Notched Fatigue Behavior under Axial and Torsion Loads

Notched Fatigue Behavior under Axial and Torsion Loads

Ali FatemiUniversity of Toledo, Toledo, Ohio

Electricite de France

28 October 2013

• Motivation and Objectives

• Experimental Program and Observations

• Analysis and Data Correlations• Conclusions

2

US Navy P‐3C Orion

New US Navy P‐8A Poseidon

• Due to increasing number of cracks developing in aging fleet, full scale fatigue tests were performed

• Many cracks were found to initiate from rivet holes, especially in lower wing skin

• Normal and shear stress histories at different wing locations were obtained

A Portion of the A-T Stress History (1/700th, about 106 total reversal points)

5

Fatigue Crack Growth in Aluminum 2xxx Specimens under VA A‐T Loading

• Crack nucleation and growth each constitutes about half of total fatigue life


Part I: Crack Nucleation Aspects

Part II: Crack Growth Aspects

7

• What is the crack nucleation mechanism (tensile or shear)?

• What is the notch effect on fatigue life?

• Can the traditional fatigue criteria (i.e. von Mises effective stress or strain) correlate nucleation life under simple constant amplitude axial and torsion loads?

• Does intermittent axial load in cyclic torsion or intermittent torsion load in cyclic axial loading affect the behavior?

• Is there a difference in behavior between different metals regarding the above aspects (i.e. steel versus aluminum)?

Objectives

8

• Materials:– Structural carbon steel

– 2024‐T3 and 7075‐T6 aluminum alloy series

• Specimens used were thin‐wall tubes with or without a transverse circular hole.

• Crack development and growth was monitored with:

– Digital microscopic camera for notched specimens

– Acetate replicas for smooth specimens

Experimental Program

9

• The loading was mainly constant amplitude pure axial and pure torsion

• Some constant amplitude axial tests with intermittent pure torsion cycles and vise versa

• Some combined in‐phase and pit‐of‐phase axial‐torsion tests

• Most tests load‐controlled and some axial tests with strain control

• Incremental step cyclic deformation tests conducted in axial and torsion to provide stress‐strain relations

Experimental Program (Loading)

10

Experimental Program (Specimens)

Tension Kt= 3.29 Kt= 3.21 Torsion Kt = 3.98 Kt= 3.89

Structural Steel

24 mm OD, 1.1 mm thickness3.4 mm diameter hole

Aluminum 2xxx

29 mm OD, 1.9 mm thickness3.2 mm diameter hole

11

Experimental Program (Materials)

Structural Steel Aluminum 2xxx

0

50

100

150

200

250

300

350

400

450

500

0.0% 0.5% 1.0% 1.5%

Stress, M

PaStrain, %

Monotonic Curve

Cyclic Curve

Cyclic Axial Data

Cyclic Stress‐Strain Correlations

• Incremental step tests

• Substantial amount of cyclic hardening for the material

• von Mises effective stress and strain correlates torsion and combined axial‐torsion cyclic data with experimental data from axial test

13

Axial and Torsion Un‐notched Fatigue Behaviors (Structural Steel)

Axial Loading Torsion Loading

0.01%

0.10%

1.00%

1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07

Strain Amplitu

de

Reversals to Failure, 2Nf

Total Strain data

Plastic Strain data

Elastic Strain data

14

Axial and Torsion Un‐notched Fatigue Behaviors (Aluminum 2xxx)


50.00

500.00

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07

Shea

r Stres

s Amplitu

de (M

Pa)

Cycles to failure

Torsion smooth data

50.00

500.00

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07

Stress Amplitu

de (M

Pa)

Cycles to failure

Axial smooth data

0.01%

0.10%

1.00%

1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07

Shear S

train Am

plitu

de


Total Strain data

Plastic Strain Data

Elastic Strain Data

15

Axial and Torsion Un‐notched Cracking Behaviors(Shear Mechanism)


Aluminum2xxx

StructuralSteel

16

Correlation of Axial and Torsion Un‐notched Fatigue Data with von Mises Effective Stress


von Mises effective stress does not correlate un‐notched specimen axial and torsion data of either material.

