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AFWAL-TR-84- 3080VOLUME Vl
ADVANCED LIFE ANALYSIS
METHODS - User's Manual
for "LUGRO" Cemputer Program
Ln to Predict Crack Growth in
~ Attachment Lugs
K. Kathiresan
S Lockheed-Georgia CompanyMarietta, Georgia 30063
T. R. Brussat
Lockheed-California CompanyBurbank, California 91520
September 1984
Final Report for Period 3 September 1980 to 30 September 1984
C...D
Lii.5J Approved for Public Release; Distribution Unlimited.
__ Flight Dynamics Laboratory - CTEAir Force Wright Aeronautical Laboratories rAir Force Systems Command "iMAR 3 1985Wright-Patterson Air Force Base, Ohio 45433
A
NOTICE
When Government drawings, specifications, or other data are used for anypurpose other than in connection with a definitely related Governmentprocurement operation, the United States Government thereby incurs noresponsibility nor any obligation whatsoever; and the fact that the governmentmay have formulated, furnished, or in any way supplied the said drawings,specifications, or other data, is not to be regarded by implication orotherwise as in any manner licensing the holder or any other person orcorporation, or conveying any rights or permission to manufacture use, or sellany patented invention that may in any way be related thereto.
This report has been reviewed by the Office of Public Affairs (ASO/PA) andis releasable to the National Technical Information Service (NTIS). AT NTIS,
it will be available to the general public, including foreign nations.
This technical report has been reviewed and is approved for publication.
JAE L. RUDD FRANK D. ADAMS, ChiefProj ct Engineer Structural Integrity Branchý7 Structures & Dynamics Division
FOR THE COMMANDER
ROGER-J.ESTRM Colonel, USAFChief, Structures & Dynamics Division
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UnclassifiedSECURITY CLASSIFICATION OF THIS PAGE
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2. SECURITY CLASSIFICATION AUTHORITY 3. DISTRIBUTION/AVAILABILITY OF REPORT
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4 PERFORMING ORGANIZATION REPORT NUMBER(S) 5. MONITORING ORGANIZATION REPORT NUMBER(S)
LG82ERO117-Y(6 AFWAL-TR-84-3080, Volume VI
6a NAME OF PERFORMING ORGANIZATION b. OFFICE SYMVGOL 7a NAME OF MONITORING ORGANIZATION(Itfapplicable) Air Force Wright Aeronautical
Lockheed-Georgia Company Laboratories (AFWAL/FTBEC)
6c ADDRESS (City, State and ZIP Code) 7b. ADDRESS (City State and ZIP Code)
86 South Cobb Drive Wright-Patterson Air Force BaseMarietta, Georgia 30063 Ohio 45433
as NAME OF FUNDING/SPONSORING 8ab. OFFICE SYMR1L 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER
ORGANIZATION (if applicable)
AFWAL/FIBEC _ F33615-80-C-3211Bc ADDRESS (City. State and ZIP Code) 10. SOURCE OF FUNDING NOS
Wright-Patterson Air Force Base PROGRAM PROJECT TASK WORK UNIT
Ohio 45433 ELEMENT NO. NO. NO 'JO
11 TITLE (Irclude Security Clasificatlion), 62201F 2401 01 38See Reverse I
12 PERSONAL AUTHOR(S) K. Kathiresan, Lockheed-Georgia Company, Marietta, GeorgiaT.R. Bruasat a Lorkh~pd-Ca] ifgrni n Company- Burhank. California
13a TYPE OF REPORT 13b. TIME COVERED . 14. DATE OF REPORT (Yr. ,.o., Day) 15. PAGE COUNTFinal Report FROM Sa.t"8 TOSe.&4 84-9-17 130
16 SUPPLEMENTARY NOTATION
17 COSATI CODES 18( SUBJECT TERMS (Continue on reverse if necessary and identify by block number)
FIELD GROUP SUB GR 1%•Attachment Lugs, Aircraft, Damage Tolerance, Residual1 3 1 1 Strength and Crack Growth Prediction, Computer Program,1 3 3 User's Manual, Input Instructions, Sample Problems.4y,&
N•ABSTRACT (Continue on reverse if necessary and identify by block number)
This report is Vol. VI of a 6-part final report on the work conducted under AFWAL contract.. 1 o- u-c-31~-1.The objective of this research program is to develop the design
criteria and analytical methods necessary to ensure the damage tolerance of aircraftattachment lugs. This volume describes the computer program LUGRO developed under thiscontract and provides user input instructions and input and output data for some sampleproblems. LUGRO is an automated computer program which has bean developed using thestate-of-the-art methodologies to predict the residual strength and fatigue crack growthbehaviors of single through-the-thickness cracks and single corner cracks at attachmentIlugs.
