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Crack Path Determination for Non-Proportional Mixed-Mode Fatigue

Shelby HighsmithDoctoral Thesis Defense

13 March 2009

Introduction: Crack path in damage tolerance risk assessment

•Crack path prediction is essential to accurate life prediction & risk assessment

‣ Crack growth rate through varying stress fields

‣ Energy of fracture ligament in rotating turbomachinery

•Current crack growth models still need development for complex mixed-mode loading

Project objectives

•Assess the ability to extend current knowledge of crack path selection and crack growth mode to non-proportional fatigue crack growth

•Validate new specimen design for testing a broad range of mixed-mode loading

•Contribute to material database for aerospace superalloy Inconel 718 under mixed-mode crack growth

•Enhance crack path prediction capabilities of linear elastic fracture mechanics (LEFM)-based fracture modeling software FRANC3D

Background: Mixed-mode crack path

•Crack growth largely considered in terms of Mode I (opening loads)

•Microstructure, geometry, load transients can perturb crack angle or applied load

‣ Addition of Mode II

•What is expected behavior of crack trajectory?

Δθ?

KI

KII

τrθ

Early models of fracture extension angle

•Erdogan & Sih (1963) - max tangential stress (σθθ) criterion (MTSC)

•Hussain et al (1974) - max strain energy release rate G (“Griffith” or MERR criterion)

•Sih (1974) - min strain energy density S

θ σθθ

σrrr

•All generally predict same crack deflection as function of mode mixity Φ (0° ~ Mode I, 90° ~ Mode II)

Prediction of symmetric fracture

Δθ

φ0°(KI)

90°(KII)

0°

-45°

-90°

Gmax

Smin

MTSC

! = tan!1

!KII

KI

"

ϕ

Beyond the inherent assumption of symmetric fracture

•Any criterion for non-zero angle crack branching under non-zero Mode II loading will predict stable Mode I growth

•Under high KII, stable mixed-mode or Mode II growth is observed

‣Mode I to Mode II-dominated transition (to max shear plane) around Φ = 40° in 7075-T6 (Hallback & Nilsson, 1994)

‣ Transition to shear crack growth in range of 68° < Φ < 75° in 2024-T3 (Amstutz et al, 1995)

‣ Transition to co-planar at Φ = 45° in HY130 steel at RT (Maccagno & Knott, 1992)

Critical stress criteria

• Chao & Liu (1997) argue that crack propagation occurs along most critical mode

‣ Follows plane where either τ or σ first goes criticalσθθ

σθθ

θ*

σrr

τrθr

τrθσrr

rθ**

Critical stress criteria

• Chao & Liu (1997) argue that crack propagation occurs along most critical mode

‣ Follows plane where either τ or σ first goes critical

• Competition b/w MTSC and max shear stress criterion (MSSC) based on loading path (mixity)

‣ Transition between the two is based on ratio of material props τcrit/σcrit

MTSC

Expected bimodal data

Angle θ** of max τrθ

Angle θ* of max σθθφcrit

Problem: Non-proportional loads

•Different points of waveform have different mixities φ

•Which parameters can be used to predict θ?

•Can we do so using only LEFM / K?

Max tension of constant torque or

OOP test

Max torque of constant tension or

OOP test

Research in non-proportional crack growth direction

•Much work in rolling contact fatigue (RCF) for rail application

‣Sequential KI-KII sub-cycles

‣Generally studying conditions leading to co-planar mixed-mode growth or Mode I crack branching

‣KII usually fully reversed -- not a clear case for current study

‣Elastic-plastic analysis of residual crack opening displacements & closure/interference

•Significant opportunities for expanding modal transition criteria

Experimental approach

•Development & validation of novel specimen design

‣ Inclined through-crack round (ITCR) specimen

‣Developed for 3-mode testing, enhanced 2-mode testing

•NASA testing of conventional notched thin-walled tube

•Four fatigue load cases tested

‣Proportional in-phase (baseline)

‣KI/ΔKII and ΔKI/KII

‣ 180° out-of-phase (sinusoidal) ΔKI/ΔKII

2mmEDM

thru-slot

Tension-torsion notched thin-walled tube

• Inconel 718 per AMS 5662

• 17 specimens tested at NASA Marshall Space Flight Center

‣ Added to this research program during development of ITCR specimen

• Uniaxial compression then tension pre-cracking

• Measure initial deflection angle from pre-crack upon mixed-mode loading

• Examine fracture surface morphology

OD 30.5mm ID 25.4mm

254mm

70mm

SIFs for tubular T-T specimen

•FRANC3D linear elastic boundary element model



•Each specimen precrack geometry modeled using fracture surface measurements



•Each specimen precrack geometry modeled using fracture surface measurements

•Tension & torsion applied individually and together to verify separability

NASA Mixed mode test plan

•Some initial tests prior to collaboration

•Baseline in-phase tests over range of mixity

•Constant tension (KI) / cyclic torsion (KII)

