ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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The second materials selection guide is the use of alloy compositions and thermomechanical treatments for

existing alloys that improve their fatigue-crack propagation resistance, as described elsewhere in this Volume

and in a variety of mechanical properties handbooks (Ref 45, 46, and 47).

Soft coatings provide a “sacrificial,” low-shear strength layer that reduces the magnitude of the oscillatory shear

stresses transmitted into the substrate. Both a lower coefficient of friction and a lower shear strength contribute.

A coating that dynamically recrystallizes under service conditions would be expected to be effective. Situations

that result in creep of the soft coating must be avoided, as the introduction of excessive clearance or a decrease

in preload on bolts or washers can occur. In addition, low friction of soft coatings can lead to larger relative

displacements for load-controlled fretting.

Diffusion treatments, such as sulfidized coatings on steel, were shown to be effective in delaying the initiation

of a propagating fatigue crack in carbon steels in the laboratory when impregnated with a suitable oil-in-water

emulsion (Ref 48) and subsequently applied successfully to compressor-blade roots (Ref 42).

Hard coatings minimize the areas of real contact and penetration by opposing asperities and are less prone to

adhesive wear. However, hard coatings have high friction coefficients. As such, high shear stresses are

transmitted into the coating, which can limit their effectiveness. Care must be taken in design of coating

thickness to avoid high shear stresses at the depth of the coating/substrate interface, which is typically a plane

of weakness.

Additionally, hard coatings, such as chromium platings, are often filled with cracks; sprayed molybdenum

coatings usually contain pores. These defects in the coatings can serve as initial sites for fatigue cracks to

develop and propagate into the substrate. Postcoating shot peening is recommended. Improvement in both

electrodeposited chromium and nickel coatings was achieved by thermal diffusion processing followed by shot

peening (Ref 42).

While hard coatings can reduce the overall fatigue strength compared with that of samples tested without prior

fretting, under fretting fatigue conditions they typically show an improvement over uncoated materials. A

pretreatment, such as shot peening or vapor blasting, may be required to compensate for the reduction in normal

fatigue strength due to the hard coating. In the case of carbon steel, sprayed molybdenum coatings were found

to increase the fretting fatigue strength from 33 to 72% of the normal fatigue strength compared with uncoated

samples (Ref 49).

Nonmetallic coatings offer improvement in fretting fatigue resistance by lowering the coefficient of friction and

preventing metal-to-metal welding at asperity contacts. The same types of substances that are considered solid

“boundary” lubricants for wear control can be used. Conversion coatings produced by phosphating and

anodizing, polymer sheets of nylon or polytetrafluoroethylene, and polymerized epoxy resins can all be used. In

the case of porous coatings, impregnation with oils or greases can provide effective means of reducing or

eliminating the occurrence of fretting fatigue when operating in the full-slip regime over the supply life of the

lubricant.

References cited in this section

24. R.B. Waterhouse, Fretting Fatigue, Int. Mater. Rev., Vol 37 (No. 2), 1992, p 77–97

39. R.B. Waterhouse and D.A. Saunders, The Effect of Shot-Peening on the Fretting Fatigue Behaviour of

an Austenitic Stainless Steel and a Mild Steel, Wear, Vol 53, 1979, p 381–386

40. G. Leadbeater, B. Noble, and R.B. Waterhouse, The Fatigue of an Aluminum Alloy Produced by

Fretting on a Shot Peened Surface, Advances in Fracture Research, Vol 3 (Fracture 84), 4–10 Dec 1984,