20 DISTRIBUTION/AVAILABILITY OF ABSTRACT 21 ABSTRACT SECURITY CLASSIFICATION
UNCLASSIFIED/UNLIMITED (3 SAME AS RPT C{- OTIC USERS 0 Unclassified
22a NAME OF RESPONSIBLE INDIVIDUAL 22b TELEPHONE NUMBER 22c OFFICE SYMBOL(Include Area Code)
J.L. Rudd (513) 255-6104 AFWAL/FIBEC
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11. TITLE
ADVANCED LIFE ANALYSIS METHODS - User's Manual for "LUGRO" Computer Programto Predict Crack Growth in Attachment Lugs (Unclassified)
Unclassified
FOREWORD
This is Volume VI of six final report volumes on Contract F33615-80-C-
3211, "Advanced Life Analysis Methods." The work reported herein was
conducted jointly by Lockheed-Georgia Company and Lockheed-California
:-. Company under contract with Air Force Wright Aeronautical Laboratories,
"Wright-Patterson AFB, J. L. Rudd is the Air Force project leader.
~c-siC~T'or
J - 1'
4 •.
•-.-
" ~iii:4
TABLE OF CONTENTS
Section Title
•J
T INTRODUCTION AND COMPUTER PROGRAM DESCRIPTION
II INPUT INSTRUCTIONS 9
III SAMPLE PROBLEMS 23
4v
LIST OF FIGURES
Figure No. Title Page
1-1 Flow-Chart of the Computer Program LUGRO 7
2-1 Geometries and Nomenclatures of Attachment Lugs 11
2-2 Definitions of Crack Lengths 12
3-1 Through-the-Thickness Crack Growth Data and 30Prediction, Aluminum Lug, R /Ri = 2.25,a = 6 ksi, R - 0.1
3-2 Cornea Crack Growth Data and Prediction, Steel 56Lug, R o/Ri = 3.0, 0O = 14 ksi, R = 0.1
3-3 Stress Distribution Along y-Axis for an Aluminum 64
Lug with Ro/Ri = 2.25
3-4 Through-the-Thickness Crack Growth Data and Pre- 70diction, Aluminum Lug, R /R= 2.25, 07 = 15 ksi,R = 0.5 0 1 0
3-5 Corner Crack Growth Data and Prediction, Aluminum 77Lug, R /Rl 2.25, 0 = 15 ksi, R = 0.5
o0 0
3-6 Schematic of Block Spectrum Loading 79
3-7 Through-the-Thickness Crack Growth Data and Pre- 85diction, Aluminum Lug, R /R. = 2.25, Block SpectrumLoading, 01omax = 7.5 ksi° 1
3-8 Corner Crack Growth Data and Prediction, Steel 111Lug, R l/R 3.0, Cargo Spectrum Loading0 1
3-9 Through-the-Thickness Crack Growth Data and 122Prediction, Steel Lug with Steel Bushing,R 0 /r. =225, tB = 0.09 Inch, a0 14 ksi,R° 1 I 1 0.008 Inch
F.°
•VI.
[•e vi
LIST OF TABLES
Table No. Title Page
2-1 Input Instructions for Crack Growth Pnalysis 13Program 'LUGRO' for Attachment Lugs
2-2 Input Variables Description 16
3-1 Details of Block Spectrum Loading 79
3-2 Missions Definition for Cargo Spectrum 87
3-3 One Pass of Sequence of Missions of Cargo Spectrum 90
v
vii
SECTION I
INTRODUCTION AND COMPUTER PROGRAM DESCRIPTION
This report is the sixth and last volume of the final report generated
under Air Force contract F33615-80-C-3211 entitled "Advanced Life Analysis
Methods". The objective of this contract is to develop the design criteria
and analytical methods necessary to ensure the damage tolerance of aircraft
attachment lugs. In this contract, an extensive analytical and experi-
mental investigation was conducted to characterize and predict fracture and
growth behavior of cracks in attachment lugs. The titles of the six volume
final report generated under this contract are listed below.
