ShieldingCorrected MixedMode Thresholds

1
7th National Turbine Engine HCF Conference
Role of Crack Size and Microstructure in
Influencing Mixed-Mode High Cycle Fatigue
Thresholds in Ti-6Al-4V
R.K. Nalla, J.P. Campbell and R.O.
Ritchie Department of Materials Science and
Engineering, University of California, Berkeley,
CA 94720 May 15, 2002
Work supported by the U.S. Air Force Office
of Scientific Research under Grant No.
F49620-96-1-0418 under the auspices of the
Multidisciplinary University Research Initiative
(MURI) on High Cycle Fatigue to the University of
California.
2
Motivation

• High Cycle Fatigue (HCF) has been identified as
  the single biggest cause of failures in military
  turbine engines. Such failures result in costly
  engine damage/loss and related down-time, in
  addition to loss of human life
• A successful solution would save 2 billion
  over the next 20 years
• A damage-tolerant approach may offer an
  alternative over the combination of Goodman
  Diagram/ Safe Life (S/N) based approach used
  now
• The basis of the MURI has been to seek a physical
  understanding behind the development of such a
  damage- tolerant approach

• High Cycle Fatigue (HCF)
• Low Cycle Fatigue (LCF)
• Foreign Object Damage (FOD)
• Fretting

3
Why Study Multiaxial Fatigue?

• Common in turbine engines - e.g., in association
  with fretting in the dovetail/disk contact region
  
• High frequencies involved (1-2 kHz) may
  necessitate a threshold-based methodology
  incorporating mode-mixity effects
• Presence of shear loading known to dramatically
  reduce mode I threshold (John et al, in
  Mixed-Mode Crack Behavior, ASTM STP 1359, 1999)
• No information on HCF mixed-mode thresholds for
  small cracks
• Multiaxial fatigue research goes back to only
  1969 (Iida and Kobayashi, J. Bas. Eng., 1969),
  while fatigue research goes back well over a
  century (Albert, Archive für Minerlogie,
  Geognosie, Bergbau und Hüttenkunde, 1838)
• Only two studies on Ti-6Al-4V in the archival
  literature - by Pustejovsky (Eng. Fract. Mech.,
  1979) and Gao et al (Multiaxial Fatigue, ASTM STP
  853, 1985)

4
Problem Statement and Objective

• Very little data have been reported on the role
  of mode-mixity in influencing fatigue thresholds
  in Ti-6Al-4V alloys
• Similarly, little information is available on how
  microstructure can affect such mixed-mode
  thresholds
• There is no information on the role of crack size
  on mixed-mode thresholds in any material
• Hence, our objective is to
• - compare the mixed-mode HCF threshold behavior
  for two microstructures in Ti-6Al-4V with
  widely differing micro- structural
  dimensions, i.e., bimodal (STOA) and lamellar
• - characterize the effect of mode-mixity and
  load ratio on mixed-mode thresholds for
  cracks with widely differing dimensions,
  i.e., large (gt4 mm) and short (200 mm)
  through-thickness cracks and small (lt50 mm)
  surface cracks

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Material Microstructures Investigated
Alloy Composition (wt)
A
Ti Al V
Fe O N
H Bal. 6.29 4.17
0.19 0.19 0.013 0.0041
bimodal (STOA) structure 64 primary a, grain
size 20 mm a lath spacing 1-2 mm
Uniaxial Tensile Properties
Yield Strength Ultimate Tensile Reduction
Fracture Toughness (MPa)
Strength (MPa) in Area () KIc
(MPa?m) A 930 978
45 64
B 975 1055
10 100
B
?-annealed lamellar structure prior-b grain size
1 mm a colony size 500 mm, a lath spacing
1-2 mm
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Small Fatigue Cracks
Cracks that can be considered small
Ritchie and Lankford, Mater. Sci. Eng. A, 1986
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Large, Short and Small Fatigue Cracks

• Large in all dimensions

• Small in one dimension
• Reduced crack-tip shielding

• Small in all dimensions
• Reduced crack-tip shielding
• Biased microstructural sampling

Ritchie and Lankford, Mater. Sci. Eng., 1986
8
Asymmetric Four-Point Bend Specimen

• The offset s, from the load-line is used to
  control the degree of mode-mixity, DKII /DKI, and
  hence the phase angle, ? tan-1 (DKII /DKI)
• Range of mixities studied DKII/DKI from 0 to
  7.1 b from 0? to 82?
• Linear-elastic stress-intensity solutions from He
  and Hutchinson, J. Appl. Mech., 2000
• KI

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Large Crack Thresholds

• Lamellar microstructure shows superior
  resistance, especially at low phase angles
• Load ratio, R, and mode mixity, b, can reduce
  DKI significantly for both microstructures

Nalla, Campbell Ritchie, Fat. Fract. Eng.
Mater. Struct., 2002
10
Single Parameter Characterization
DG (DKI2 DKII2)/E'

• Lamellar microstructure shows superior
  resistance, especially at low phase angles
• Threshold DGTH measured in pure mode I can be
  considered as worst-case

Nalla, Campbell Ritchie, Fat. Fract. Eng.
Mater. Struct., 2002
11
Large Fatigue Crack Profiles

