High Cycle Fatigue: A Mechanics of Materials Perspective part 64 docx

To account for the combined effects analytically, an initiation model for combined cyclic fatigue CCF is coupled with a threshold fracture mechanics crack propagation model to predict fa

is provided, it shall be demonstrated once during each shut down Components such as air-oil coolers with exposure to inlet sand and dust conditions shall be considered inlets for this test but a rig test may be performed to satisfy the requirements herein Following the post-test performance check, the engine shall be disassembled to determine the extent of sand erosion, and the degree to which sand may have entered critical areas in the engine The test will be considered satisfactorily completed when the criteria of 3.3.2.4 have been met and the teardown inspection reveals no failure or evidence of impending failure.” Background:

The recommended text decreases the operational time in the extreme sand and dust environment from ten hours to two hours for turbofan and turbojet engines Engine contractors have been unwilling in the past to guarantee their engines for ten hours (helicopter subjected to the severe Vietnam sand and dust environment typically used inlet filtration systems) The time requirement will have to be negotiated with each engine contractor in specific future specification negotiations based upon the intended usage in regions of the world where sand will be a concern

The sand concentration should be calculated with customer bleed air extraction The anti-icing switch should be activated five times during each hour of sand ingestion at equally spaced intervals The test should be conducted with a thrust bed and load cell measurement of thrust in lieu of calculating thrust by EPR Disassembly and inspection between the coarse and fine sand tests should be conducted for 45.4 kg/s (100 lb./sec) airflow or smaller engines

VERIFICATION LESSONS LEARNED (A.4.3.2.4)

The Engine V sand and dust test did not use the recommended sand and dust mixture due to commercial unavailability of the mixture The specification for fine sand calls for

a particle size distribution which cannot be obtained commercially Specifically, calcite and gypsum could not be obtained with a particle size distribution to match the specified particle size distribution Table XXXVIa and b shows the closest particle size distributions which the Engine V sand and dust test team could find along with the required size distribution

Appendix I

Computation of High Cycle Fatigue Design Limits under Combined High and Low Cycle Fatigue

Joseph R Zuiker

ABSTRACT

Applications in rotating machinery often result in stress states that produce both low cycle fatigue (LCF) damage in addition to the damage produced from the high frequency or high cycle fatigue (HCF) vibratory loading While the Haigh diagram takes into account the vibratory as well as the steady stress amplitudes for a fatigue limit corresponding to

a (large) given number of cycles, it does not consider the combined effects of LCF and HCF To account for the combined effects analytically, an initiation model for combined cyclic fatigue (CCF) is coupled with a threshold fracture mechanics crack propagation model to predict fatigue thresholds for CCF The results are contrasted with the HCF allowable stresses represented in a constant-life Haigh diagram Experimental data from the literature for a Ti-6Al-4V alloy are used to demonstrate the viability of the analysis and the limitations of the use of the Haigh diagram in design Comments on the limitations

on the use of a Haigh diagram for combined HCF–LCF loading are presented

NOMENCLATURE

CCF combined cycle fatigue

di initiation phase damage parameter

Kt stress concentration factor

LEFM linear elastic fracture mechanics

∗This document was contributed by Dr Joseph Zuiker, a former employee of the Air Force Research Laboratory.

It is based on unpublished work conducted by him while with the Air Force Dr Zuiker is currently with General Electric Company Power Systems Division.

617

m Paris-Walker law constant

NiCCF number of cycles to crack initiation in CCF loading

NiHCF number of cycles to crack initiation in HCF-only loading

NiLCF number of cycles to crack initiation in LCF-only loading

Q stress intensity range ratio= KHCF/KLCF

r exponent for initiation life equation

R stress ratio= min/max

 crack growth rate acceleration factor

KHCF stress intensity factor range of HCF cycles

KLCF stress intensity factor range of LCF cycles

Kth threshold stress intensity factor range

Konset KLCF value at which HCF crack growth becomes active in CCF

Ktho Kth at R= 0 (in CTOD-based model)

HCF strain range of HCF cycle

end endurance limit stress range below which no initiation damage is caused

HCF stress range of HCF cycle

LCF stress range of LCF cycle

∗ constant for initiation life equation

a alternating stress

aeq equivalent alternating stress at R= 0 for a stress state at R = 0

aHCF alternating stress of HCF cycle to be converted to equivalent R= 0 cycle

fs alternating stress causing failure in a specified number of cycles at R= −1

mHCF mean stress of HCF cycle to be converted to equivalent R= 0 cycle

ult ultimate strength

INTRODUCTION

Design of components for HCF must generally account for the detrimental effects of a superimposed mean stress This accounting is often in the form of an alternating versus mean stress (Haigh) diagram that shows allowable vibratory stress amplitude as a function

of applied mean stress for a specified life In many cases little or no data are available for conditions other than fully reversed loading where the stress ratio R= min/max=−1, and tensile overload R= 1 or ultimate stress, and assumptions such as a straight line fit must be made in order to interpolate between these limiting cases