Volume I Cracking Data Survey and NDI Assessment for AttachmentLugs.
Volume II Crack Growth Analysis Methods for Attachment Lugs.
Volume III Experimental Evaluation of Crack Growth Analysis Methodsfor Attachment Lugs.
Volume IV Tabulated Test Data for Attachment Lugs.
Volume V Executive Summary ano Damage Tolerance Criteria Recommen-dations for Attachment Lugs.
Volume VI User's Manual for "LUGRO" Computer Program to PredictCrack Growth in Attachment Lugs.
This volume (Volume VI) describes the crack growth analysis computer
program LUGRO developed under this contract and provides user input
instructions and some sample input and output data.
LUGRO is an automated computer program which has been developed using
the state-of-the-art methodologies to predict the residual strength and
fatigue crack growth behaviors of single through-the-thickness cracks and
single corner cracks at attachment lugs.'Žhis section further describes
the operation of the program, functions of the main program and the
subroutines, and a flow-chart of the computer program.
I 7'i I I I I I i III II I II I III l I II i I I I I I I I IIII d I I I II i
The program includes the following four basic elements:
o Stress intensity factor solution
o Baseline crack growth rate relationship
o Applied load sequence
o Spectrum load-interaction model
Stress intensity factor solutions for attachment lugs developed under
this contract for a variety of structural and loading complekities can be
found in Volume II of this final report. Some of these solutions have been
embedded in this computer program, which can be used to interpolate the
data to the desired lug geometry. The program also has the option to input
the user-generated stress/stress intensity data.
The optional baseline crack growth rate relationships embedded in the
program are those of Paris, Forman, and Walker. The optional spectrum load-
interaction models incorporated in the program are: the Wheeler,
Willenborg, Generalized Willenborg, and Hsu models, or assuming no load
interaction. The crack growth rate equations and the spectrum load-
interaction models are discussed in detail in Volume II of this final
report. The stress levels which comprise each individual mission segment,
and from which a mission mix spectrum can be generated, may be input in
five optional ways: as maximum stress (ormax) and stresss ratio (R); omax
and minimum stress (a or); Gmax and mean stress (a ); a and alter-min ma mean) ameannating stress ( ait); or R and stress range (aa). The program predicts
the crack growth using a block-by--block integration technique.
For through-the-thickness cracks, either the compounding solution or
0 the Green's function solutioa can be used in the prediction. In predictln,
the growth behavior of a single corner crack, the through-the-thickness
crack solution may be modified by either the one-parameter (compounding
method with constant a/c ratio) or two-parameter method (Green's function
method). For one-parameter analysis, the prediction is straightforward and
is similar to trough-the-thickness crack prediction. For two-paramneter
analysis, it is assumed that for a given number of applied load cycles, theextension of the quarter elliptical crack border is controlled by the
stress intensity factors at the intersection of the crack periphery at the
2
hole wall and the lug surface, i.e., KA and K C* In general, the stress
intensity factors at these two locations are different, resulting in
different crack growth rates. Therefore, the new flaw shape aspect ratio
after each crack growth increment will be different from the preceding one.
The new crack aspect ratio is computed using the new crack lengths on both
the hole wall and lug surface. The process is repeated until the crack
length along the hole wall is equal to the lug thickness. At that time the
transitional crack growth criterion is used, until the crack has achieved a
uniform through-the-thickness shape. After that, if the failure has not
occurred, a one-dimensional through-the-thickness crack analysis is used to
continuously predict the subsequent crack growth life. The analysis is
considered to be complete when fracture occurs due to fracture toughness or
net-section yield criterion or when the desired final crack length or the
maximum usage time is reached.
The LUGRO program contains one main program and 14 subroutines. The
functions of the main program and the subroutines are aescribed below.
MAIN - The main program receives the input of basic data for the
crack growth life prediction; interfaces with the sub-
routines; and outputs the predicted crack growth history.
DADNDK - This subroutine reads the baseline constant Amplitude
crack growth rate data in the form of da/dN vs AK or
directly as materiai constants. In the former case, for
each straight line segment of da/dN vs AK data (in log-
log scale), the subrouti,.e calculates the material crack
growth rate constants using the crack growth rate equa-
tion specified by the user.
