service Characteristics of Carbon and Low-Alloy Steels

Define the problem and logical steps to a solution Overview and achieve these types of surface alloying are general fatigue discussed in Volume 2 of the 8th Edition design considerations and Volume 4 of the 9th Edition of Metals Handbook. In these processes, carbon, ni- trogen, or both elements are introduced into the surface layer of the steel part. The Evaluate basic materials properties Materials solute atoms strengthen the surface layer of properties the steel and increase its bulk relative to the metal below the surface. The case and core of a carburized steel part respond different- ,L ly to the same heat treatment; because of its Choose analytical or experimental approach Effect of processing higher carbon content, the case is harder (or a combination) on fatigue after quenching and harder after . performance To achieve maximum effectiveness of sur- I face alloying, the surface layer must be much thinner than the thickness of the part to maximize the effect of the - Consider how the fatigue properties Service history I Vehicle es; however, the surface layer must be thick of the real part might differ determination simulation enough to prevent operating stresses from affecting the material just below the surface Define the acting on the structure layer. Figure 19 shows the improvement in fatigue limit that can be achieved by nitrid- Translate loads into stresses and/or Strain measurement I Numerical ing. A particular advantage of surface alloy- strains and likely sites for crack initiation and flaw detection analysis methods ing in the resistance to fatigue is that the alloyed layer closely follows the contours of the part. Evaluate fatigue life and failure location Structural life I Fatigue life Surface Hardening. Induction, flame, la- evaluation prediction ser, and electron beam hardening selective- I I ly harden the surface of a steel part; the steel must contain sufficient carbon to per- mit hardening. In each operation, the sur- Determine whether there is either a Assessment of results I face of the part is rapidly heated, and the prediction or occurrence of fatigue and consideration part is quenched either by externally ap- failures. If so, consider alternatives of further actions I plied quenchant or by internal mass effect. I This treatment forms a surface layer of martensite that is bulkier than the steel beneath it. Further information on these Examine documented case histories for Failure I Case I processes may be found in Volume 2 of the suggestions of possible course of action analysis histories 8th Edition and Volume 4 of the 9th Edition I of Metals Handbook. Induction, flame, la- Do failure analysis to help clarify the source(s) of the problem ser, and electron beam hardening can pro- duce beneficial surface residual stresses Evaluate the need to make changes I If fatigue design problems that are compressive; by comparison, sur- in the design and/or analysis are evident, reexamine all pertinent elements face residual stresses resulting from through of the design and analysis hardening are often tensile. Figure 20 com- pares the fatigue life of through-hardened, carburized, and induction-hardened trans- Fig. 15 Checklist of factors in fatigue analysis. Source: Ref 11 mission shafts. Figure 21 shows the importance of the on AISI-SAE 4340 notched specimens that residual stresses at the surface of a part can proper case depth on fatigue life; the hard- have been heat treated to a strength level of improve its fatigue life; tensile residual ened case must be deep enough to prevent 1860 MPa (270 ksi) reduces the fatigue limit stresses at the surface reduce fatigue life. operating stresses from affecting the steel almost as much as a notch with K t = 3. Beneficial compressive residual stresses beneath the case. However, it should be When subjected to the same heat treat- may be produced by surface alloying, sur- thin enough to maximize the effectiveness ment as the core of the part, the decarbur- face hardening, mechanical (cold) working of the residual stresses. Three advantages ized surface layer is weaker and therefore of the surface, or by a combination of these of induction, flame, laser, or electron beam less resistant to fatigue than the core. Hard- processes. In addition to introducing com- hardening in the resistance of fatigue are: ening a part with a decarburized surface can pressive residual stresses, each of these • The core may be heat treated to any also introduce residual tensile stresses, processes strengthens the surface layer of appropriate condition which reduce the fatigue limit of the mate- the material. Because most real compo- • The processes produce relatively little rial. Results of research studies have indi- nents also receive significant bending and/ distortion cated that fatigue properties lost through or torsional loads, where the stress is high- • The part may be machined before heat decarburization can be at least partially est at the surface, compressive surface treatment regained by recarburization (carbon resto- stresses can provide significant benefit to ration in the surfaces). fatigue. Mechanical working of the surface of a Residual Stresses. The fatigue properties Surface Alloying. Carburizing, carboni- steel part effectively increases the resis- of a metal are significantly affected by the triding, and nitriding are three processes for tance to fatigue. Shot and skin residual stresses in the metal. Compressive surface alloying. The techniques required to are two methods for developing com- Fatigue Resistance of Steels / 681