•Constant torsion (KII) / cyclic tension (KI)

•180° out-of-phase

Results: NASA in-phase tests

MSSC

MTSC

Mixity

Fractographsfollowing…

• In-phase deflections follow Max Tangential Stress criterion as expected up to critical φ value, then see transition to Max Shear Stress

• Torque limitations prevented further MSS testing

In-phase fractography - 500x

• Clear morphology difference reinforces transition in crack path deflection mechanism‣ Mode I transgranular crystallographic cracking observed previously (Mercer 1999)‣ Mode II appearance ~ slip-enhanced transgranular cleavage

Tensile crack (MTS) deflectionθ = -27°

Shear crack (MSS) deflectionθ = 18°

In-phase fractography - 2000x

• Fine microstructural features on shear crack flats suggest they are not the product of crack face contact

• In-phase transition as expected


Shear crack (MSS) deflectionθ = 18°

Effect of pre-crack shape, N09

• Bifurcation between branch modes at mid-thickness corresponds to change in due to irregular crack shape‣ The reason for Appendix A

Results: Constant KI / Cyclic KII

•Two distinct groups of crack path deflection•No clear indicator of transition criterion

Max loadcondition

Mixity

Fractography - Constant Tension / Cyclic Torsion 500x

• More pronounced morphological difference but similar to in-phase• What are the respective driving forces?

Shear crack (MSS) deflectionθ = +2°


Local kink tip reference frame

•Local stress intensity factors (SIFs) at small kink, k1 & k2

• In first order approximation, identical to considering primary crack tip stresses

KI

KII

k1, k2

k1 =!

2!r "!! = cos#

2

!KI cos2

#

2" 3

2KII sin #

"

k2 =!

2!r "r! =12

cos#

2

!KI sin # + KII(3 cos # " 1)

"

Kink tip SIFs, N13

•Tensile crack branch between k1max and local Δk1max

•Shear crack branch between k2max and Δk2max

•This pattern evident for all branch angles

k1maxk2max

•Start from (da/dN)max approach to incorporate mean stress/R-ratio effect in two parameter crack growth law

‣Prior implementations not directly applicable

•Rearrange Walker equation

‣

•Apply in terms of kink SIFs k1 and k2 and maximize

‣What is w?

Effective SIF range

da

dN= C0!K

m

!K =!K

(1!R)1!w= !KwK1!w

max

Fitting Walker ΔK

• Initial estimate of w=0.3 from prior superalloy data

‣ Good correlation b/w Δk1 and tensile branches (lower square data points)

‣ k1max stronger driver than Δk1

• Shear branches follow more closely to Δk2max than k2max

‣ Swap exponents on Δk2 and k2max in Walker form (upper triangle data pts)

‣ w1=0.3, w2=0.7

‣ Mode-dependent weighting not without precedent

!k1

!k2

!K = !KwK1!wmax

Perfectprediction

Defining a modal transition

•Using w1=0.3, w2=0.7 in this approach also allows for a clear demarcation of branch mode transition

‣ Critical ratio of Δk2max to Δk1max denoted by slope of lines from origin

‣ Shear & tensile branches (open & solid symbols) separate on either side for w1=0.3, w2=0.7 (red squares); not for other cases

Results: Constant KII/cyclic KI

•Single cluster of deflection angles, presumably tensile‣ “Tilted” by steady torque-induced crack tip tensile stress at -70°

Max loadcondition

Fitting Walker ΔK -constant KII / cyclic KI

•Unlike previous case, Δk1 stronger driver than k1max

‣w1=0.7 better fit

‣Was 0.3 for prior case

•No modal transition for comparison

!K = !KwK1!wmax

Results: 180° out-of-phase

• Apparently alternating deflection behavior with increasing KII/KI based on traditional framework‣ Positive angle, to negative, to divergent with increasing KII

• Driving forces not as expected

ϕ(KIImax/KImax)

Results: 180° out-of-phase

• Highest and lowest KII/KI tests produce tensile branches even at positive angles (w1=0.3), and a second local maximum for N18

• Middle KII/KI test turns out to have highest Δk2max (w2=1)

N19 - Fractography

•Ambiguous fracture surface appearance likely contact-smeared tensile branch features

500x 2,000x

N18 (right) - Fractography

•Highly faceted crystallographic cracking appearance as previous tensile branches (500x)

ITCR Specimen Development

ITCR specimen design


•4 specimens fabricated in-house (β = 0°)

‣ 4 β = 30° also fabricated but not tested

•Solid bar with through-thickness EDM slot pre-flaw

ITCR specimen design


• Originally designed for combined Mode I-II-III testing (inclined crack)

• 4 specimens fabricated in-house (β = 0°)

‣ 4 β = 30° also fabricated but not tested

• Solid bar with through-thickness EDM slot pre-flaw

• Generates range of mode mixity as KII increases with radius (with torsion)

b

2b

SIF solution for ITCR

• FRANC3D modeling of multiple specimen configurations a/r, β‣ Essentially same boundary

conditions as NASA model

• FRANC3D modeling of multiple specimen configurations a/r, β‣ Essentially same boundary

conditions as NASA model

• Linear fits across crack front

SIF solution for ITCR

KI =!o!