Pergmon Press

41. D.E. Taylor, Fretting Fatigue in High Temperature Oxidising Gases, Fretting Fatigue, R.B. Waterhouse,

Ed., Applied Science, 1981, p 177–202

42. R.B. Waterhouse, Avoidance of Fretting Fatigue, Fretting Fatigue, R.B. Waterhouse, Ed., Applied

Science, 1981, p 221–240

43. J.R. McDowell, in Symposium on Fretting Corrosion, STP 144, ASTM, 1952

44. E. Rabinowicz, Wear Coefficients—Metals, Wear Control Handbook, American Society of Mechanical

Engineers, 1980, p 475–501

45. AFML-TR-68-115, Aerospace Structural Metals Handbook, Materials and Ceramics Information

Center, Battelle Columbus Laboratories, 1991

46. MCIC-HB-OIR, Damage Tolerant Design Handbook, Materials and Ceramics Information Center,

Battelle Columbus Laboratories, 1983

47. MIL-HDBK-5F, Military Handbook for Metallic Materials and Elements for Aerospace Vehicle

Structures, U.S. Department of Defense, 1990

48. R.B. Waterhouse and M. Allery, The Effect of Non-Metallic Coatings on the Fretting Corrosion of Mild

Steel, Wear, Vol 8, 1965, p 112–120

49. D.E. Taylor and R.B. Waterhouse, Sprayed Molybdenum Coatings as a Protection Against Fretting

Fatigue, Wear, Vol 20, 1972, p 401–407

Fretting Fatigue Testing

S.J. Shaffer and W.A. Glaeser, Battelle Memorial Institute

Acknowledgments

This article was adapted from S.J. Shaffer and W.A. Glaeser, Fretting Fatigue, Fatigue and Fracture, Vol 19,

ASM Handbook, ASM International, 1996, p 314–320.

Fretting Fatigue Testing

S.J. Shaffer and W.A. Glaeser, Battelle Memorial Institute

References

1. R.B. Waterhouse, Ed., Fretting Fatigue, Applied Science, 1981

2. M.H. Attia and R.B. Waterhouse, Ed., Standardization of Fretting Fatigue Test Methods and

Equipment, STP 1159, ASTM, 1992

3. D.A. Hills and D. Nowell, Mechanics of Fretting Fatigue, Kluwer Academic Publishers, 1994

4. R.B. Waterhouse, Fretting Corrosion, Fretting Fatigue, Pergamon Press, 1972

5. Proc. Specialists Meeting on Fretting in Aircraft Systems, AGARD-CP-161, Advisory Group for

Aerospace Research and Development, 1974

6. R.D. Mindlin, Compliance of Elastic Bodies in Contact, J. Appl. Mech., Vol 16, 1949, p 259–268

7. R.B. Waterhouse, Theories of Fretting Processes, Fretting Fatigue, Applied Science, 1981, p 203–220

8. D.J. White, Proc. Inst. Mech. Eng., Vol 185, 1970–1971, p 709–716

9. C. Ruiz and K.C. Chen, Life Assessment of Dovetail Joints between Blades and Disks in Aero-Engines,

paper C241/86, Proc. Conf. Fatigue of Engineering Materials and Structures, Institute of Mechanical

Engineers, 1986, p 187–194

10. M. Takeuchi and R.B. Waterhouse, Fretting-Corrosion-Fatigue of High Strength Steel Roping Wire and

Some Protective Measures, Proc. Int. Conf. Evaluation of Materials Performance in Severe

Environments, EVALMAT 89, Iron and Steel Institute of Japan, 1989, p 453–460

11. J.A. Collins, Fretting, Fretting Fatigue, and Fretting Wear, Failure of Materials in Mechanical Design—

Analysis, Prediction, Prevention, 2nd ed., John Wiley & Sons, 1992, p 504–524

12. K. Nishioka and K. Hirakawa, Fundamental Investigations of Fretting Fatigue, Part 3, Some Phenomena

and Mechanisms of Surface Cracks, Bull. Jpn. Soc. Mech. Eng., Vol 12 (No. 51), 1969, p 397–407

13. K. Nishioka and K. Hirakawa, Fundamental Investigations of Fretting Fatigue, Part 5: The Effect of

Relative Slip Amplitude, Bull. Jpn. Soc. Mech. Eng., Vol 12 (No. 52), 1969, p 692–697