A more general Haigh diagram can be produced using data at various values of mean stress and a specified number of cycles to failure, e.g 107, as obtained from S–N curves and plotting the locus of points For any of these plots, the number of cycles is typically taken to be those corresponding to a “runout” condition, perhaps 108 or even 109, but there are few data available to demonstrate that a true runout condition ever exists for a material This has been shown to be the case in several studies on titanium (cf [1, 2]) For convenience and practicality, the number of cycles chosen is taken to correspond to the region where the S–N curve becomes nearly flat with increasing number of cycles,

or is selected such that the number of cycles exceeds that which might be encountered in service In some cases, neither condition may be satisfied For design purposes, because

of the statistical variability of fatigue data, particularly in the long-life regime where S–N curves tend to be close to horizontal, Haigh diagrams commonly represent a statistical minimum For the purposes of the present discussion, only average material property data will be discussed

The straight line Goodman assumption and corresponding Haigh diagram are widely used in design for HCF Henceforth, we shall consider only the Goodman assumption, but

it is understood that any discussion of the Haigh diagram is equally valid for any other assumptions regarding the shape of the diagram A critical issue in the use (or misuse) of the Haigh diagram in design is the degree of initial or service induced damage that may

be present in a component, but may not be present in the material used for generation of the Haigh diagram In the present study, we deal with damage induced by superimposed LCF If such damage is present, the Haigh diagram is not valid for the material because

it represents “good” or undamaged material Therefore, a design methodology which considers the development of damage from sources other than the constant amplitude HCF loading must be used to account for the different state of the material Turbine engine components, for example, which are subjected to HCF, are typically subjected to LCF in addition because the non-zero mean stress is achieved through the centrifugal loading typical of operation Each startup and shutdown constitutes an LCF cycle Thus, the component experiences combined HCF and LCF or CCF and, for design purposes, the effect of LCF loading on the HCF life should be considered

In this appendix, we present a simple model for the CCF of a typical turbine engine alloy and use data from the literature to predict the effect of superimposed LCF on the HCF capability of the material Here, LCF refers to large amplitude, low frequency cycles whose total number is typically less than 103–104, while HCF refers to small amplitude, high frequency cycles at high mean stress, whose number generally exceeds 106–107

In the following sections, a prediction methodology is described including descriptions

of the initiation life model, the propagation life model, the experimental data used to calibrate the model, and the assumptions concerning the interaction of the HCF and LCF cycles Then, numerical predictions are presented to confirm the model accuracy and

show its sensitivity to a variety of factors Finally, we close with a discussion of the results, conclusions, and possible future efforts

It is important to note a principal difference between this work and the majority of the previous studies on CCF While most of the literature has been concerned with the effect

of superimposed HCF on the LCF life of materials and structures, this appendix deals with the effect of superimposed LCF on the HCF capability of the material and further and, further, addresses total life as a sum of initiation and propagation phases, the latter

of which uses fracture mechanics analysis

LIFE PREDICTION METHODOLOGY

In order to illustrate HCF–LCF interactions, analytical predictions are made of the total fatigue life and presented as a Haigh diagram for a material experiencing 107HCF cycles divided equally over N LCF loading blocks It is assumed that total life can be divided into two distinct phases: a crack initiation phase, and a crack propagation phase Each CCF loading block consists of a low frequency cycle over which the material is loaded from zero stress to a given mean stress and held while n=107/N high frequency cycles are superimposed about the mean stress as shown schematically in Figure I.1 The details

of the analysis follow

Initiation life

During initiation the material is assumed to be uncracked Initiation damage, di, is accumulated over each HCF and LCF cycle until di=1 at which point it is assumed that

a crack of depth ai has initiated The number of LCF cycles required to reach di=1 is

σm

σa

2σLCF

2σHCF

Time

ONE CCF LOAD BLOCK

Figure I.1. Idealized combined cycle fatigue load block.

defined as NiLCF For LCF-only cycling applied at R= 0  =2a=2m , a power law function of the applied stress range using a form similar to the Basquin equation is used such that