50.00

500.00

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07vo

n Mises Equ

ivalen

t Stres

s Amplitu

de, M

PaCycles to failure

Axial smooth data

Torsion Smooth Data

17

Correlation of Axial and Torsion Un‐notched Fatigue Data with von Mises Effective Strain


von Mises effective strain does not correlate un‐notched specimen axial and torsion data of either material.

0.10%

1.00%

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07

Effective Strain Amplitu

de


Axial Smooth data

Torsion Smooth data

18

Notched Behavior under Axial and Torsion Loadings

Maximum Shear Stress Distribution

Axial Loading

Maximum Principal Stress Distribution

Torsion Loading

Stress Distributions Around the Hole under Axial and Torsion Loadings

Both max shear stress and max principal stress locations around circumference of the hole are at 45° for torsion loading and 0° for axial loading

Torsion Axial

21

Axial and Torsion Notched Cracking Behaviors(Shear Mechanism)

Axial Loading Torsion LoadingAluminum

Aluminum

SteelSteel

Definition of Crack Nucleation for the Notched Specimens

A crack length of 0.2 mm was used as crack nucleation for both materials

100

1000

0.001 0.01 0.1 1

Stress Ran

ge (M

Pa)

Crack Length, a (mm)

Kitagawa‐Takahashi Diagram – 2xxx Aluminum

delta fatigue limit

delta (K)th / (pi*a)^0.5

delta (K)th / (pi(a+ao))^0.5

. ⁄

aaaK

KfFK

f

etth

2321

21212

Kujawski, D., 1991, “Estimations of stress intensity factors for small cracks at notches”, Fatigue and Fracture of Engineering Materials and Structures, Vol. 14, pp. 953‐965.

23

Axial Notched and Un‐notched Fatigue Behaviors


CK

K tf

11

1

50.00

500.00

1.E+00 1.E+02 1.E+04 1.E+06

Axial Nom

inal Stres

s Amplitu

de, M

Pa

Cycles to failure

Axial smooth data

Axial Notched Data (0.2 mm crack)

Axial Notched Data (1.0 mm crack)

S‐N Prediction Line

24

Torsion Notched and Un‐notched Fatigue Behaviors


25.00

250.00

1.E+00 1.E+02 1.E+04 1.E+06

Shea

r Nom

inal Stres

s Amplitu

de (M

Pa)

Cycles to failure

Torsion smooth data

Torsion Notched Data (0.2 mm crack)

Torsion Notched Data (1.0 mm crack)

S‐N Prediction Line

25

Correlation of Axial and Torsion Un‐notched and Notched Fatigue Data with von Mises Effective Stress


von Mises effective stress does not correlate smooth and notched specimens axial and torsion data of either material.

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07Pred

icted Cycles to

Failure, N

fExperimental Cycles to Failure, Nf

Axial SmoothTorsion SmoothAxial NotchedTorsion Notched

26

Notch Strain from Neuber’s Rule and FEA under Axial and Torsion Loads for Structural Steel

Axial Load Torsion Load

• Notch stress state is plane stress• Neuber and FEA notch strains are close for both loadings

27

Correlation of Axial and Torsion Notched and Un‐notched Fatigue Data with von Mises Effective Strain


von Mises effective strain does not correlate un‐notched specimen axial and torsion data of either material.

0.10%

1.00%

10.00%

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07

von Mises Strain Am

plitu

deReversals to Failure, 2Nf

Axial Smooth dataTorsion Smooth dataAxial Notched dataTorsion Notched data

28

Correlation of Axial and Torsion Notched and Un‐notched Fatigue Data with FS Critical Plane Approach

Structural SteelAluminum 2xxx

Critical plane damage parameter correlates all data well since it represents damage mechanism

0.1%

1.0%

10.0%

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07

FS Param

eter


Axial Smooth Data

Torsion Smooth Data

Axial Notched Data

Data Correlation

• Smooth & notched specimens• Tubular & plate specimens• Axial & torsion loadings• In‐phase & out‐of‐phase A‐T