14. M.H. Wharton, R.B. Waterhouse, K. Hirakawa, and K. Nishioka, The Effect of Different Contact

Materials on the Fretting Fatigue Strength of an Aluminum Alloy, Wear, Vol 26, 1973, p 253–260

15. D. Nowell and D.A. Hills, Crack Initiation Criteria in Fretting Fatigue, Wear, Vol 136, 1990, p 329–343

16. D.A. Hills and D. Nowell, Mechanics of Fretting Fatigue, Kluwer Academic Publishers, 1994, p 210

17. S.C. Gordelier and T.C. Chivers, A Literature Review of the Palliatives for Fretting Fatigue, Wear, Vol

56, 1979, p 177–190

18. J.A. Collins and S.M. Marco, The Effect of Stress Direction during Fretting on Subsequent Fatigue Life,

Proc. ASTM, Vol 64, 1964, p 547–560

19. K. Nishioka and K. Hirakawa, Fundamental Investigations of Fretting Fatigue, Part 4: The Effect of

Mean Stress, Bull. Jpn. Soc. Mech. Eng., Vol 12 (No. 51), 1969, p 408–414

20. M.H. Wharton, D.E. Taylor, and R.B. Waterhouse, Metallurgical Factors in the Fretting Fatigue

Behaviour of 70/30 Brass and 0.7% Carbon Steel, Wear, Vol 23, 1973, p 251–260

21. R.B. Waterhouse and D.E. Taylor, The Initiation of Fatigue Cracks in a 0.7% Carbon Steel by Fretting,

Wear, Vol 17, 1971, p 139–147

22. R.B. Waterhouse and M. Allery, The Effect of Powders in Petrolatum on the Adhesion between Fretted

Surfaces, Trans. ASLE, Vol 9, 1966, p 179

23. D.J. Gaul and D.J. Duquette, The Effect of Fretting and Environment on Fatigue Crack Initiation and

Early Propagation in a Quenched and Tempered 4130 Steel, Metall. Trans. A, Vol 11, Sept 1980, p

1555–1561

24. R.B. Waterhouse, Fretting Fatigue, Int. Mater. Rev., Vol 37 (No. 2), 1992, p 77–97

25. J.A. Collins and F.M. Tovey, Fretting-Fatigue Mechanisms and the Effect of Motion on Fatigue

Strength, J. Mater., Vol 7 (No. 4), 1972, p 460–464

26. M.M. Hamdy and R.B. Waterhouse, The Fretting Fatigue Behavior of Ti-6Al-4V at Elevated

Temperatures, Wear, Vol 56, 1979, p 1–8

27. M.M. Hamdy and R.B. Waterhouse, The Fretting Fatigue Behavior of a Nickel-Based Alloy (Inconel

718) at Elevated Temperatures, Wear of Materials, American Society of Mechanical Engineers, 1979, p