NiLCF= ∗2

where a is the alternating stress amplitude and ∗ and r are constants In fitting the response of actual materials, multiple sets of constants are used over specific ranges

of a such that Equation (I.1) forms a piece-wise linear approximation to the actual material response when plotted on a log-log scale Equation (I.1), which is written for LCF-only loading R= 0 , can also be used for HCF cycles at R = 0 by substituting an equivalent alternating stress amplitude, aeq The equivalent alternating stress is obtained

by moving along a line of constant life on a Haigh diagram from the point defining the HCF cycle m a at R= 0 to a point at R = 0 The form of the constant life line must be assumed Here, we postulate that the straight-line Goodman assumption governs mean stress effects on initiation life in the same manner as it governs mean stress effects

on total life That is, straight lines passing through ult 0 exhibit constant initiation life The fully reversed stress to initiation, fsi is defined as the y-axis intercept of a line passing through points defining the HCF load cycle at R= 0 mHCF, aHCF and

ult 0 Fully reversed initiation stress, fsi can be defined in terms of aHCF, mHCF, and ult; and substituted into the modified Goodman equation for fs, the fully reversed alternating stress amplitude The equivalent alternating stress is then obtained by setting

a=m=aeq and solving for aeq, as

1

ult+ 1

aHCF− mHCF

aHCFult

Thus, the initiation life due to HCF cycles, NiHCF, is obtained via Equation (I.1) by replacing a with aeq from Equation (I.2)

To determine the initiation life under combined HCF–LCF loading, the linear damage summation model [3, 4] is used such that the initiation life, in CCF blocks, is

NiCCF= 1

1

NiLCF + n

NiHCF

where NiCCF is the initiation life under CCF in terms of CCF load blocks The linear damage summation model has been criticized for its inability to account for load sequenc-ing affects However, it is noted that when different cycles are mixed evenly over the life of a component, the Palmgren–Miner rule gives acceptable results (cf [5, 6]) More advanced nonlinear damage summation models have been proposed While many give

better results than the linear damage summation model, they are often limited to specific materials or conditions and require experience to be used with confidence [7]

After NiCCFloading blocks, a crack, which is amenable to fracture mechanics techniques for predicting crack growth, is assumed to have formed in the component and grows according to LEFM to failure The size, shape, and location of the crack must be assumed and, here, will be taken from experimental data in the literature

For cases in which NiCCF1, it may be sufficiently accurate to round NiCCFto the nearest integer and begin crack propagation with the next load block In other cases this may not be accurate and it is important to determine at what point in the load block the crack initiates and crack propagation begins As a first approximation, it is assumed that all initiation damage in each cycle occurs during the loading portion of the cycle Thus, if NiCCFis fractional, the first portion of the fractional cycle is attributed to the LCF cycle; the remainder of the fractional initiation damage is attributed to HCF cycles, and during the remaining portion of the load block the crack is assumed to have initiated and begins to grow in HCF

Initiation example

Consider the case of a specified loading sequence consisting of n= 8000 HCF cycles per CCF load block For a specified maximum stress and HCF stress range, the initiation lives are found as NiLCF=16×104and NiHCF=3×107 In this case, the initiation damage per CCF load block due to LCF is diLCF=1/NiLCF=6250 × 10−5, the initiation damage per CCF load block due to HCF is diHCF=n/NiHCF=2667×10−4, the total initiation damage per CCF load block is diCCF= diLCF+ diHCF= 3292 × 10−4, and N

iCCF= 1/diCCF= 3037975 Thus, after 3037 CCF load blocks, di=0999679 During the loading portion

of the LCF cycle in load block 3038, diincreases by 6250× 10−5 to 0999742× 10−n. Each HCF cycle then increases the damage by 3333×10−8 until the crack initiates after

7740 HCF cycles in load block 3038 Thus, during HCF cycle 7741 in CCF load block

3038, the crack is considered to have initiated and begins to grow under the assumptions

of fracture mechanics

Propagation life

During the crack propagation phase, the crack grows under the assumptions of linear elastic fracture mechanics Short crack behavior is neglected During LCF and HCF cycles, the crack is assumed to grow in mode I following the Paris law as modified by Walker [8] to account for stress ratio effects as

da

dN∗ = CK m

Here, C and m are material constants describing the crack growth rate at R=0, and d is

a material constant accounting for the higher crack growth rate at higher R for the same

K, an effect attributed to Kmaxor mean stress effects For LCF cycles, N∗ corresponds

to a single LCF cycle, KLCF replaces K, and R=0 For HCF cycles, N∗ corresponds

to a single HCF cycle, K is replaced by KHCF, and in general R > 0 Equation (I.4) holds for K >Kthfor individual LCF cycles as well as individual HCF cycles provided that the appropriate stress range and value of R are used in each case In accordance with experimental observations, Kthis assumed to be a decreasing function with increasing

R The values of KLCF and KHCF are calculated from LCF and HCF which are shown in Figure I.1 It can be deduced from the figure that KHCF is typically less than

KLCF for a given crack length and, therefore, the threshold in LCF should be reached before that in HCF However, when considering growth rate per block of cycles, the number of cycles per block, n, if large, could dominate the growth rate if both values of

K for HCF and LCF are above threshold

In the case of tension–compression cycling R < 0 , the crack tip is assumed to be open, and the crack growing, only when the applied stress is positive Thus, the minimum effective stress is always positive or zero, and R never drops below zero in Equation (I.4) This is, however, a minor point as we are most interested in loading typical of turbine engine components in which the mean stress is high, the vibratory stress is relatively low, and RHCF>0