SPECTM This subroutine reads and generates one complete block of
stress spectrum to be used in the crack growth predic-tion. This block of stress spectrum will be repeated
until the computed maximum stress intensity factor
reaches the fracture toughness value or the net-section
stress value reaches the yield strength of the material.
3
The prediction will also be terminated when the crack
len'th or the accumulated flight time in terms of blocks
reaches the specified maximum value in the input.
GROWA - This subroutine estimates the crack length as a function
of accumulated flight time (or usage). The computations
for through-the-thickness cracks are made in this sub-
routine. For corner cracks, the computations are made in
subroutine CORNER, which is called by this subroutine.
The predictions will be terminated if the computed Kmax
reaches Kc, or the net-section stress value reaches the
yield strength of the material, or the current crack
length or the accumulated flight time exceeds the maximum
value specified in the input.
SIF - The stress intensity factors for a through-the-thickness
crack are generated in this subroutine for crack lengths
ranging from 0.0001 inch to the desired maximum crack
length specified in the input. This subroutine calls the
appropriate subroutines to calculate stress intensity
factors using the compounding method or Green's function
methods, or interpolating the tabulated data that have
been input or are already available internally in the
program.
S1F8 - This subroutine computes the stress intensity factors at
0 the intersection points of a quarter-elliptical crack
front at the hole wall and lug surface by modifying the
through-the-thickness solution with various correction
factors.
BACKS - This subroutine estimates a back surface correction fac-
tor for a part-through corner crack.
CORNER - This subroutine calculates the two-dimensional growth of
a corner crack as a function of accumulated flight time
0 4
(or usage). This subroutine does the same functions as
the subroutine GROWA, except that this is for a corner
crack. Also calls the appropriate subroutines and com-
putes the transition and subsequent through-the-thickness
crack growths.
COMPND - This subroutine computes the stress intensity factors
using the simple compounding method.
K, GREENF - This subroutine computes the stress intensity factors
using the Green's function method.
TRANSG This subroutine computes the transitional crack growth
from when the corner crack breaks through the back
surface to when the crack becomes a uniform through-the-
thickness crack.
DADP - This subroutine calculates the average crack growth per
block of stress spectrum as a function of any given crack
length.
DADNJJ - This subroutine calculates the crack growth rate for eachcomputed effective stress intensity factor range (AK eff)
and ratio (K mineff/Kmaxeff).
EFFKDA This subroutine calculates effective stress intensity
factor range ( AK) and ratio (K mineff/K maxeff), and
estimates the corresponding crack growth increment using
the specified crack growth retardation equation.
DIRCAL This subroutine contains the stress intensity factors and
the stress distributions as a function of outer-to-inner
radius ratio of lug in a tabular form. The user has the
option to use these tables and interpolate the data for
the desired lug geometry.
5
Two more subroutines are referenced in the program. They are FUNCTION
subroutines GIRC and DTAB2, which are UNIVAC library subroutines. GIRC is
a single variable Aitkin interpolation subroutine and DTAB2 is a two vari-
able interpolation subroutine.
A flow-chart showing the interactions between the main program and the
subroutines is shown in Figure 1-1. The main program first processes the
material crack growth data in DADNDK and develops the loading spectrum in
SPECTM. Then it starts the crack growth analysis by calling the subroutine
GROWA. The through-the-thickness stress intensity factor solutions are
computed first by calling the subroutine SIF. Based on the input specified
by the user, these stress intensity factors are obtained by using one of
the various methods as shown in the flow-chart. Then depending on the
crack shape (through-the-thickness or corner) the program branches to com-
pute the crack growth behavior using subroutines DADP, EFFKDA and DADNJJ.
In the case of corner cracks, the through-the-thickness crack solutions are
modified with various correction factors for corner crack stress intensity
factors in subroutine SIF8. Subroutine TRANSG computes the transitional
crack growth behavior of corner cracks.
o",
r
DIRCALGREENFGRANSSo0 CO S :MPN DAD P
DATASIF FROM TABLES TH ETUOA IR FMUNTHOD S T RACK
© UE TH U FUNCTION S TINE DTABZ
.;,, . I[ _- I[METHOD .
DICA GREEN D, ,P DF DAP T;
o•---• ~INPUT/,.
