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ATIC"Crack Growth

Retardation Model

Using an

Effective Stresd Concept

J. Willenborgg.M. Engle 93-25604BA. Wood IEhlIuIIlmmI

Technical Memorandum 71-I-FDR

January 1971

Approved for public release; distribution unlimited.

93 10--"22 008

"1 e PFPL-TH-71-i-FBR

• s*

S•UsI FO -orCrack Growth - I- T

, DTIC TAB O

Retardation Model Unanuouneed LJ

J nus t '1f i Ga t i o il• -- ..-

Using an ---

Effective Stress Concept .. i

Avatlabi l t -- Codon

J. Willenborg DI44 S 0 isa "R.M. EngleB.A. Wood.....i..

Technical Merocrandumn 71-1-FBR

*January 1971 U NA N N 0 0 f

This document has been approved for public,* release and sale; its distribution is unlimited.

REPORT DOCUMENTATION PAGE i ,,"I....M ,N,,,a

1. AGENCY USE ONLY (Loire bink , | 12 EpOR, T i IFPORT TYPE ANr) )A ES (OVND" anýuary 97 1Final...

TiTLE A ) SUP.TIL . :UONG NJUiBERS

A Crack Growth Retardation Model Using An Effective Project 1467Stress Concept Task 146704

6. AUTHOR(S)J. WillenborgR. M. EngleH. A Wood

$7. PERFORMING ORGANIZATION NAME(S, AND ADORESS([S) i 8. PrRi.OtiMINc ORGANItATIONRLPO0,4 NO-MtISRAir Force Flight Dynamics Laboratory

"Director of Laboratories: ~AFFDL-TM-7 i-1I-FBRAir Force Systems CommandWright Patterson Air Force Base, Ohio

9. SPONSORiNG, MONITORING AGENCY NAMIrC• AND ADDRESS((S) '1. SPONSORINC ,MONITORINGe : AGENCY REPORT NUA4JMR

Same as above

L 11. SUPPL[MENTARY NOTES

I12a- nIcRI8IflON, AVAII A,)i| 11, TA Tt,"I .;T 1.b. DISII URI lON (O 00

Approved for Public Release; Distribution is Unlimited

13. ABSTRACT ,imurn ?2()C wivds)

This report describes a crack growth retardation model which utilizes an"effective stress" concept to reduce the applied stresses and hence the cracktip stress intensity factor. The derivation of the model is presented as wellas comparisons with existing experimental and analytical spectrum crack growthdata for D6ac steel and 7075-T6 aluminum.

20

Uc sfdn siilsidU lassifie

Unclassified Unclassified ! Unclassified i Unclassified

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FO'RM, ORID

This work was conducted by the authors under the supervision

Qf Mr. R.M. Bader, Technical Manager, Analysis Group at the Air

Force Flight Dynamics Laboratory, under project 1467, "Structural

Analysis Methods," Task 146704, "Structural Fatigue and Fracture

Analysis Methods for Aerospace Vehicles."

The manuscript was released by the authors in January 1971.

This Technical Memorandum has been reviewed and is approved.

•/

FRANCI RChaSoli "CChandc" B=.Ch

Structures Division

ABSTIRACT

This repbrt describes a crack growth retardation model which

utilizes-an "effective stress" concept to reduce the applied stresses

and herpce the crack tip stress intensity factor. The derivation of

the model is presented as well as comparisons with existin g experi-

mental and analytical spectrum crack growth data for D6ac steel

4ý4

and 775-T aluinum

= ,,

•:: i

CONI'ENTS

Section

I Introduction I

II. Description of the Model

III Correlation.

"IV Di-scussion 7

V References

SINTRODUCTION

Current pr~dictive analysis techniques for crack propagation

under cyclic loading rely on the integration of basic constant amplitude

growth rate data derived from laboratory tests on simple coupons. Such

an automated procedure is contained in Reference 1.

Variations between predicted and actual growth- lives have been

noted for cases of variable amplitude spectrum loading due to the

in teraction of the stress applications (1Leferencos 3 and 4). The occurrence

of a tensile oerload will retard growth below that normally expected.

To neglect these interaction effects results in grossly tonservative

prediction of crack growth life.

Severc! attempts at developing mathenatical models for growth

retardation have been made. (References 2 and 5). In Reference 2,

Wheeler calculates a retardation factor Cp which operates direc.tly by

reducing growth rate da/du. The procedure requires previous spectrum

growth data to derive a retardation exponent "m". Moderate success

has been achieved by the author in fitting existing spectrum data.

In the current study, retardation is accounted for by operating

directly on the crack growth driving function AK. An effective value

of the stress intensity factor range is computed by assuming a form of

the residual crack tip stress present after the application of the

overload. Once obtained, the modified AK is used in conjunction with

ordin ary constant growth rate data and the CRACKS computer routine

(Reference 1) to calculate life. No other empirtcal dath or fnciors

are required.

Tihe motdel duvelopment Is contained in Section II. Application

of the. jeet'edure to exiiting D6ac and 7075-T6 spectrtun dath is in notaIned

"ii ec'. I l /I - .. •... • " '

I

SBCTION ITI

DESCRIPTION OE THE MODEL

To best descibe the operation of the r~tardation model, consider

the simple spectrum as 6hown in Figure 1. The step-by-step sol'ution

of this problem is outlined below:

1. Load layer 1 is applied. Using the maximuuu streas, c

the plastic zone radius, ap , is calculated and saved for reference.