The specimen is assumed to fail when Kmax surpasses KIC, or when the crack depth exceeds an appropriate length scale indicative of tensile overload in the specimen, whichever occurs first Crack growth is calculated for each HCF and LCF cycle, and is assumed to occur during the loading portion of each cycle Thus, growth increments are determined sequentially for an LCF cycle, n HCF cycles, another LCF cycle, and so on Under these assumptions, several failure sequences are possible The particular sequence encountered is a function of four characteristic crack depths that, in turn, are a function of the material properties and LCF and HCF stress ranges They are

• ai – the crack depth at initiation, which is defined by experimental data

• acrit – the crack depth at which KICis exceeded at the crack tip (or a depth appropriate

to the specimen size if acrit exceeds characteristic specimen dimensions), which is a function of HCF, LCF, and KIC

• agLCF – the crack depth beyond which the crack grows during LCF cycles, which is

a function of LCFand Kth (at R=0 for LCF cycles) and

• agHCF – the crack depth beyond which the crack grows during HCF cycles, which is

a function of HCFand Kth (at R for HCF cycles)

There are 24 possible permutations of these four crack depths, any of which will produce one of seven failure sequences which are shown in Figure I.2 Path 1 is not likely if reasonable initiation data are available Path 2 is unlikely for load levels of interest Paths

4 and 7 produce HCF-only crack propagation, which is a possible failure mode if Kth

in HCF (at high R) is sufficiently small in comparison with K in LCF (at R=0),

a crit ≤a i ? 1) Fast fracture immediately

after initiation

a crit≥a g, LCF and a i≥ag,HCF?

a crit ≥ag,HCF and a i≥ag,LCF?

2) No propagation after initiation Infinite life

3) Initiation followed by crack growth in CCF to failure

4) Initiation followed by crack growth in HCF only to failure

5) Initiation followed by crack growth in LCF only to failure

6) Initiation followed by crack growth in LCF only followed by crack growth in CCF to failure

7) Initiation followed by crack growth in HCF only followed by crack growth in CCF to failure

Yes

Yes

Yes

Yes

Yes

Yes

No

No

No

No

No

No

Figure I.2. Flow chart of possible failure sequences under CCF.

and HCF is sufficiently large to grow the crack While this situation depends on the assumed relation of Kth with R, neither of these HCF-only crack propagation modes has been observed in any of the numerical calculations reported here Paths 3, 5, and 6, then, are of the most practical interest

Model Calibration

In order to calibrate and exercise the model, crack initiation and propagation data on surface-cracked round bars [9] are used In this study, electropotential drop techniques

cracks in mildly notched KT=2 Ti-6Al-4V round bars with an / microstructure Total life was measured in both mildly notched and smooth bars Chesnutt et al [10] and Grover [11] reported total life measurements on Ti-6Al-4V materials with a similar microstructure at lower stress levels (and longer lives) at various values of KT Using these data, total life estimates for long life tests at KT= 2 were interpolated and are shown, along with the short life data by Guedou and Rongvaux [9], in Figure I.3 A multi-part power law fit to the initiation life curve was generated by connecting the ultimate stress at N=1 to the LCF data from Guedou and Rongvaux [9] A power law fit to the experimental data was extrapolated to lower stress values Two scenarios were considered for low stresses In the first, alternating stress ranges below 300 MPa R=0 cause no damage Thus the life is infinite for lower stresses and the final portion of the S–N curve is a horizontal line This stress range was chosen to agree approximately with the observed runout behavior in the long life tests [10, 11] The contrasting scenario assumes that no endurance limit exists Any alternating stress causes a finite amount of damage In this scenario, the S–N curve extends downward continuously Both cases are shown in Figure I.3 The corresponding total life curve was generated by adding the analytical estimate of the propagation life to the initiation life measurement and correlated well with the experimentally measured total life values shown in Figure I.3

Crack propagation data at R=005 and 0.85 [9] were used to determine parameters

C, m, and d for the Paris–Walker relation in Equation (I.3) The values used here are

C=5376 × 10−12, m=3409, and d=13 The values of Kth for Ti-6A1-4V are taken

200

300

400

500

600

700

800

900

1000

NI Kt = 2 (Guedou and Rongvaux, 1988)

NT Kt = 2 (Guedou and Rongvaux, 1988)

NT Kt = 1 (Chessnutt et al., 1978)

NT Kt = 3.4 (Chessnutt et al., 1978)

NT Kt = 2 (Interpolated)

NI Kt = 2 (Predicted)

NT Kt = 2 (Predicted)

N

NO ENDURANCE LIMIT

Figure I.3. Predicted and measured values of N i and total life N T as a function of applied stress range

at R =0.