TRSES EFF KDA EF D
S"• STRESS
w~ wT A BL E S
6 "=• 0 USES THE UNIVAC LIBRARY FUNCTION SUBROUTINE GIRC
"" O USES THE UNIVAC LIBRARY FUNCTION SUBROUTINE DTAB2
"Figure 1-1. Flow-Chart of the Computer Program LUGRO
Il 7
SECTION II
INPUT INSTRUCTIONS
This section describes the input instructions for the computer program
LUGRO. The program can be used to predict the residual strength and
fatigue crack growth behaviors of single through-the-thickness cracks and
single corner cracks at attachment lugs.
The program is capable of analyzing attachment lugs with and without
interference-fit bushings. Figure 2-1 shows the geometries and nomencla-
tures of attachment lugs with and without bushings. In the case of corner
cracks, there are three distinct regions of crack growth, namely corner
crack growth until the crack breaks through the thickness, transitional
growth until the crack reaches a uniform through-the-thickness shape and
the subsequent through-the-thickness crack growth. These three regions of
crack growth and corresponding definitions of crack length are illustrated
in Figure 2-2.
The input instructions for the computer program LUGRO to predict the
residual strength and crack growth behaviors are provided in Table 2-1.
There are 25 different lines of input as shown in the table. Some lines
may have to be repeated several times depending on the nature of input.
These are indicated under the column 'COMMENT'. For example, the da/dN vs
AK data (Line 4) have to be repeated 'KPOINT' times, vnich is specified in
Line 3. The table also describes the variables, type of variables and the
columns in which tne data are input for all the 25 lines of input. Suffi-
cient instructions are provided in the table to choose the right set of
input lines. For example, appropriate lines 3, 4 and 5 should be input
based on the value of 'IEQU', which specifies the selectea crack growth
rate equation. The table also describes the cases when there will be no
V inputs for some specific lines. For example, when the value of 'IBETA' is
-w equal to -1, there are no inputs for lines 20, 21 and 22.
The input variables specified in the 25 lines of Table 2-1 are
described in detail in Table 2-2. The table also describes some of the
terminologies used in the description and two important notes (Notes A and
B) at the end of the table. The units with which the inputs need to be
9
specified are also given in the table. This section is followed by the
sample problem section in which details of input and output are provided to
aid the user.
?.
:-N,
illoS. . . . . . . . . . . .. . . . . . . . . . .
R 0
2FR.
Cao0I
0
(a) Simple Attachment Lug
ro,
C
D 2
1: a0
(b) Attachment Lug With an Interference-Fit Bushing
Figure 2-1. Geometries and Nomenclatures of Attachment Lugs
3•i
i•11
2R 0
I2 R.
B IE CORNER CRACK
C
aCIB
TI
0 TRANSITIONAL CRACK
JTHROUGH-THE-THICKNESSCRACK
Figure 2-2. Definitions of Crack Lengths
12
TABLE 2-1. INPUT INSTRUCTIONS FOR CRACK GROWTH ANALYSISPROGRAM 'LUGRO' FOR ATTACHMENT LUGS
LINE COLUMN VARIABLE TYPE OF VARIABLE COMMENT
1-80 TITLE ALPHANUMER I CAL
