Taylor [16], in a review of environmental effects on fretting fretting-fatigue, points out that the environment “can have a profound effect on the nature and degree of the resultant surf
Trang 10 1 2 3 4 5
Kσ
K P
Kσ+KP
Figure 6.16. Stress intensity from contact stresses and far field stress = 10.
0 0.5 1 1.5 2
Kσ
KP
Figure 6.17. Stress intensity from contact stresses and far field stress = 100.
and 1000, respectively In Figure 6.16, it is clearly seen that for = 10, the local contact stresses are dominant up to a crack length of approximately a/b= 005 and, as mentioned above, there is a significant decrease in K up to that crack length Figure 6.18, on the other hand, shows that the far-field stress, , is dominant for all crack lengths and K
is a continually increasing function Finally, the intermediate case shown in Figure 6.17 illustrates a similar contribution from and P at a crack length of approximately a/b= 001 From these observations, it is demonstrated that the relative magnitude of the local contact stresses compared to the far-field stresses is a major factor in determining the
Trang 20 0.5 1 1.5 2
Kσ
KP
Kσ+ KP
Figure 6.18. Stress intensity from contact stresses and far field stress = 1000.
tendency or lack thereof for a crack to initiate and then to either continue propagating or arrest A consequence of this is the interpretation of experimental data and observations where the far-field stresses should be considered in deciding if a crack arrest phenomenon
is likely or possible to occur
6.6 MECHANISMS OF FRETTING FATIGUE
The history of fretting goes back almost an entire century The first report of fretting appears to be that of Eden et al [10] in 1911 while the first systematic experimental investigation of the process is attributed to Tomlinson [11] in 1927 Fretting has tradition-ally been linked closely with corrosion, oxidation, or other environmental effects In the early days of fretting-fatigue research as we now define it, the topic was commonly called
“fretting corrosion” (see Forrest [12], for example) The definition of the phenomenon does not seem to have changed According to Forrest [12] in 1962,
If two solid surfaces in contact are subjected to a repeated relative movement of small amplitude, some damage to the surfaces may occur and this is known as fretting corrosion Its presence is usually recognized by the corrosion products formed, which consist of finely divided oxide particles The appearance of oxide particles is usually accompanied by localized pitting of the surfaces in the fretted region and this can result in serious reductions
in fatigue strengths The mechanism of fretting corrosion is not yet fully understood and this
is reflected by the number of alternative terms used to describe the same process, for example friction oxidation, wear oxidation, chafing, and false brinelling The process is a form of mechanical wear which can occur without corrosion, but which can be greatly aggravated if corrosion occurs simultaneously
Trang 3In recent times, fretting fatigue has been addressed by some researchers almost entirely from a mechanics viewpoint, irrespective of the corrosion process There is no question, however, that environmental effects play an important role in the process, even if the only consideration in a mechanics approach is the evolution of the COF Poon and Hoeppner [13], for example, found that the number of cycles to failure in fretting-fatigue experiments on 7075-T6 aluminum in vacuum was between 10 and 20 times longer than that tested in laboratory air They concluded that the chemical factor plays the dominant role in reducing specimen life when fretting occurs simultaneously with fatigue It is hoped and certainly believed by the author that the purely mechanics approach that uses realistic values of the COF, as successful as it has been, will not fall into the following category noted by Schütz [14] in his review of the history of fatigue: “In every time period there are one or more unrealistic ideas and solutions which at the time are followed enthusiastically by some distinguished scientists and engineers; with the benefit
of hindsight, however, their delusions appear incredible!”
