High Cycle Fatigue: A Mechanics of Materials Perspective part 23 pdf

While the behavior of the baseline cycle defined by OLR = 1.0 is predictable with linear summation of the LCF and HCF cycles, the additional effect of the overload is both to reduce the

the LCF cycles can be considered to be an underload on the baseline HCF cycles On top

of this simple spectrum, a single overload is added to the baseline LCF cycle Defining the overload ratio as OLR= Kmax/Kss, experiments were carried out to see when the onset

of HCF activity occurred The results, based on the use of a number of values of OLR, are presented in Figure 4.51 The curves shown are the best fit to the actual data points which are not shown for clarity OLR = 1 represents the case where there is no overload

in the baseline LCF–HCF cycle The pure LCF curve is also shown The results show that as OLR increases, the retardation effect of the single overload diminishes the growth rate until the minor cycles have almost no influence on the baseline LCF cycle at a value

of OLR = 2.0 This work, conducted on Ti-6Al-4V, also shows that the apparent onset of HCF activity is delayed by the overload cycle In this case, there is both an underload in the baseline combined cycle as well as a superimposed overload While the behavior of the baseline cycle defined by OLR = 1.0 is predictable with linear summation of the LCF and HCF cycles, the additional effect of the overload is both to reduce the minor cycle contribution to the growth rate and to reduce the threshold where minor cycle activity begins

The natural conclusion arising from these studies is that growth rates and thresholds from constant amplitude loading cannot always be used directly in spectrum loading without consideration of interaction effects Both retardation and acceleration effects have been noted in various studies, with overloads usually observed to retard crack-growth rates while underloads are found to accelerate the growth rates While these observations are common, the exceptions prove that a single rule cannot be applied in all cases

In [52], HCF and LCF tests were used to establish baseline material properties, and simple mission tests were used to assess additional failure modes that may exist if

10 –1

10–2

10–3

10 –4

10 –5

10–6

OLR = 1.0 OLR = 1.15

OLR = 1.45

OLR = 2.0

LCF only

Ti-6Al-4V

n = 1000

Figure 4.51. Fatigue crack growth for various overload ratios, R = 07, 1000 minor cycles per block.

LCF–HCF interactions are important This was explored with mission tests at 75F with Ti-6Al-4V and were based on the following criteria: (a) tests that avoid specimen ratcheting failure modes (typically high stress, high R) that are not representative of component failures, (b) LCF stresses that are in the main regime of design interest for turbine engines (average Nf∼ 10000 cycles), (c) HCF stresses that are in the regime of design interest (R > 05 and HCF > 107 cycles), (d) mission histories that include LCF + periodic HCF cycles until mission failure, and (e) tests that can be run economically in the laboratory A double-edge V-notch specimen geometry was used to avoid ratcheting for load-control testing and loads were selected to keep the fatigue lives in the regime

of design interest Baseline notch LCF tests at R= 01 were run to identify stresses for an LCF failure of ∼10000 cycles while baseline notch HCF tests were used to identify the value of R for an average HCF failures of∼107 cycles All interaction tests were missions or blocks of cycles that were repeated until failure Missions included an LCF load-up R= 01+10000–100000 repeated HCF cycles R = 07–09 + an LCF unload reversal R= 01 for each mission The baseline and mission test conditions for the notch geometry are given in Table 4.3 Stresses are reported in units of ksi

The first group of mission tests was used to assess the HCF capability when minimal LCF damage is present This was evaluated with 10,000–100,000 HCF cycles/mission with an HCF cycle from 56 to 80 ksi (R= 07) These conditions were intentionally selected to avoid significant predicted LCF damage The number of HCF cycles to failure for these mission tests is compared to the number of cycles to failure for HCF alone with probability plots shown in Figure 4.52 Given the similarity of these distributions

Table 4.3. Baseline and LCF–HCF mission tests

LCF LCF HCF HCF HCF/mission Freq Expt HCF Expt missions Pred life

HCF + LCF HCF

99

95

90

80

70

60

50

40

30

20

10

5

1

HCF cycles to failure

Figure 4.52. Capability of notched HCF tests compared to the HCF capability of LCF–HCF mission tests

when HCF damage dominates.