30

Axial Tests with Intermittent Torsion Cycles and Torsion Tests with Intermittent Axial Cycles (Structural Steel)

• Axial tests with intermittent torsion cycles A1000‐T100• Torsion tests with intermittent axial cycles A100‐T1000• Tests with equal axial and torsion cycles A1000‐T1000

A1000‐T100 A100‐T1000 A1000‐T1000

31

Axial Tests with Intermittent Torsion Cycles and Torsion Tests with Intermittent Axial Cycles (Structural Steel)

• A1000‐T100 test fatigue lives are similar to axial tests• A100‐T1000 test fatigue lives are similar to torsion tests• A1000‐T1000 test fatigue lives are puzzling!

32

Conclusions (1)

• Crack nucleation mechanism for both smooth and notched specimens and both materials is shear.

• The commonly used von Mises effective stress or strain cannot correlate either smooth or notched data under simple axial and torsion loadings.

• Neuber’s rule gives an accurate estimate of the notch deformation under both axial and torsion loadings.

• Critical plane life prediction model can correlate smooth and notched axial and torsion data well, as it correctly represents the operating damage mechanism.

33

Conclusions (2)

• While results from a few intermittent axial cycles in torsion test and a few intermittent torsion cycles in axial test are as expected, results from tests with equal number of axial and torsion cycles are puzzling.

• In spite of the structural steel and aluminum alloy having very different microstructures and properties, the aforementioned observed behaviors are similar for both materials.


Part I: Crack Nucleation Aspects

Part II: Crack Growth Aspects

35

Variable Amplitude Axial‐Torsion Tests with Service Load History (Test Results)

• Crack nucleation and growth each constitutes about half of total fatigue life

36

• What are the crack growth mechanisms and why the difference in smooth and notched crack growth mechanisms?

• Can crack growth rates be correlated with stress intensity factor range in both short and long crack regimes?

• Does intermittent axial load in cyclic torsion or intermittent torsion load in cyclic axial loading affect the behavior?

• Is there a difference between different metals regarding the above aspects (i.e. steel versus aluminum)?

Objectives

37

Experimental Program (Specimens)

Tension Kt= 3.2 Torsion Kt = 3.9

Structural Steel Aluminum 2xxx Aluminum 7xxx

24 mm OD 1.1 mm thickness3.4 mm hole dia.

29 mm OD1.9 mm thickness3.2 mm hole dia.

70 mm OD2.4 mm thickness6.35 mm hole dia.

Loading Conditions and Nomenclature

A Axial

T Torsion

A-T-IP In-Phase combined Axial-Torsion

A-T-OP Out-of-Phase combined Axial-Torsion

A1000-T1 1000 Axial cycles followed by 1 Torsion cycle

A1000-T10 1000 Axial cycles followed by 10 Torsion cycles



A-Tm Axial cycles with mean Torsion

A-TRandom Axial cycles with random amplitude Torsion cycles

Crack Growth Mechanism (Tube vs Pre-cracked Plate Behavior in Shear)

• In tubes or shafts, cracks initiated in shear (i.e. torsion) continue to grow in shear (Mode II and/or III)

• In pre‐cracked plate geometries of the same material, cracks grow in Mode I under shear loading.

• This is true for most metals (Al, carbon steels, alloy steels, super‐alloys, stainless steel, etc)

• Which growth mechanism is assumed to operate has a significant implication in life prediction.

40

Four-Point Plate Specimen Loading

41Crack turns to Mode I crack growth direction, regardless of the KII/KI ratio chosen

Observed Short Crack Growth Paths

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0

x (mm)

y (m

m)

crack tip

Mode I

42

Observed Crack Growth Paths (Mode I)

KII/KI = 0R ~ 0.05

KII/KI = 0R ~ 0.05

KII/KI = 0.6R ~ 0.05

KII/KI = 1.3R = 0.5

KII/KI = 11R ~ 0.05

Crack Growth Mechanism

• Is the difference due to specimen geometry (i.e. curvature effect)?