The effects of corrosion cannot be dismissed in a mechanics-based approach to fretting fatigue, even if it is just to adjust the COF to represent what occurs during the fretting process In one of the earliest works on fretting corrosion, Tomlinson et al [4] concluded that for surfaces in closely fitting contact subjected to vibration, that corrosion is mechan-ical rather than chemmechan-ical in character Vibration or alternating surface stress alone was not expected to cause corrosion It was the relative surface slip, alternating in direction, that was the necessary condition They surmised that slip effectively causes corrosion, even if it is reduced to the order of molecular dimensions, and is always present including
on lubricated surfaces In one experiment where a total slip amplitude of 23× 10−6 in. (0058 m) was used, surfaces subjected to 300 000 reversals resulted in a slight but nar-row ring of corrosion debris [4] In an earlier experimental investigation, Tomlinson [11] concluded that the fretting action was a particular manifestation of molecular cohesion between the surfaces These early observations led to conclusions that the fretting-fatigue process involved corrosion in association with slip and the attrition of the mating surfaces
is caused in some way by the severance of cohesion bonds For these and other reasons, the terminology “fretting corrosion” was widely used to describe an event that occurs on and near the surface as distinguished from fatigue that is associated with cyclic straining
of the material as a whole
It is not surprising, therefore, to find that adhesion has been considered in developments
in the mechanics of contact fatigue Giannakopoulos et al [15] have shown, for example, that in the contact between a cylinder and a flat surface the pressure is bounded and zero at the edge of contact without adhesion, but that the presence of strong adhesion would cause the pressure to become singular at the new edge of contact Even for weakly adhered surfaces, stresses near the adhered stick zone boundary are square root singular These local stress fields are entirely different than those calculated without consideration
of adhesion
Trang 4The environment in which fretting takes place still has to be considered in fretting-fatigue life prediction Taylor [16], in a review of environmental effects on fretting fretting-fatigue, points out that the environment “can have a profound effect on the nature and degree
of the resultant surface damage and fatigue crack generation.” He points out the need to consider the possible interactions between fretting and corrosion in the crack initiation stage In particular, he notes that the resultant corrosion products can lead to a reduction
in the COF and development of protective surface films The major conclusions of the overview by Taylor [16] are:
The mechanism of fretting fatigue includes chemical and mechanical factors, the observed damage commonly resulting from both The factor which dominates is dependent on the particular circumstances prevailing Most researchers favour the chemical factor as playing the major role in reducing fretting fatigue life with the mechanical damage serving to disrupt surface films and expose underlying chemically reactive sites Cathodic protection which removes deleterious electrochemical effects on both the generation and propagation of fatigue cracks greatly improves fretting fatigue performance, usually returning values to or above those found in air
The fretting fatigue behaviour can be significantly affected by the nature of the corrosion products forming within the fretted region Thick layers of such product may reduce the coefficient of friction between contacting surfaces and also provide some protection to the surfaces, thereby delaying the generation of fatigue cracks
Another aspect of the corrosion effect in fretting fatigue that has not received a large amount of attention, at least in a quantitative sense, is the role that corrosion debris has
on the crack propagation behavior in the contact region In particular, debris that forms and lodges in the crack can play an important role in developing crack closure that, in turn, can reduce the effective stress intensity by keeping the crack tip open at low applied loads Conner et al [17] characterized the mechanisms of damage in fretting fatigue using three different test systems and four different pad geometries They observed that the wear mechanism, which is reported to increase with slip displacement as described in the work of Vingsbo and Söderberg [1], also results in an increase in the production of wear particles that can enter cracks and retard crack propagation They observed cracks of the order of 5 m in length that were filled with debris The growth of such cracks would be influenced by the presence of debris in the crack wake, and the presence of this debris was observed to be independent of contact geometry or loading conditions This is just another factor that should be considered in the development of a robust analysis of the fretting-fatigue phenomenon
6.7 MECHANICS OF FRETTING FATIGUE
The application of mechanics to predict fretting-fatigue lives has used crack initiation (or nucleation), crack propagation, or a combination of both as the basis for life prediction
Trang 5or the determination of fatigue limit conditions for HCF applications An investigation
by Faanes and Fernando [18] used a fracture mechanics approach because the authors determined that the “fracture process is dominated by crack growth.” Using a BS L65Al 4% Cu alloy, the authors used a simple short crack correction, like the one described for treating short cracks at notches in Chapter 5, by correcting the fatigue threshold Using a bridge pad fixture where a wide range of slip amplitudes could be achieved, they found good correlation of experimental fretting-fatigue lives with crack propagation analysis as shown in Figure 6.19 Their experiments covered a range in lives from below
105 cycles to beyond 106 cycles as shown in the figure They found that the behavior
of short cracks, accounted for in their analysis, was especially important for long lives approaching the HCF regime They also noted that the behavior of short cracks seemed
to have less influence on the lifetime in fretting fatigue compared to plain fatigue Of particular note is their use of an initial crack length for the fracture mechanics (crack growth) calculations assumed to be equal to the surface roughness which was reported to
be of the order of 5m for polished specimens The assumption of crack growth being dominant in fretting fatigue is also supported by the observations of Waterhouse [19] who observed that in normal fatigue, crack initiation may account for 90% of fatigue life However, in fretting fatigue, he observes that initiation could occur in only 5% or less of the fatigue life
Other investigations, such as that of Hills et al [20], support the contention that fretting fatigue is an initiation-controlled process In that study, a standard fretting-fatigue fixture (described later as a “partial load transfer fixture”) was used to conduct experiments
on HE15-TFAl-4wt.%Cu alloy up to run-out at 107 cycles The authors concluded that initiation is the dominant part of life in these long-life tests because fracture mechanics was
104
10 5
106
10 7
16.5 mm 34.35 mm
6.35 mm
Predicted (cycles) Pad span
Figure 6.19. Comparison of fretting fatigue lives with experiments for fracture mechanics calculations
cor-rected for short crack threshold [18].