for the small set of data presented, a significant LCF–HCF interaction does not seem to

be present for cases when HCF damage dominates

The second group of tests was run to assess if LCF failure modes are influenced when minimal predicted HCF damage exists Minimal HCF damage was evaluated with mission tests that included an LCF load-up reversal R= 01 + 10 000 repeated HCF cycles (Smax= 80 ksi Smin= 72 for R = 09 or 65 ksi for R = 082) The HCF parameters were selected near the minimum allowable stress for a 107HCF limit so that HCF could

be ignored as a contributing factor, assuming no LCF–HCF interactions The number

of LCF cycles to failure for the notch mission tests as compared to Nf for the notch specimens with LCF alone is shown in Figure 4.53 The values for predicted Nf used

an average smooth specimen Sequiv fatigue curve with the modified Manson-McKnight fatigue parameter The local stresses from the notch were obtained from elastic-plastic analysis and notch life was predicted with the local notch stresses and notch gradients using the effective stressed area, Fs approach described in Appendix E (see Chapter 5 for a detailed discussion of notch fatigue) The tests are seen to be well predicted within the 2X scatter bands that are representative of a reasonably accurate LCF life method Neglecting LCF–HCF interactions is shown here to be a reasonable assumption for these mission tests where the predicted HCF damage is minimal From the viewpoint of design,

it appears that one can use an HCF limit based on minimum properties such that HCF can be ignored as a failure mode in the type of mission used here that contains HCF and LCF conditions

Ti-6Al-4V notches with LCF + Min allowable HCF (predictions with smooth specimen curve plus Fs)

1,000 1,000

10,000 10,000

100,000 100,000

Observed LCF to failure

LCF Only

Figure 4.53. Notched LCF tests compared to the LCF of LCF–HCF mission tests with minimal HCF damage.

REFERENCES

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and J.I Diskson, eds, 3, EMAS, Warley UK, 1993, pp 1575–1580

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on the Low Cycle Fatigue Behavior of a Superalloy at Elevated Temperature”, Low Cycle Fatigue, ASTM STP 942, American Society for Testing and Materials, Philadelphia, PA, 1988,

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Low Cycle Fatigue”, Low Cycle Fatigue, ASTM STP 942, American Society for Testing and

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Minor Stress Cycles on Fatigue Crack Growth”, Second International Congress on Fatigue (Fatigue ’84), 1984, pp 893–902.

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Structures, 19, 1996, pp 217–227.

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Overloads”, AIAA Paper No 73-325, 1973; see also AIAA Journal, 12, 1974, pp 330–335.

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Crack Growth Retardation in HP-9Ni-4Co-30C Steel”, Journal of Engineering Materials and

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of Aircraft, 12, 1975, pp 699–705.

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on Fatigue Crack Propagation”, Fatigue Crack Growth Under Spectrum Loads, ASTM STP

595, American Society for Testing and Materials, Philadelphia, 1976, pp 41–60.

40 Hopkins, S.W., Rau, C.A., Leverant, G.R., and Yuen, A., “Effect of Various Programmed

Over-loads on the Threshold for High-Frequency Fatigue Crack Growth”, Fatigue Crack Growth Under Spectrum Loads, ASTM STP 595, American Society for Testing and Materials,

Philadel-phia, 1976, pp 125–141

41 Frost, N.E., “Notch Effects and the Critical Alternating Stress Required to Propagate a Crack

in an Aluminum Alloy Subject to Fatigue Loading”, J Mech Eng Sci., 2, 1960, pp 109–119.

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and Related Phenomena”, International Journal of Fatigue, 21, 1999, pp S233–S246.

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46 Ritchie, R.O., “Small Cracks and High Cycle Fatigue”, Proceedings of the ASME Aerospace Division, J.C.I Chang, ed., AMD-Vol 52, ASME: New York, NY, 1996, pp 321–333.

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“Thresholds for High-Cycle Fatigue in a Turbine Engine Ti-6Al-4V Alloy”, International

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48 Campbell, J.P., Thompson, A.W., and Ritchie, R.O., “Mixed-Mode Crack-Growth Thresholds

in Ti-6AL-4V under Turbine-Engine High-Cycle Fatigue Loading Conditions”, Proceedings of

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UK, 3, 1984, pp 1671–1682.

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Crack Growth”, Int J Fatigue, 25, 2003, pp 827–834.