• How about a tubular geometry with a fatigue crack vs machined pre‐crack?

Notch dimensions of 0.25 mm wide, 1 mm long, and 0.5 mm deep

Smooth specimen crack length of 0.8 mm

In which direction will the crack grow in cyclic torsion?

Crack Growth Mechanism

Different growth mechanisms:

• In tube with natural fatigue crack, growth mechanism is by coalescence, driven by plasticity of the gage section (nominal plasticity), Mode II growth

• In tube with machined pre‐crack, growth mechanism is by Mode I, driven by plasticity of the crack tip (local plasticity)

Natural fatigue crack

Machined pre‐crack

45

Axial and Torsion Un‐notched Crack Growth Behavior(Shear Mechanism, Aluminum 2xxx)

Axial Loading

Torsion Loading

Crack growth mechanism is a coalescence process of multiple nucleated shear cracks (i.e. mode II nucleation AND growth)

46

Axial and Torsion Un‐notched Crack Growth Behavior(Shear Mechanism, Aluminum 2xxx)

• Example of Smooth Torsion

• Nf = 180,288 cycles

• Coalescence of cracks leading to failure

47

Crack Coalescence and Shielding Processes

Coalescence Shielding

200 m

Crack Network

48

Axial and Torsion Un‐notched Crack Growth Behavior(Aluminum 2xxx)

Formation of multiple small cracks with little growth of each crack prior to their coalescence (i.e. formation of crack networks, rather than growth of dominant cracks)

0

0.2

0.4

0.6

0.8

1

1.2

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Half C

rack Len

gth, a, (mm)

N/Nf

a vs (N/Nf) for Smooth Axial and Torsion Specimens

Smooth Axial_failure crack

Smooth Torsion_secondary crack a

Smooth Torsion_secondary crack b

Cracking in A and T Loadings of Notched Specimens

Aluminum 2xxx

Torsion

Structural Steel

Mechanism is growth of independent cracks in mode I nucleated at the stress concentration (but its growth is independent of notch plasticity)

Aluminum 7xxx

Axial

50

Axial and Torsion Notched Crack Growth Behaviors(Aluminum 2xxx)

Process of continuous growth of dominant cracks nucleated at the notch

0

1

2

3

4

5

6

0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95

Crack Length (m

m)

N/Nf

Crack Length Vs. N/Nf for Axial Loaded Tubular Specimens

Hole radius

T09‐NA_S = 145 MPa

T19‐NA_S = 145 MPa

T18‐NA_S = 115 MPa

T24‐NA_S = 98 MPa

T23‐NA_S = 130 MPa

0

1

2

3

4

5

6

0.5 0.6 0.7 0.8 0.9 1

Crack Length (m

m)

N/Nf

Crack Length Vs. N/Nf for Torsion Loaded Tubular Specimens

Hole radiusT15‐NT_2,4_T = 101 MPaT15‐NT_1,3_T = 101 MPaT21‐NT_2,4_T = 85 MPaT21‐NT_1,3_T = 85 MPaT20‐NT_2,4_T = 85 MPaT20‐NT_1,3_T = 85 MPaT22‐NT_2,4_T = 71 MPa

Axial Torsion

51

Comparison of Axial and Torsion Smooth vs Notched Crack Growth Behaviors (Aluminum 2xxx)

Process of crack growth by coalescence in smooth specimens vs continuous growth of dominant cracks nucleated at the notch for notched specimens

Implication of Cracking Mechanism Observation

• Cannot use the common technique of using pre‐cracked specimens to characterize fatigue crack growth behavior if a crack network exists

Crack Growth Rates in Axial and Torsion Tests

Higher CGR in torsion compared to axial loading at the same max principal stress level

Aluminum 7xxx Aluminum 2xxx Structural Steel


Torque τ=144 MPa

Mode I

144 MPa 144 MPa


• A compressive tangential stress acts parallel to crack growth path in torsion

• The tangential stress increases plastic zone size and crack driving force, increasing crack growth rate


