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WRIGHT PATTEF,-SO' AIR FORC E DIRSE WO,1
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.
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