"a cos2 #!0.8162 + 0.8286

a

r

"

± $o!

"a sin # cos #!"0.018 + 0.759

a

r

"

KII =x

b

!!o!

"a cos #

"0.7114 + 2.3439

a

r" 4.6816

#a

r

$2%&

KIII =!o!

"a sin# cos #!0.8513 + 0.3933

a

r

"

± $o!

"a#sin2 # " cos2 #

$ !"0.0199 + 0.6846

a

r

"

ITCR specimen test matrix

•Proportional in-phase

‣Match NASA’s highest KII/KI at mid-span




•Constant KI/ΔKII

‣Match 2 NASA tests x/b ~ 0.4-0.6






•Constant KII/ΔKI






•Constant KII/ΔKI

•180° out-of-phase

Crack angle measurement

•Thin-walled tube crack angles directly observed

• ITCR specimen measured by incremental grinding of resin replicas of fractured specimen along x/b axis

ITCR specimen results: in-phase

ITCR specimen results: in-phase

• Generally follows standard MTS-MSS criteria & transition (Φ~55°-58°)‣ Slight offset in the direction of diminished KII influence

- NASA specimens similar shift in tensile branches

Increasing KII

ITCR results: Constant KI/cyclic KII

ITCR results: Constant KI/cyclic KII

• Use of same Δk formulation (w1=0.3, w2=0.7) as NASA KI/ΔKII data works reasonably well for direction‣ Mode II improves with higher w2

‣ Transition condition ambiguous as data falls in a narrow band of Δk2/Δk1

(w1=0.3, w2=0.7)

!K = !KwK1!wmax

ITCR results: Constant KII/cyclic KI

(Note lip at onset of fatigue cracking)

ITCR results: Constant KII/cyclic KI

• Small lip of initial kink angle bound by w1=0.7 employed in NASA data• Higher w1=0.95 for stable crack angle indicates diminished influence

of k1max for ITCR compared to thin-walled tube

!K = !KwK1!wmax

ITCR3-bottom

Rotation

Up

Up

Down

Down

Final FractureLigament

Final FractureLigament

ITCR results: 180° out-of-phase

ITCR results: 180° out-of-phase

• Even more challenging than NASA OP test data ‣ Requires assumption of full-range Δk1

‣ Crack face contact under negative k1 reducing Mode II-enhanced closure

2

Summary / conclusions

• Crack branch modal transition observed in Inconel 718

‣ In-phase, KI/ΔKII, 180° out-of-phase (thin-walled only)

‣ Verified by clear fracture surface morphological differences

• Walker effective SIF range at kink tip is a very good predictor of crack angle within most mixed-mode fatigue load cases

‣ Though relative influence of kmax & Δk varies by load condition

• Constraint delays modal transition from ϕ ~ 44° in plane-stress (thin-walled tube) to ~55°-58° in solid bar ITCR

• Check your specimen pre-crack shapes

Contributions

• Generated necessary mixed-mode crack branching data for Inconel 718 under multiple conditions

‣ Provided an initial basis for modeling mixed-mode crack path in LEFM framework

‣ Showed the varying influence of LEFM parameters and moved the research question from determining crack branch angles to refining the physical basis for the varying crack-driving forces

‣ Expanded envelope of mixed-mode FCG data beyond the focused realm of RCF research

‣ Generated a library of mixed-mode fractography

• Analyzed & validated a novel specimen design for generating a wide range of data in a single test, producing 3-mode load conditions, and adding different constraint data to standard tubular specimen data

Recommendations

•Full 3-D FEM analysis of specimens should compare in-plane and transverse constraints and their influence on transition

•Elastic-plastic analysis of crack tip deformations by load path may physically justify the varying SIF contributions to crack driving force in the Walker effective SIF framework

‣ Including residual crack opening displacements as they affect closure/interference

• Incorporation of KIII may refine quantification of modal transition criteria through contribution to shear stresses

‣Non-zero β ITCR specimens can contribute significant data

Acknowledgements• My advisor, Dr. Steve Johnson, for his patience & acceptance

• My committee, Dr. Rick Neu, Dr. Jianmin Qu, Dr. Tom Sanders, Dr. Naresh Thadhani, for being ready when I finally was

• MPRL’s Rick Brown & Robert Cooper, for keeping my hands attached & load frames running just long enough

• Dr. Rick Pettit at Pratt & Whitney for conceiving & guiding this whole project, Dr. Greg Swanson & Dr. Tarek Sayyah at NASA MSFC for adding test data & insight, and Michael Middlemas for the SEM fractography library

• My parents for their constant support in every way

• My friends in Atlanta for sharing in research, politics, apartments

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