• Observed crack paths follow a path of maximum
  tangential stress (MTS), i.e., one of KII 0,
  for the bimodal microstructure
• For the coarser-grained lamellar microstructure,
  significant deviations were observed from MTS
  predictions the role of microstructure becomes
  critical, especially in the precrack wake

Campbell Ritchie, Metall. Mater. Trans. A, 2001
12
Correction for Crack-tip Shielding

• Mode I shielding, in the form of crack closure,
  determined from the compliance curve for the
  opening displacements from the first deviation
  from linearity on unloading DKI,eff KI,max
  Kcl
• Mode II shielding, in the form of asperity
  rubbing and interlock, determined in an analogous
  fashion from the compliance curve for shear
  displacements DKII,eff DKII,maxtip -
  DKII,mintip

Campbell Ritchie, Eng. Fract. Mech., 2000
13
Shielding Corrected Thresholds

• Effects of mode-mixity, load ratio and
  microstructure markedly reduced after taking
  account of crack-tip shielding from mode I
  closure and mode II crack-surface interference

Nalla, M.S. Thesis, U.C. Berkeley, 2001
14
Short-Crack Thresholds

• The role of crack-tip shielding is evident from
  the substantially lower thresholds
• The technique for estimating the mixed-mode
  shielding by Campbell et al gives reasonable,
  though slightly overestimated, values for the
  thresholds

Nalla, Campbell Ritchie, Fat. Fract. Eng.
Mater. Struct., 2002
15
Definition of the Mixed-Mode Threshold

• G calculation based on precrack

direction of subsequent propagation
G (KI2 KII2)/E'
where k1 KI k2 KII

• G calculation based on infinitesimal kink

Geff (kI2 kII2)/E'
where k1 aII(a) KI aI2(a) KII k2
a2I(a) KI a22(a) KII
b ltlt a
Nalla, Campbell Ritchie, Int. J. Fatigue, 2002
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Definition of the Mixed-Mode Threshold

• In general, the trend is to reduce the computed
  values of DKeq,TH somewhat, except at very high
  phase angles
• At b 26o, however, the large crack DKeq,TH
  threshold is reduced by as much as 40 this
  translates into a reduction in threshold DKeq,TH
  values by between 1 and 2 MPa?m
• Effects are far less significant for short cracks

• Nalla, Campbell Ritchie,
  Int. J. Fatigue, 2002

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Small Crack Thresholds in Mode I

• Optical micrograph showing a typical initiation
  site for the bimodal microstructure - Initiation
  predominantly occurs in the primary-? grains.
• SEM image of crack initiation and early growth
  along planar slip bands leading to facet type
  fracture surface - EBSD analysis of fractured
  a-grains 1 to 3 revealed near-basal orientation
  of the fracture plane.

(Courtesy Dr. J.O. Peters)
Nalla et al, Metall. Mater. Trans. A, 2002
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Mixed-Mode Small-Crack Testing
KI Newman Raju, Eng. Fract. Mech., 1981
KII He Hutchinson, Eng. Fract. Mech., 2000
wide bend bar specimen

• the tensile loading component, ?22 induces the
  mode I contribution
• the shear loading component, ?12 induces the mode
  II and mode III components
• the in-plane component, ?11 makes no contribution.

small inclined-crack specimen
Nalla, Campbell Ritchie, Fatigue Fract. Eng.
Mater. Struct., 2002
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Inclined Semi-Elliptical Surface Crack

• A typical crack path taken by a
  microstructurally-small crack under mixed-mode
  loading (R 0.1, ? 28o, ?G 20 J/m2, angle of
  inclination ? 50o)
• Strong influence of local microstructure near the
  crack tip is evident on the crack path

?
Nalla, Campbell Ritchie, Fatigue Fract. Eng.
Mater. Struct., 2002
20
Mixed-Mode Small-Crack Thresholds

• Thresholds for small cracks (lt50 ?m) are
  significantly lower than for large (gt4 mm) and
  short (200 ?m) cracks, especially under
  shear-dominant loading
• Large reductions in DKEQ,TH (up to 7 times) and
  DGTH (up to 50 times) with respect to large
  cracks seen for microstructurally-small cracks

Nalla, Campbell Ritchie, Fatigue Fract. Eng.
Mater. Struct., 2002
21
Conclusions

• Marked effect of mode-mixity and load ratio on
  mixed-mode fatigue thresholds for large (gt 4 mm)
  through-thickness cracks
• Thresholds DGTH values measured in pure Mode I
  represent a worst-case condition
• Lamellar structure generally exhibited higher
  large-crack thresholds
• Thresholds for short (200 ?m) through-thickness
  cracks were considerably lower and were
  relatively insensitive to load ratio, mode-mixity
  and microstructure. This was attributed to a
  reduced role of crack-tip shielding
• Thresholds for microstructurally-small (lt 50 ?m)
  surface cracks in the bimodal microstructure were
  similarly insensitive to load ratio and
  mode-mixity, and were substantially lower than
  those for large cracks. This was related to
  limited crack-tip shielding and biased
  microstructural sampling associated with the
  small cracks.