351–355

28. M.P. Overs, S.J. Harris, and R.B. Waterhouse, in Wear of Materials, American Society of Mechanical

Engineers, 1979, p 379–387

29. C. Poon and D.W. Hoeppner, The Effect of Environment on the Mechanism of Fretting Fatigue, Wear,

Vol 52, 1979, p 175–191

30. R.B. Waterhouse, Fretting Fatigue in Aqueous Electrolytes, Fretting Fatigue, R.B. Waterhouse, Ed.,

Applied Science, 1981, p 159–177

31. K. Endo, Practical Observations of Initiation and Propagation of Fretting Fatigue Cracks, Fretting

Fatigue, R.B. Waterhouse, Ed., Applied Science, 1981, p 127–141

32. K. Nishioka and K. Hirakawa, Some Further Experiments on the Fatigue Strength of Medium Carbon

Steel, Proc. Mech. Behav. Mater., Vol 3, 1971, p 308–318

33. M.H. Wharton and R.B. Waterhouse, Environmental Effects in the Fretting Fatigue of Ti-6Al-4V, Wear,

Vol 62, 1980, p 287–297

34. D.W. Hoeppner, Environmental Effects in Fretting Fatigue, Fretting Fatigue, R.B. Waterhouse, Ed.,

Applied Science, 1981, p 143–158

35. D. Godfrey and J. Bailey, Early Stages of Fretting of Copper, Iron and Steels, Lub. Eng., Vol 10, 1954,

p 155–159

36. G. Sachs and P. Stefan, Chafing Fatigue Strength of Some Metals and Alloys, Trans. ASM, Vol 29,

1941, p 373–401

37. R.K. Reeves and D.W. Hoeppner, Microstructural and Environmental Effects on Fretting Fatigue, Wear,

Vol 47, 1978, p 221–229

38. K. Endo and H. Goto, Initiation and Propagation of Fretting Fatigue Cracks, Wear, Vol 38, 1976, p 311–

324

39. R.B. Waterhouse and D.A. Saunders, The Effect of Shot-Peening on the Fretting Fatigue Behaviour of

an Austenitic Stainless Steel and a Mild Steel, Wear, Vol 53, 1979, p 381–386

40. G. Leadbeater, B. Noble, and R.B. Waterhouse, The Fatigue of an Aluminum Alloy Produced by

Fretting on a Shot Peened Surface, Advances in Fracture Research, Vol 3 (Fracture 84), 4–10 Dec 1984,

Pergmon Press

41. D.E. Taylor, Fretting Fatigue in High Temperature Oxidising Gases, Fretting Fatigue, R.B. Waterhouse,

Ed., Applied Science, 1981, p 177–202

42. R.B. Waterhouse, Avoidance of Fretting Fatigue, Fretting Fatigue, R.B. Waterhouse, Ed., Applied

Science, 1981, p 221–240

43. J.R. McDowell, in Symposium on Fretting Corrosion, STP 144, ASTM, 1952

44. E. Rabinowicz, Wear Coefficients—Metals, Wear Control Handbook, American Society of Mechanical

Engineers, 1980, p 475–501

45. AFML-TR-68-115, Aerospace Structural Metals Handbook, Materials and Ceramics Information

Center, Battelle Columbus Laboratories, 1991

46. MCIC-HB-OIR, Damage Tolerant Design Handbook, Materials and Ceramics Information Center,

Battelle Columbus Laboratories, 1983

47. MIL-HDBK-5F, Military Handbook for Metallic Materials and Elements for Aerospace Vehicle

Structures, U.S. Department of Defense, 1990

48. R.B. Waterhouse and M. Allery, The Effect of Non-Metallic Coatings on the Fretting Corrosion of Mild

Steel, Wear, Vol 8, 1965, p 112–120

49. D.E. Taylor and R.B. Waterhouse, Sprayed Molybdenum Coatings as a Protection Against Fretting

Fatigue, Wear, Vol 20, 1972, p 401–407

Fretting Fatigue Testing

S.J. Shaffer and W.A. Glaeser, Battelle Memorial Institute

Selected References

• R.B. Waterhouse, Fretting Wear, Friction Lubrication and Wear Technology, Vol 18, ASM Handbook,

ASM International, 1992, p 242–256

• R.B. Waterhouse and T.C. Lindley, Fretting Fatigue, ESIS 18, Mechanical Engineering Publications,

1994

• O. Vingsbo and S. Söderberg, On Fretting Maps, Wear, Vol 126, 1988, p 131–147

• D.W. Hoeppner et al., Fretting Fatigue: Current Technologies and Practices, STP 1367, ASTM, 2000

Fatigue Crack Growth Testing

Ashok Saxena, Georgia Institute of Technology; Christopher L. Muhlstein, University of California, Berkeley

Introduction

FATIGUE is generally understood to be a process dominated by cyclic plastic deformation, such that fatigue

damage can occur at stresses below the monotonic yield strength. The process of fatigue cracking generally

begins from locations where discontinuities exist or where plastic strain accumulates preferentially in the form

of slip bands. In most situations, fatigue failures initiate in regions of stress concentration, such as sharp

notches, nonmetallic inclusions, or at preexisting cracklike defects. Where failures occur at sharp notches or

other stress raisers, cracks first initiate and then propagate to critical size, at which time sudden failure occurs.