Trang 6found to predict that “the time taken for the crack to grow from threshold to catastrophe
is only a small fraction of the measured life.” Similar conclusions have been drawn by Szolwinski and Farris [21] from calculations for experiments on a 4% Cu aluminum alloy For a life in excess of 106cycles, nucleation was found to consume over 95% of the total life of the specimen In their fracture mechanics calculations, an initial crack length of
1 mm deep was assumed as the transition size from nucleation to crack propagation Contrast these findings with those of Golden and Grandt [22] who found, in exper-iments on a Ti-6Al-4V titanium alloy, that at long lives in excess of 106 cycles, crack propagation life is an order of magnitude longer than initiation life In their fracture mechanics calculations, the initial crack length was assumed to be 25 m although the crack propagation life was found to be relatively insensitive to the starting crack size for the apparatus they were using Mutoh and Xu [23] reached similar conclusions based
on their experiments using bridge-type fixtures They note that a fretting-fatigue crack generally initiates in the very early stage (few percent of the whole life) for most metallic materials However, they point out that some materials like titanium alloys show very long fretting-fatigue crack initiation life
While no definitive conclusion can be drawn from the above examples, it is important
to note that crack propagation life can be sensitive to the material and its COF, the assumed initial flaw size that separates the initiation from the crack propagation phases, and the geometry of the test fixture or component The sensitivity of the analytical fracture mechanics computations to the type of test fixture and geometry, particularly at long lives
or threshold conditions for HCF, is discussed later
6.8 STRESS ANALYSIS OF CONTACT REGIONS
One of the features that makes the analysis and life prediction of a fretting-fatigue problem
so difficult is the unusual nature of the stress field in a region of contact While a square punch on an elastic body is known to have a singular∗ stress field at the edge of contact
(see [24] for example), even a flat pad with a blending radius produces a locally intense
stress field with steep gradients Solution of such problems with finite element methods demands sophisticated approaches involving very fine mesh sizes as well as methods for handling sliding contact between two bodies The case of a rounded punch on an infinite body with a flat surface was one of the first problems to be solved analytically While the stress field due to a normal force is smoothly distributed, a shear force produces
a singular (shear) stress field at the edge of contact if displacements are assumed to
∗
A singular stress field is one where the stresses become mathematically infinite as the distance from the origin
of the singularity goes to zero according to elasticity theory Stress ahead of a crack in fracture mechanics is
an example of a common singularity.
Trang 7P Q p
μp
–c –b
Stick region
Slip region
q
c
Figure 6.20. Stress distribution for cylinder on flat contact.
be continuous across the interface [25] Figure 6.20 illustrates the stress field of the cylindrical or spherical indentor on a flat, infinite surface The so-called Mindlin problem† assumes identical elastic materials, an infinite body, and no oscillatory bulk stresses The cylindrical contact pad is used widely because of the availability of a closed-form analytical solution Figure 6.20 illustrates some of the features that are characteristic of fretting-fatigue contact problems In this case, the normal stresses, p, due to the applied normal force, P, are smoothly distributed going from zero at the edge of contact,±c,
to a maximum at the center The shear stresses, q, due to an applied shear load, Q, are singular if the contact is perfect In the Mindlin solution, the displacements are assumed continuous between the contacting bodies, that is no slip occurs In reality, the shear stresses are limited by assumed Coulomb friction and, therefore, cannot exceed p at any location [25], where is the COF This results in a stick–slip contact, shown in the figure, where the bodies do not slide in the “stick” region between x= ±c, and sliding occurs in the “slip” zone between x= ±c and x = ±b, where q = p
†
The Mindlin solution is widely reported to have been developed independently by Cattaneo in Italy The paper
by Cattaneo is referenced in Mindlin’s article as having been pointed out to him by Dr Stewart Way, since two identical equations had been developed by Cattaneo The author is only familiar with the Mindlin solution because he studied elasticity under Prof Mindlin at Columbia University and, further, speaks or reads no Italian For completeness, the other reference is: Cattaneo, C., “Sul Contatto di Due Corpi Elastici: Distribuzione Locale
Delgi Sforzi,” Rendiconti dell’ Accademia dei Lincei, 27, Saeries 6, 1938, pp 342–348, 434–436, 474–478 (in
Italian).