1-5 I EL' INTEGER4-10 LDADN INTEGER11-15 LL'.AD INTEGER16-20 L.EC0 INTEGER
SI,4,5 (A). IF IEOU = 1, WALKER'S EQUATIONI IS USED, THEN
-5 K'O I NT INTEGER
4 1-10 EFFK(I) REAL1-2(3 DADN(I) REAL REPEAT '*KPOINT' TIMES
* I-i0 CM REAL11-20 RC REAL
3,4,5, kB). IF iEQUI = 2, FORMANWS EC.UATION IS USED, THEN
T. 1-5 KPOINT INTEGER4-130 INCFNF INTEGER
4 4 1-10 EFFK(I) REAL INPUT ONLY IF INCFNF = 0,-I1-20' DADN(I) REAL REPEAT 'KPOINTý TIMES
-1-10 FC ( I) REAL11-20 FN(I) REAL INPUT ONLY IF INCFNF = i,"Z 21-30 EFFK( I) REAL REPEAT "KPOINT=I TIMES
1 - 1( FKC REAL,1-2(3 FR REAL- 1-.:') RC REAL
"-,4,5 (C). IF !EiUI 3, PARISý EQUATION IS USED, THEN
1-5 KPOINT INTEGER4- I . INIcPNP INTEGER
4 1-10 EFFK(I) REAL INPUT ONLY IF IMC.PNP (3,
!1-20 DADN(I) REAL REPEAT ýKPOINT' TIMES
4* 1-10 PC. (I) REAL11-20 PN(I) REAL INPUT ONLY IF INCPNP - 1,21-3(3 EFFK(I) REAL REPEAT - KPOINT-l' TIMES
%5 1-10 RC REAL
13
'TABLE 2-1. (CONTINUED)
A 1-1t 0 THREK' REAL!1-20 C PITfC REAL
FTY REAL1-, IRETAR INTEGER
" .4- 1) IMODEL !NTEOER
I :,.iJF.T ONLY IF IRETAR = 1
-- ILANE INTEGER..-- 5 EXPM REAL EXP'M 1S INF'UT ONLY" IF t.MCDEL = 4
XFNXTH REAL "1XTH AND SOS ARE INPUT ONLY26.- _. •, CS REAL IF IMODEL = 2
I -5 MS INTEGER;T- 'READ INTEGER
11 - i 5 ILAYER INTEGER
J,-, 1-:30 TITLEM ALPHANUhERICAL
,1-0 SRAT I0 REAL11-20 HOURM REAL
1-10 SMAX REAL11 -20 R REAL INPUT ONLY IF IREAD=I, REPEAT21-30 CpFl REAL THIS LINE 'ILAYER' TIMES
----------------------------------------------- -----------------------------------------12* 1 - 10 SNAX REAL
11-20 SMIN REAL INPUT ONLY IF IREAD=2, REPEAT21--0 CPF REAL THIS LINE 'ILAYER' TIMES
1-10 S1MAX REAL11!-20 SMEAN REAL INPUT ONLY IF IREAD=3, REPEAT21-.0 CP_7 REAL THIS LINE -lLAYER" TIMES
-----------------------------------------------------------------------------------12"* 1-10 ShEAN REAL
I1-20 SALT REAL INPUT ONLY IF IREAD=4, REPEAT21-3') CPF REAL THIS LINE "ILAYER' TIMES
, 12*-'1-1-0 SEIEL REAL11 -20-1" R REAL INPUT OINLY IF IREAD=5, REPEAT:1-30 CF'F REAL THIS LINE 'ILAYER- TIMES
- REPEAT LINES ") TO 12 FOR ALL POSSIBLE MISSIONS, AND THENINPUT "0" ON COLUMN 5 TO SIGNAL END OF MISSION PROFILES.
1-5 N-PA,,F'.S0 INTEGER0 NSEGT II'ITEGER
i5 1-5 NFLTS INTEGER-- l) hI $I ON I NTEGER REPEAT THIS LINE rNSEGT- TINMES
5': i-S ITHRU INTEGERt 6 Z- rIETHOD INTEGER
IT IETA INTEGERNAM' I FTY F INTEGER iOFTYP i.1FUT ONLY IF METN0D 2 2
V -2
_ 14
TABLE 2-1. (CONTINUED)
S1-10 PAIDTh'S PEAL1 i -20 W TS¢EAL
REAL
--- •"181 1:'IL RAC :'° REA L1-:0 "RAI-: . REAL
C., AO 1j- N EALIF1TR1" I-.0 AO2IN IEAL INPUT ONLY IF ITHRU = 0
-- - - - - - - - - - - - - - - - - - - - ---- - - - - - - - - - - - - - - - - - -
- 1 2 IPUT ONLI iF IBETA = I
-1 1 :: T i T LED ALFPHANUMERICAL
-3 NEDF T INTEGER.5 REAL
1-10 e:1VERD REALI 1-20 3ETATB REAL REPEAT "'NPT TIMES
2- 1. 22 I' 13ETA = -1 THERE ARE NO INFPUTS FOR LINES. 26, 21, 22
2-:, 24, 25 INPUT ONLY IF IBETA =)
,-3 ,.10 !INTEGERSIRS1 INTEGER
-! 11-15 IWRITEA INTEGER
-, 24 1-6 T -' R REALEL REAL
S2- EDEL REAL INFUT ONLY IF IRSIG = -1 OR1 -40 DELD REAL METHOD = -2
41-50 RPOL REAL5 1.60 PO-' PEAL
25 1-10 YO REAL I-NPUT ONLY IF IR Si = 0
:i - 2 XSIG REAL AND METHOD = 2-"EPEAT 'NSIG/ TIMES.