•.4J

2. The first load cycle in layer 2 is applied. The maxiumum

stress, a , is• compared to a Since c is l.(-ess than a , the2 1 2 1

retardation model is applied.

3.- The first step is to determine the applied stress, rap

required to reach ap. This stress is dekterniined as follows:

The yield zone radius for Gai, is given by

R ==<• _- ( o ..-

O~C

Solving for oap we obtain

where dic is the crack length at the beginning of the load cycle or

load layer. 1Hencc, for the first cycle of layer 2, eqtuat:.on (2)

..--

becomies

4. Next, we obtain the reduction in the applied stress, Ored

due to the progress through the plastic zone for a given layer.

* -

For layer 2 , equation 3 becomes

When the crack has propagated through the plastic zone, ared 1.

set equal to zero since the crack propagation is no longer being

retarded.

5. Effective values of the maximum and ,nimunium applied stresses

are then calculated as follows:

4 Y,

4

If elither of the effective tre . i: less. than zero, it If-

net equal Vo zero.

6. .:ffcctlvc values of P and AK arc now calcolited u.-Ang ,quk|t. i o|

* : - 3 . ---.

4 and 5. The crack growth lIw.% tben appliA'd dxiroctly• using the

effective R and &K, .to obtain the growth during the Interval. At

thi end of the first cycle of layer 2 .. 2 obtain d"2,1

7. Compare the.current value a2 with ctP, Since a0 is

1ess than ap , the growth is still. retarded. We now return to step 3.

Nov we obtain

CY -U - a -

We see Chlit eV p diminishes as ac approaches a.. "Whet a~kP

equals Gmax a 0 red is zero and retardation is no longer present.

S RC• r 0 N I I I£

COhRRELATION

Ia o•dor to tasc the validity of the model, a few problems

were solved involving two different matarials Subjected to different

types of spectra. Tie model was incorpornted into the CRACKS

computer program (Reference 1) to provide rapid solution capability.

Tfh• first pioblem is taken from T)r. Wheeler's report (Reference

2, figure 8). The spectrum is shown in figure 2 and the correlation

with test data a3 well as Dr. Wheeler's retardation model is given

in figure 3. The material was D6ac steel. The Paris form of the

crack Rrowth law was

EL.. . O.0 /I-7- 0 X-"

In thils emimple, the Paris form of the growth law wans assumed

valld for all. values uf load ratio, R = cminoulax

A second problem, also a s•(rface flaw in a D6ac steel specimen,

was run using Forman's form of the crack growth equation,

do-. 1) o. iýA1 AK

Both the 5g and 7,33g vcr!ious of the spectra wore used.

The spectra from Referenct- 3 is given in figure 4 and the cor-

relation is shown in figures 5a and 5b. For the 5.Or spectrum, four

laboratory test,- were conducted. Specimen 131,3 and P11035 Indicate

the scýat:'er of the Lost data. Alsc imdicated on Figure 5a and 5b

are predIcLcoln based oil the Wh\elfr model us1ing the same asi.c

growth rati. dat•.

. . ... J5... . .. ...)

Another material, 7075-T6 aluminum was also examined. A

twei.ve inch wide center-cracked panel was subjected to various

simple spectrum loadings (Reference 4.) The cnectra and correlation

dza are prcsented in figure 6. For this example, the plane stress'

for.n of the yield zone was considered.

IV DISCUSSION

Although of preliminary nature, the data presented in this

report have demonstrated the ability of the proposed crack retard-

ation model to account for the growth delay due to the application

of tensile overloads in a complex spectrum.

The most.significant feature of the model is its ability to

predict growth retardation without the assistance of empirical

.*factors or test data. This is clearly demonstrated in examples 1

and 2 of Section III, where widely diffe):eiLc values of the Wheeler

parameter "m" are required to fit the spectrum data. This would

indicate that "m." is sensitive to factors other than material

difference.

Work is continuing to further validate the model with additional

simple and complex spectra including the occurrence of single spike

overloads. A test program currently underway at AFFDL will [xovide

additional data for D6ac steel, 7075-T6 aluminum and 6al-4V titanium.

The successful use of the analysis scheme, of course, requires

valid and adequate basic growth rate data. Current efforts are

investigating the sensitivity of p:ediction, to the normal vaziation

in.reported da/dn vs AK data.

SSECTION V

REFEM ENCES

1. Engle, R.M., 'CRACKS - A FORTRAN IV Digital Computer Program

for Crack Propagation Analysis-," AFFDL-TH-70-107, October 1970.

2. 9heeler, O.E., "Crack Propagation Under Spectrum Loading,"

FZM-5602, 30 June 1970., General Dynamics, Fort Worth Division

3. Wood, H1.A., Haglage, T.L., "Test Results and Analysis of Crack

Propagation Under Variable Amplitude Spectrum Loading for D6ac Steel,"

AFEDL-T14-FPBR-71-2 , January 1971.

4. Butler, J.P., The Boeing Company, "The Material Selection and

Structural Development Process for Aircraft Structcal' Integrity

Under Fatigue Conditions," presented at the Air Force Conference on

Fatigue and Fracture of Aircraft Structures and 4Iaterlals, December

15-18, 1969, Mianri l3each Fl, ida.

5. Elber, Wolf, NASA, "The Signif cance of Fatigue Crack Closure,"

Presented at the 1970 annual meeting of the American Society for

Testing and Materials, Toronto, Canada, 21-26 June 1970.

S.

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