Trang 8–2000 –1000 0 1000 2000
x (mm)
p(x)
q(x)
σxx
Figure 6.21. Stress field distribution in contact region of a dovetail fretting experiment [26].
Other contact geometries produce complex but not necessarily singular stress fields
in the contact region An example of a typical stress distribution under a contact pad is shown in Figure 6.21, taken from [26], where the contact pad has a 1 mm wide flat and
a 3 mm blending radius The figure shows that the local normal and shear stresses near the edge of contact have high local peaks The deformed edge of contact is beyond the flat portion of the pad due to the local elastic deformation due to the applied pressure Here, px , the pressure at the interface, is shown positive in compression The stress
of greatest interest is the axial stress in the specimen parallel to the surface denoted as
xx At the edge of the specimen where the applied bulk load is the highest (commonly referred to as the “trailing edge of contact”), the axial stress is maximum and has a very steep stress gradient in the x direction It will be seen later that a steep gradient also exists in a direction normal to the surface into the depth of the specimen The steep gradients combined with the biaxial stress states make life prediction from a fatigue initiation viewpoint a difficult problem In the example cited, where the material was Ti-6Al-4V, the peak stresses determined from an elastic analysis exceed the yield stress
of the material (930 MPa) The complexity of the stress analysis increases significantly if elastic-plastic analysis has to be conducted
6.8.1 Multiple crack considerations
The analysis of fretting fatigue is difficult because the damage process may involve multiple cracks [27, 28] The aspect ratio for a single crack changes drastically when individual cracks link up and produce long shallow cracks with highly irregular shapes The existence of multiple cracks that eventually link up is an equally difficult problem for developing initiation criteria as well as for applying fracture mechanics to track crack growth An example of multiple cracks developed under fretting fatigue is shown in Figure 6.22 where the fracture surfaces show the linking up of multiply initiated cracks
Trang 9100 μ m
200 μ m
Figure 6.22. SEM images of fretting fatigue cracks (contact region is on the top half of the images) and
corresponding fracture surface (below) The dark region on the fracture surface indicates the depth of the crack at the time the contact was removed (a) 700 m cracks Specimen edge is shown to the left of the images (b) 12 mm crack Specimen edge is shown to the right of the images The three separate dark region on the fracture surface indicate the size of the cracks at the time the contact was removed [29].
The reality of the formation of multiple cracks serves to point out the extreme difficulty that can be encountered when trying to develop models for the fretting-fatigue process
6.8.2 Analytical solutions
A common contact geometry that is used widely in fretting-fatigue experiments and one which models actual contact geometries such as those in a dovetail slots in turbine engines
is the flat pad with blending radii, shown in Figure 6.23 Closed-form solutions now exist for this contact geometry subject to the assumptions of a semi-infinite body as the substrate, elastic behavior for both materials, no bulk loads in the substrate, and similar properties for the two materials For the simplest case of two identical materials for the punch and substrate, the equations below are due to Ciavarella et al [30] who also handle the case of dissimilar materials In the nomenclature for Figure 6.23, the semi width, a,
c a b
c a b
y
x
P Q
Punch
Substrate
Figure 6.23. Schematic of flat indentor with blending radius.
Trang 10represents the flat portion of the punch that is in contact with the substrate The deformed edge of contact is at x= ±b, while the boundary between the slip region and the stick region is denoted by x= ±c For the case of the cylindrical punch, a subset of the more general case shown here, the flat dimension goes to zero and a= 0 in the solutions below For the cylindrical case, the exact solution given in [30] gives the contact pressure as
a→ 0 for the cylinder on flat as
px =2P
b
while for the other extreme of a flat punch with a sharp corner, where D→ 0 and b → a, the flat-on-flat contact pressure is given by
The relation between the contact half width, b, and the normal load, P, is [30]
PD
a2E∗ =
where the composite contact stiffness, E∗, for identical materials, is
From the same paper [30], the size of the stick zone due to a tangential load, Q, is
Q
P = 1 −c
b
2 − 2 − sin2
or
Q
where
and mu is the COF In the limit, as a→ 0, the classic case of the cylinder on flat is recovered
Q
P = 1 −c
b
2
(6.14)