The fatigue life consists of crack initiation as well as crack propagation. On the other hand, when fatigue

failures are caused by large inclusions or preexisting cracklike defects, the entire life consists of crack

propagation. Such situations are commonly encountered in service failures. A typical example of such a failure

in a railroad track is shown in Fig. 1. The light area in the photograph is the region of fatigue crack growth, and

the surrounding darker area is the region of fast fracture. The dark spot within the light area is the origin of the

failure, which is a preexisting defect due to a hydrogen flake.

Fig. 1 Fatigue failure of a railroad track

Testing of smooth or notched specimens generally characterizes the overall fatigue life of a specimen material.

This type of testing, however, does not distinguish between fatigue crack initiation life and fatigue crack

propagation life. With this approach, preexisting flaws or cracklike defects, which would reduce or eliminate

the crack initiation portion of the fatigue life, cannot be adequately addressed. Therefore, testing and

characterization of fatigue crack growth is used extensively to predict the rate at which subcritical cracks grow

due to fatigue loading. For components subjected to cyclic loading, this capability is essential for life

prediction, recommendation of a definite accept/reject criterion during nondestructive inspection, and

calculation of in-service inspection intervals for continued safe operation.

Fatigue Crack Growth Testing

Ashok Saxena, Georgia Institute of Technology; Christopher L. Muhlstein, University of California, Berkeley

Fracture Mechanics in Fatigue

Linear elastic fracture mechanics (LEFM) is an analytical framework that relates the magnitude and distribution

of stress in the vicinity of a crack tip to the nominal stress applied to the structure; to the size, shape, and

orientation of the crack or cracklike imperfection; and to the crack growth and fracture resistance of the

material. The approach is based on the analysis of stress-field equations, which show that the elastic stress field

in the region of a crack tip can be described by a single parameter, K called the stress-intensity factor. This

same approach is also used to characterize fatigue crack growth rates (da/dN) in terms of the cyclic stress-

intensity range parameter (ΔK).

When a component or specimen containing a crack is subjected to cyclic loading, the crack length (a) increases

with the number of fatigue cycles (N) if the load amplitude (ΔP), load ratio (R), and cyclic frequency (ν), are

held constant. The da/dN increases as the crack length increases during a given test. The da/dN is also higher at

any given crack length for tests conducted at higher load amplitudes. Thus, the following functional

relationship can be derived from these observations:

(Eq 1)

where the function f is dependent on the geometry of the specimen, the crack length, the loading configuration,

and the cyclic load range. This general relation is simplified with the use of the ΔK parameter as summarized

below.

Correlation between da/dN and ΔK. In 1963, Paris and Erdogan (Ref 1) published an analysis with considerable

fatigue crack growth rate (FCGR) data and demonstrated that a correlation exists between da/dN and the cyclic

stress intensity parameter, ΔK. They argued that ΔK characterizes the magnitude of the fatigue stresses in the

crack-tip region; hence, it should characterize the crack growth rate. Such a proposition is in obvious agreement

with the functional relationships of Eq 1. The parameter ΔK accounts for the magnitude of the load range (ΔP)

as well as the crack length and geometry. A number of later studies (Ref 2) have confirmed the findings of Paris

and Erdogan. The data for intermediate FCGR values can be represented by the following simple mathematical

relationship, commonly known as the Paris equation:

(Eq 2)

where C and n are constants that can be obtained from the intercept and slope, respectively, of the linear log

da/dN versus log ΔK plot. This representation of FCGR is a useful model for midrange FCGR values (Fig. 2).