14/sec

1113/4/sec

//

22

1

u

u

dNdadNda

• Brown and Miller considered adjustment of the crack tip plastic zone size based on extension of Dugdale’s model to biaxial loading of a mode I crack by adding the T‐stress

da/dN1 Equibiaxial value of crack growth rateΛ Biaxial stress ratiou Ultimate strength

Crack Growth Rates in Axial and Torsion Tests(Structural Steel)

IP vs OP Loading and Crack Branching in OP Loading (Aluminum 7xxx)

In‐Phase Out‐of‐Phase

A-T10

A-T13

A-T4

A-T6

Crack Growth Rates in IP and OP Loading(Aluminum 7xxx)

Crack branching in OP loading causes:

• Periods of decreased CGR (a‐N plot)

• Much data scatter

• Slower CGR compared to IP loading

Variation od Principal Stress Value and Its Orientation During One Load Cycle

All planes in the range of ±42 to the horizontal axis are subjected to more than 90% of the maximum principal stress amplitude.

Effect of Alternating Loading Mode on Crack Growth Behavior

Structural Steel

A1000‐T100

A100‐T1000

A100‐T1000

A100‐T10

A1000‐T100

Aluminum 7xxx

Crack Growth Rates for Tests with Alternating Loading Mode

• Increased CGR with increased number of torsion cycles in axial loading.

• Much scatter, more detailed CGR analysis accounting for closure is needed.

Aluminum 7xxxStructural

Steel

Crack Growth Rates for Tests with Alternating Loading Mode

• Reduced roughness due to intermittent torsion cycles during axial loading?

• Crack growth due to intermittent axial cycles during torsion loading.

144 MPa σ

Axial cycles on 0° plane

Torsion cycles on 0° plane

144 MPa 144 MPa

72 MPa

144 MPa σ

Torsion cycles on 45° plane

Axial cycles on 45° plane

144 MPa 144 MPa 72 MPa 72 MPa

72 MPa

Axial Loading with Torsion Cycles Torsion Loading with Axial Cycles

Axial Cycles with Random Torsion Cycles(Aluminum 7xxxx)

Axial Cycles with Random Torsion Cycles(Aluminum 7xxx)

• Crack growth on the maximum principal stress amplitude plane (i.e. perpendicular to tube axis)

• Faster crack growth rate, compared to pure axial test at the same axial stress level

• Reduced roughness‐induced closure from torsion cycles?

Comparison of CGR at K = 5 MPa√m(Aluminum 7xxx)

‐ CGR is higher in T than in A loading due to increased plastic zone size from the tangential compressive stress.

‐ CGR is slowest for OP loading, as compared to all loading conditions. This is due to roughness and repeated bifurcation at the crack tip in OP loading.

Conclusions (1)

Cracks grew on the maximum shear stress plane (mode II)in smooth (i.e. un‐notched) specimens for all the loadingconditions considered.

Cracks grew on the maximum principal stress plane (modeI) in notched specimens for all the loading conditionsconsidered.

Crack growth in smooth specimens was due to a crackcoalescence process, while for notched specimens thecrack(s) nucleated at the notch root dominated crackgrowth life.

For the same max principal stress amplitude, CGR washigher in torsion than in axial loading.

Conclusions (2)

In out‐of‐phase (OP) A‐T tests fatigue CGR was lower than inin‐phase (IP) tests due to crack branching and a torturouscrack path from repeated bifurcation at the crack tip.

Intermittent torsion cycles increased axial CGR. Randomtorsion cycles in constant amplitude axial test also increasedCGR. Both effects may be explained by reduced roughness‐induced closure from cyclic shear.

Little or no effect of mean torsion on axial fatigue life or CGRwas observed.

Experimental results were consistent for the structural steeland the two aluminum alloys considered.

68

Acknowledgments

• Financial Support:

• Navair (Aluminum data), Dr. Nam Phan

• Fullbright Scholar Program and Kyiv Polytechnic Institute (Dr. M. Gladsky and structural steel data)

• Load History: Dr. Nagaraja Iyyer, TDA

Notched Fatigue Behavior under Axial and Torsion Loads

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