Notch Fatigue

5.1 INTRODUCTION

A notch in a component can be considered to be a defect since it produces a local stress concentration or stress raiser that can ultimately be the location of an HCF failure Thus,

it is important to understand the effect of a notch on the FLS and to be able to predict the strength without having to conduct extensive experiments for each notch geometry

An alternate reason for understanding and modeling notch behavior is that it represents

a condition where there are stress gradients in going from maximum stress at the notch root to lower stress at locations beneath the notch Stress gradients also arise in fretting fatigue, discussed later in Chapter 6 Additionally, FOD, discussed later in Chapter 7, often produces some type of geometric discontinuity To be able to predict the effect of the discontinuity or damage to stresses induced by vibratory HCF loading requires an understanding of notch effects in fatigue For these reasons, we present an overview of notch fatigue as related, primarily, to the fatigue limit or threshold for crack propagation

5.2 STRESS CONCENTRATION FACTOR

In notch fatigue, the primary aim is to be able to predict the fatigue behavior of a material

or component with a stress concentration from smooth bar data The majority of fatigue data available is in either the LCF regime or corresponds to fatigue lives below the endurance limit, if such a limit exists at all The first aspect of addressing notch fatigue strength is to define the severity of the notch or stress concentration To do this, the elastic stress concentration factor, kt, is used.∗ Here, ktis defined as the ratio of the peak stress at the root of a notch to the average stress over the net cross section:

kt= peak stress at notch root average stress over the net cross section

∗

The symbol used for the elastic stress concentration factor throughout the literature is either K t or k t The former definition was commonly used before fracture mechanics was developed, when K was introduced as the stress intensity factor However, Kt is still widely used In this book, the term kt will be used wherever possible for consistency Note, however, that many drawings made early in the preparation of this manuscript

or taken from the literature will still show Kt as the stress concentration factor For this inconsistency and possible confusion, the author expresses his sincere apologies.

213

Values of kt can be found in tables or handbooks and have been obtained from closed-form elastic solutions for simple geometries, photoelasticity experiments in the early days, and finite element calculations in the more recent literature The value of kt is a measure of the severity of the notch or discontinuity and is used to predict fatigue lives in many engineering applications There are numerous cases in components with complex geometries where ktcannot be defined as stated above because there is no well-defined

“net-section.” An example of such a geometry would be at the root of a notch in a dovetail attachment region where the cross section has a continuing variable geometry In such a case, the net-section stress is hard to define because a section is difficult to be identified uniquely Similarly, a notch in a complex 3-d geometry has an undefined value of kt when the cross-section stresses, wherever the cross section is defined, are highly variable

in all directions Even if kt is formally defined, it may have no meaning for engineering and design purposes for HCF applications

In Figure 5.1, three geometries are shown schematically under far-field uniform tensile loading In (a), a mild notch is depicted, and the stress at the notch tip is slightly higher than the net-section stress over the width, w Note that if the gross cross section

width= d is used (incorrectly), then a large stress concentration factor will result with resulting misleading approximations for the fatigue strength All calculations for kt are based on linear elastic material behavior and are independent of material and depend only

on geometry In (b) and (c), two identical notch radii are shown, but the two do not have the same value of kt In (b), the average stress is more influenced by the local notch field than in (c) which is closer to that of an infinite body The stress concentrations are

w d

(a)

(c)

(b)

d d

Figure 5.1. Three geometries illustrating the definition of k

different, therefore, and this demonstrates that both the notch geometry and the overall geometry are important in determining kt

5.3 WHAT IS K t ?

There are a number of industrial applications where accounting for damage is necessary, even though the amount and severity of such damage is hard to quantify In cases such

as those with FOD, discussed later in Chapter 7, a knockdown factor in the form of an equivalent value of kt is often used While the design procedure may quote kt= 3, for example, as the guideline, the intent seems to be to reduce the fatigue limit by a factor

of 3 in this example, so the guideline should be kf= 3 instead.∗

The fatigue notch factor,

kf, is defined and discussed later in Section 5.4

The ambiguous meaning of quoting a value of kt to represent damage is illustrated in

a simple example here Not only is ktnot unique in terms of the geometry it represents, but for a given geometry the value of kt also depends on the loading condition In this example, a rectangular plate with a U-shaped notch is loaded in tension or bending,

as shown in Figure 5.2 With the nomenclature and loading as depicted in the figure, values of kt are presented for several r/d ratios for tension as well as bending loading

in Figure 5.3 For a fixed value of kt, any of a number of values of r/d can be used to produce that value Further, for a fixed geometry with specified values of D/d and r/d, the value of ktis different under axial load than under pure bending Thus, the specification

of a value of kt to represent a damage state is rather ambiguous and, as mentioned above, is a misuse of the term when a fatigue notch factor, kf, is probably what was intended

M

r

d/2 d/2

D

M P

Figure 5.2. Nomenclature for plate with U-shaped notch under tension and bending.

∗

In recognition of the intent to reduce fatigue strength for FOD damage in ENSIP in preliminary design, kt= 3 was introduced in the original document The latest versions of ENSIP now use k = 3 as the guideline.