Fig. 2 Fatigue crack growth regimes versus ΔK

It has been shown and it is generally believed that specimen thickness has no significant effect on the FCGR

behavior (Ref 3). The ability of ΔK to account for so many variables has tremendous significance in the

application of the data. Thus, the FCGR behavior expressed as da/dN versus ΔK can be regarded as a

fundamental material property analogous to the yield and ultimate tensile strengths and plane strain fracture

toughness, K

. From the knowledge of this property, prediction of the crack length versus cycles behavior of

any component using that material and containing a preexisting crack or cracklike defect can be obtained, as

long as the fatigue stresses in the component are known and a K expression for the crack/load configuration is

available.

Crack-Tip Plasticity during Fatigue. The cyclic stress-intensity parameter, ΔK, is based on LEFM, and it

characterizes only the elastic stress field beyond the plastic zone. However, fatigue is a process dominated by

cyclic plastic deformation. Even when fatigue damage occurs at stresses below the monotonic yield strength,

the process of fatigue cracking begins from locations where there are discontinuities, such as nonmetallic

inclusions, or from surfaces where plastic strain accumulates preferentially in the form of slip bands (Ref 4).

Therefore, a brief explanation is given for why ΔK can characterize fatigue crack growth behavior.

When a cracked body is subjected to cyclic loading, a monotonic plastic zone develops at the crack tip during

the first loading cycle. If predominantly linear elastic conditions are maintained during loading, as are

necessary for ΔK to be a valid crack-tip parameter, compressive stress develops within this plastic zone during

unloading. Compressive stress develops, because the elastic forces in the overall body tend to restore the

original shape (Ref 2). The magnitude of the maximum compressive stress increases as the crack tip is

approached. In a small region within the monotonic plastic zone, the maximum compressive stress exceeds the

yield strength, resulting in plastic flow in compression. This small region of reversing plastic flow is called the

cyclic plastic zone. A simple estimate of the size of this zone was made by Paris (Ref 2) and Rice (Ref 5) for

nonhardening materials by substituting 2σ

in place of σ

in the expression for monotonic plastic zone size and

by replacing K with ΔK:

(Eq 3)

where r

is the cyclic plastic zone size under plane-stress conditions. For materials that undergo cyclic

hardening or softening, a first-order estimate of the fatigue plastic zone size can be obtained by replacing σ

with the cyclic yield strength (σ

cys

) in Eq 3.

General Crack Growth Behavior. When crack growth rates over six to seven decades are plotted against ΔK, the

behavior is no longer a straight line on a log-log plot. Results of FCGR tests for nearly all metallic structural

materials have shown that the da/dN versus ΔK curves have three distinct regions. The behavior in region I

(Fig. 2) exhibits a fatigue crack growth threshold, ΔK

, which corresponds to the stress-intensity factor range

below which cracks do not propagate. Equation 2 is applicable in the midrange of da/dN values for FCGR

(region II, Fig. 2). Typically, the validity of Eq 2 is limited over a range of two to four decades for midrange

crack growth rates.

At high ΔK values (region III, Fig. 2), the K

max

approaches the critical K for instability, K

, and the crack

growth rate accelerates. In some instances, K

may be equal to K

, but this situation cannot be generalized

because the FCGR specimens or even actual components may not always satisfy size requirements for valid

linear elastic plane-strain conditions. In some materials, there is also an effect of prior fatiguing on the K value

at which instability occurs (Ref 6). In such situations, K

will not be equal to the K

of the material.

At low ΔK values (region I, Fig. 2), the crack growth rate decreases rapidly with decreasing ΔK, and ultimately

ΔK approaches a threshold value, ΔK

, when the crack growth rate approaches zero. In high-cycle fatigue

applications, ΔK

is an important design parameter. The above definition of ΔK

is an idealized definition; for

practical usage, it is important to define its value unambiguously. An operational value of ΔK

is frequently

defined as the ΔK value at a da/dN of 10

-10

m/cycle (Ref 7).