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0 0 _.:iiiiiiii!:ii!::si!ii~::ii:i:ili::i:i.::.:i:: ::ii.:: ::.i ::.::.:: ::.:.::: ~ 70 103 104 105 10~ 107 108 ,o0,',iiiiiiiiiiiiiiiiiiii iii i' i i i i i' i' iiiii , o4 .ol o 4oo1 ,0 Number of cycles to failure 20 30 40 50 60 70 Effect of decarburization on the fatigue be- Hardness, HRC Fig. 18 havior of a steel

Effect of carbon content and hardness on fatigue limit of through-hardened and tempered 4140, 4053, "~" 1 6 and 4063 steels. See the sections "Composition" and "Scatter of Data" in this article for additional tensitic, the fatigue limit will be lower (Fig. discussions. 22). Pearlitic structures, particularly those with coarse pearlite, have poor resistance to 1100 fatigue. S-N curves for pearlitic and sphe- o Small inclusions roidized structures in a eutectoid steel are • Large inclusions shown in Fig. 23. 1000 Macrostructure differences typical of 140 those seen when comparing ingot cast to continuously cast steels can have an effect 900 on fatigue performance. While there is no inherent difference between these two types 120 .~ of steel after rolling to a similar reduction in E 800 area from the cast ingot, bloom, or billet, < ingot cast steels will typically receive much larger reductions in area (with subsequent 700 100 refinement of grain size and inclusions) than will continuously cast billets when rolled to a constant size. Therefore, the billet size of 60~03 104 105 106 107 108 continuously cast steels becomes important Number of cycles to failure to fatigue, at least as it relates to the size of the material from which the part was fabri- Effect of nonmetallic inclusion size on fatigue. Steels were two lots of AISI-SAE 4340H; one lot (lower "b" 1 7 curve) contained abnormally large inclusions; the other lot (upper curve) contained small inclusions. cated. A significant amount of research has shown that for typical structural applica- pressive residual stresses at the surface of tially reduce the fatigue life of the steel, as tions, strand cast reduction ratios should be the part. The improvement in fatigue life of shown in Fig. 8. Additional information on above 3:1 or 5:1, although many designers a crankshaft that results from is contained in Volumes 8 of critical forgings still insist on reduction is shown in Fig. 19. Shot peening is useful in and 13 of the 9th Edition of Metals Hand- ratios greater than 10:1 or 15:1. These larger recovering the fatigue resistance lost book. reduction ratio requirements will frequently through decarburization of the surface. De- Grain size of steel influences fatigue be- preclude the use of continuously cast steels carburized specimens similar to those de- havior indirectly through its effect on the because the required caster size would be scribed in Fig. 18 were shot peened, raising strength and fracture toughness of the steel. larger than existing equipment. While this the fatigue limit from 275 MPa (40 ksi) after Fine-grained steels have greater fatigue may not be a major problem at this time, decarburizing to 655 MPa (95 ksi) after shot strength than do coarse-grained steels. steel trends suggest that there will be very peening. Composition. An increase in carbon con- little domestic and almost no off-shore ingot Tensile residual stresses at the surface of a tent can increase the fatigue limit of steels, cast material available at any cost within the steel part can severely reduce its fatigue particularly when the steels are hardened to next two decades. The problem will be limit. Such residual stresses can be pro- 45 HRC or higher (Fig. 16). Other alloying reduced as larger and larger casters, ap- duced by through hardening, cold drawing, elements may be required to attain the proaching bloom and ingot sizes, are in- welding, or abusive grinding. For applica- desired hardenability, but they generally stalled. tions involving cyclic loading, parts con- have little effect on fatigue behavior. Creep-Fatigue Interaction. At tempera- taining these residual stresses should be Microstructure. For specimens having tures sufficiently elevated to produce creep, given a stress relief anneal if feasible. comparable strength levels, resistance to creep-fatigue interaction can be a factor Aggressive environments can substantially fatigue depends somewhat on microstruc- affecting fatigue resistance. Information on reduce the fatigue life of steels. In the ture. A tempered martensite structure pro- creep-fatigue interaction is contained in the absence of the medium causing corrosion, a vides the highest fatigue limit. However, if article "Elevated-Temperature Properties previously corroded surface can substan- the structure as-quenched is not fully mar- of Ferritic Steels" in this Volume. 682 / Service Characteristics of Carbon and Low-Alloy Steels

