lecture 8 fatigue 2 2011

8/3/2019 Lecture 8 Fatigue 2 2011

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Investigate Fatigue Crack Growth Mechanismsand Life Prediction Methodologies

Cyclic loads and simple growth models Crack closure Newmans model Variable amplitude loads

Micro (nano) mechanisms of fatigue Incubation, nucleation, microstructurally small crack

growth, physically small crack growth, long crackgrowth

CEE 7700 Meeting 8Objectives of This Meeting


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How Do You Select An Initial Crack Size? Specified by a standard or company policy

For turbine disks, the Air Force requires that one consider a 0.050flaw at all highly stressed locations

The allowable initial flaw size for a required fatigue life may be the unknown in the analysis

The allowable initial flaw size may dictate the required inspectionand acceptance criteria for a component

Use a characteristic inherent flaw size forthe material Second phase

particles

Assume the smallest flawthat can be detected reliably

0

1

a0

probabilityof detection

NDE method 1

method 2


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How Do You Decide When to Terminate a LifePrediction Analysis?

The onset of unstable crack growth

Computed cycles exceed those required for the application

The crack reaches a specified allowable size

IcK RK

K 1

max

allowableaa

The stress intensity factor range falls below threshold

threshold K K

required N N


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increasing R

logdadN

log( K )

Load Ratio, R, Effects on FCGR

Most materials exhibit a strong correlation between crack growthrates and the load ratio, R , with increasing crack growth ratesobserved for increasing R s

Growth rates increase with R until a saturation level is reached (about0.6 to 0.7 for most steels and aluminums, but can be as low as 0.5 forsome Ti alloys). Above this level there is no increase in growth rate

with increasing R .


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K

eff K

dN da

1 0 1

R

constant applied K

Load Ratio Effects for Negative Values

Remotely applied loads

Effective crack-tip loads

global crack closure

expected due toglobal closure

observed


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strain gage

fatigue crack

s

e

E

Load Ratio Effects Are Best Explained by theCrack Closure Concept

If a strain gauge is placed ~2mm behind the crack tip, one observes that the

compliance in the near-tip region changes as the remote load is increased.

This indicates that near the crack tip, the crack faces do not separateimmediately upon the application of a remote tensile load, but remain incontact for some portion of the load cycle. This effectively reduces the SIFrange experienced by the crack tip.

e 0

s op


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K eff K max K op K K max K min

The Crack Closure Concept and the Use of K eff Was First Proposed by Elber

K op is the load level where the crack faces

open

Any of the following closure mechanisms may be present: plasticity -induced crack closure

oxide -induced crack closure roughness -induced crack closure viscous fluid -induced crack closure transformation -induced crack closure


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crack tip crack advance

crack openingcrack closure

A

B

C

D

E

F

Material loaded in compression

Material yielding in tension

permanent plastic

elongation

A Simple Model for Plasticity-induced Crack Closure

time

A

B

C

D

E

F

K max

K min

K op K eff


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The Effect of Crack Closure for a Typical

Al Alloy for Various Rs

At high R s, there is no crack closure effect becauseK op equals K min. That is, the crack faces always

remain open.

time

K

K op K K eff

R 0.0, K eff

K 0.73

time

K

K op K K eff

R 0.25, K eff

K 0.86

time

K

K op

K K eff

R 0.7, K eff

K 1.0


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0

0.5

1

1.5

2

2.5

-1 -0.5 0 0.5 1 R

a

virtual cutoff

dadN Walker

a dadN Paris

The Walker FCGR ModelAn empirical modification to the Paris model that accounts for R effects.This was proposed before crack closure concepts were well understood.As proposed, it does not account for saturation at high R s.

dadN

C K n

(1 R)1 m

The Walker model has been popular in the aerospace industry because it is:simple to apply, requires only one additional parameter ( m , usually assumed to be0.5), and gives reasonable results for many materials providing that R is not too

high.

Note: R = 0 is taken asthe base configuration

(89)


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S

2d

W

2d

W

s s

Newman, A crack -closure model for predicting fatigue- crack growth under aircraft spectrum loading, Methods and models for predicting fatigue

crack growth under random loading , Chang and Hudson, eds., ASTM STP 748, 1981, pp.53-84

Newmans Model for Crack Closure (FASTRAN)

1) analytical solutions for a crack in a plate with remote and

partial crack-face loading

2) an estimate for the plastic zone size

cW

csin 1 sin

cW

sec

S max2as 0

1


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S max S min

c c

s s

maximum stress minimum stress

3) generalized Dugdale crack with perfectly plastic bars placed in thecrack.

as 0

as 0

as 0

as 0yielding in tension

yielding in compression


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f K op

K max

max( R, A0 A1 R A2 R2 A3 R

3)

A0 A1 R

R 0

2 R 0

A0 (0.825 0.34a 0.05a 2 )[cos( 2 S max /s 0 )]

1 a

A1 (0.415 0.071a )S max /s 0 A2 1 A0 A1 A3

A3 2 A0 A1 1

Newman, A crack -opening stress equation for fatigue crack growth, Int J Fracture , Vol. 24, 1984, R131-R135

For constant amplitude loading, Newman has run his modelfor a wide range of parameters and developed an

expression for K op as a function of K max , R , S max , and s 0


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da/dN vs. K effective curves for Al-2024, Al-7075,Ti-6-4, and 4340 Steel


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176 Newman, Phillips, and Swain, Fatigue -life prediction methodology using small-crack theory and a crackclosure model, Proc FAA -NASA symposium oncontinued airworthiness of aircraft structures, Atlanta, GA, 1996

FASTRAN predictions for constant amplitude loading


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FASTRAN Predictions for Variable Amplitude Loading

Newman, Phillips, and Swain, Fatigue -life prediction methodology using small-crack theory and a crackclosure model, Proc FAA -NASA symposium oncontinued airworthiness of aircraft structures, Atlanta, GA, 1996


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log( K )

logdadN

K threshold

Short Cracks Grow Faster Than Would Be Predicted forTheir Corresponding K


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long cracks(LEFM)

crack length, a , or log K

l o g

d a

/ d N

short cracks

plastic zone

residualplastic wake

crack

Short cracks do not have a fully developed plastic wake. As it developes, K op will increase and the cracks will decelerate and possibly retard.

The Short Crack Anomaly Can Be Explained by CrackClosure Effects


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log( K )

log( dadN )

7050 T74 AL

R 0.8

R 0.4 R 0.1

The Forman model has 14 free parameters. The NASGRO program has amaterial database that includes the appropriate parameters for over 300

combinations of alloy, test environment, and product form.

dadN C (1 f )n

K n

(1

K th K ) p

(1 R)n (1 K [(1 R) K c ])q

The Forman (NASGRO) Model

State-of-the-Practice!

(90)

lecture 8 fatigue 2 2011

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