FCGR under Elastic-Plastic Conditions. There are applications when fatigue crack growth occurs under

conditions of gross plastic deformation, or at least under conditions for which dominant linear elasticity cannot

be ensured. As a crack tip parameter, ΔK breaks down under these conditions and can no longer be expected to

uniquely characterize FCGR behavior. Dowling and Begley have defined a cyclic J-integral, ΔJ, which is

determined utilizing the loading portion of the load-displacement diagram during cyclic loading (Ref 8, 9).

Metals and alloys can be assumed to deform according to the cyclic stress-strain law given by:

(Eq 4)

where Δε is the cyclic strain range, Δσ is the cyclic stress range, E is the elastic modulus, and D′ and m′ are

empirically determined material constants. The value of ΔJ for such materials can be defined (Ref 10):

(Eq 5)

The term ΔJ in Eq 5 is a path-independent integral along any given path Γ that originates at the lower crack

surface and ends on the upper crack surface traversing along the contour in a counterclockwise direction. The

definition of ΔJ is written as a direct analogy to Rice's J-integral (Ref 11), used extensively in characterizing

fracture under monotonic loading conditions. The term ΔW in Eq 5 is defined as follows:

ΔW = Δσ

d (Δε

)

(Eq 6)

Other terms in Eq 5 and 6 are:

• ΔT

is the range of the traction vector

• Δu

is the range of displacement

• ds is an element along the contour Γ

• Δσ

and Δε

are the ranges of the stress and strain, respectively

All range quantities are calculated by subtracting the values at minimum load from the corresponding values at

maximum load. When ΔJ is defined in the above manner, its value characterizes the crack-tip stress and strain

ranges according to the Hutchinson (Ref 12) and Rice and Rosengren (Ref 13) relationships. It must also be

noted that for linear elastic conditions, Eq 5 will yield the following relationship:

(Eq 7)

From the above relationship, the data from linear elastic tests and elastic-plastic or fully plastic tests can be

combined into a single plot of da/dN with ΔK or . Similarly, the data can be correlated with ΔK

/E or

ΔJ. Figure 3 shows the FCGR data for A533 and for 304 stainless steel in this manner (Ref 9, 14). These data

were developed on specimens of two geometries and, more notably, with varying sizes within those geometries.

Thus, small specimens exhibited considerable plasticity, and the large specimens were under dominantly elastic

conditions. Despite the enormous differences in the scales of plasticity among the various tests, the FCGR data

lay in a single scatter band.

Fig. 3 Fatigue crack growth rate obtained under linear elastic and elastic-plastic conditions in (a) A533

steel and (b) 304 stainless steel. CC, center-cracked specimen; CT, compact-type specimen. Source: Ref

9, 14

Crack Closure. The concept of crack closure was first introduced by Elber (Ref 15, 16) as an effect from a zone

of residual deformation left in the wake of a growing fatigue crack. According to this concept, crack surfaces at

the crack tip might stay closed during a portion of the fatigue cycle due to compressive residual stress acting at

the crack tip. Elber further postulated that this portion of the loading cycle is ineffective in growing the fatigue

crack; thus, the corresponding load should be subtracted from the applied ΔP to determine the effective value of

ΔK.

Figure 4 presents a series of schematic sketches that show the stress and strain distributions at the crack tip at

maximum and minimum load. At the maximum load, A, all the load is borne by the uncracked ligament,

because cracks are unable to transmit the load. At the minimum load, B, there are compressive stresses to the

left of the crack tip, because there is contact between opposing crack surfaces within the zone of residual plastic

deformation. This contact causes the effective stiffness of the cracked body to change, which manifests itself in

the load-displacement diagram. Thus, the crack closure load can be defined as the load at which this change in

stiffness occurs.