1200 Application of Fatigue Data 160 The application of fatigue data in engi- ,/- Nitrided crankshafts 140 neering design is complicated by the char- 1000 ~ .~~~~ 120 acteristic scatter of fatigue data; variations in surface conditions of actual parts; varia- tions in manufacturing processes such as 8°° bending, forming, and welding; and the un- ~Shotp .... d .... kshafts certainty of environmental and loading con- ~~ ::!i!S::::. 108 ditions in service. In spite of the scatter of fatigue data, it is possible to estimate ser- g ~: test bars ~" vice life under cyclic loading. It is essential = • to view such estimates for what they are, ,~ 8oo ~ ~ 80 that is, estimates of the mean or average performance, and to recognize that there heat treated / n may be large discrepancies between the 500 crankshafts zx // / / estimated and actual service lives. / Scatter of Data. Fatigue testing of test Transverse / .~, test bars specimens and actual machine components produces a wide scatter of experimental ,oo 6 results (see Fig. 25 and Ref 10 for exam- ples). The data in Fig. 25 represent fatigue 350 i life simulated-service testing of 25 lots of 12 105 lO6 ~ ~ torsion bars each. In this program, the r ,~, m coefficient of variation, CN, defined as the Fatigue limits, Z ratio of the standard deviation of the mean Cycles. to failure standard test bars value, of fatigue life was 0.28. In Table 3, Effect of nitriding and shot peening on fatigue behavior. Comparison between fatigue limits of the range of values of the coefficient of Fig. 1 9 crankshafts (S-Nbands) and fatigue limits of separate test bars, which are indicated by plotted points variation for fatigue strength is compared at right. Steel was 4340. with those for other mechanical properties. For specimens tested near the fatigue Table 2 Improvement in the fatigue limits of SAE 4340 steel with the reduction of limit, the probable range of fatigue life be- nonmetallic inclusions by vacuum melting compared to electric furnace melting comes so large that it is pointless to com- Longitudinal Transverse fatigue Ratio of pute a coefficient of variation for fatigue fatigue limit(a) limit(a) transverse to Hardness, life. Instead, values of CN are calculated for MPa ksi MPa ksi longitudinal HRC the fatigue limit. Approximately 1000 fa- Electric furnace melted ...... 800 116 545 79 0.68 27 tigue specimens were made from a single Vacuum melted ...... 960 139 825 120 0.86 29 heat of aircraft quality 4340 steel; all were (a) Determined in repeated bending fatigue test (R - 0L Source: Ref 12 taken parallel to the fiber axis of the steel. The specimens were heat treated to three different strength levels and polished to a The orientation of cyclic stress relative to ent will be elongated in the rolling direction surface roughness of 0 to 0.050 i~m (0 to 2 the fiber axis or rolling direction of a steel and will reduce fatigue life in the transverse txin.). Fatigue limits for these specimens are can affect the fatigue limit of the steel. direction. The use of vacuum melting to given in terms of the percent surviving 10 Figure 24 shows the difference between the reduce the number and size of nonmetallic million cycles (Fig. 26). It should be noted fatigue limit of specimens taken parallel to inclusions therefore can have a beneficial that the scatter increases as the strength the rolling direction and those taken trans- effect on transverse fatigue resistance (Ta- level is increased; a similar trend is shown verse to it. Any nonmetallic inclusions pres- ble 2). in Fig. 16. ,1.o [ 20 shafts

,320 6 shafts

1035 5 shafts Surface hardness, Steel HRC Hardening process

4140 ...... 36--42 Through hardened 1137 4320 ...... 4(~46 Carburized to 1.0-1.3 m (0.040-0.050 in.) 5 shafts 1035 ...... 42-48 Induction hardened to 3 mm (0.120 in.) min effective depth (40 HRC) 0.2 0.4 0.6 0.8 1.0 1.2 1137 ...... 42-48 Induction hardened to 3 mm (0.120 in.) min effective depth (40 HRC) Number ofcyclesto failure, millions Effect of carburizing and surface hardening on fatigue life. Comparison of carburized, through-hardened, and induction-hardened transmission shafts tested Fig. 20 in torsion. Arrow in lower bar on chart indicates that one shaft had not failed after the test was stopped at the number of cycles shown.