1-10 YC' REAL INPUT ONLY IF IRSIG 111-20 XsiG_, REAL AND METHOD - 22:I R"3C. ", PEAL REPEAT NSIG' TIMES
s25* 11 -20 .(S!i, REAL INPUT ONLY IF IRSIG " -1AND METHOD = 2REPEAT '1I(=NSIG)> TIMES
""* 21-30 Rs1G REAL INFvUT ONLY IF IRSIG = I'ND METHOD = -2REPEAT "Ii=(NS!G)'" TIMES;FOR THIS CASE, IN CARD 24O'NLY TBR AND EBEL NEED TO BEINPUT USING THE SAME FOaRMAT
•**~ Nil1 LINE 25 INPUT IF IRSIG = -1 AND METHOD = -2
15
TABLE 2-2. INPUT VARIABLES DESCRIPTION
BEFORE DESCRIBING THE INPUT VARIABLES, SOME TERMINOLOGIES, WH:CH ARENOT INPUT VARIALLES, ARE DEFINED HERE, FIRST TO AID THE PREPARATIONOF LOAD SPECTRUM AND TO- CHOOSE THE OUTPUT OPTION.
BLOC. - CINE COMPLETE PASS TWROLIGH THE ENTIRE SPECTRUM BEFORE ITS:REPETITION. ONE BLOCK' CONSISTS OF MULTI-NUMBER CF SEGMENTS.
;EGMENT - FRACTION OF A BLOCK. ONE SEGMENT C-O_,NiSTS OF ONE FLIGHT ORMULTIPLE NUMBER OF CONSECUTIVE FLIGHTS OF SAME MISSION.
MISSION - A TYPE OF FLIGHT IN AIRPLANE USAGE.
FLIGHT - ONE COMPLETE PASS THROUGH A GIVEN MISSION. ONE FLIGHTCONSISTS OF MULTI-NUMBER OF LOAD LAYERS.
LAYER - ONE ENTRY IN A MISSION. A LAYER CONSISTS OF A NUMBER OFCONSICUTIVE ý'YCLES OF SAME STRESS AMPLITUDES.
THE FOLLOWING DESCRIPTION IDENTIFIES ALL OF THE INPUT VARIABLES ANDTHEIR DEFINITIONS.
TITLE : PROBLEM IDENTIFICATION TITLE.
IEOU : OPTION TO USE DIFFERENT GROWTH RATE EQUATION.IF IEQU = 1, WALKER'S EQUATION IS USED,
= 2, FORMAN'S EQiUATION IS USED,= 3. PARIS' EQUATION IS USED.
LrADN j OPTION TO PRINT OUT THE INPUT GROWTH RATE DATA.IF LDADN = 0, PRINT OUT THE GROWTH RATE DATA,
= I, DO NOT PRINT OUT THE R:ROWTH RATE DATA.
LuYAD OPTION TO PRINT OUT THE INPUT LOADING SPECTF.UM.IF LLOAD = 0, PRINT OUT THE INPUT LOADING SPECTRUM,
= !, DO NOT PRINT OUT THE INPUT LOADING SPECTRUM.
E OTEIPTPTION TO FRINT OUT THE INPUT FLIGHT :-E-UENCE OF AELOC}. LOAD ` PECTRUM.!F LEEO = PRINT OUT THE INPUT FLIOHT SPECTFUM,
=, DO NOT FCrI.IT -UT THE NMFUT FLIGHT SPECTRUM.
16
TABLE 2-2. (CONTINUED)
p-•''PINT NUMSER OF FOINTS ON (DELTA K VS. DA/DN) C! FYE. BOTH ENDPOI NTS ARE I NCLUDED. NOUMBER O:F LI NEA;R SCET USEDTO REPRESENT THE GROWTH RATE C*URVE WILL BE = KPOINT-1.NOTE : MAXLiMUM KPOINT VALUE IS SO.
EFF*'( : DELTA K OR EFFECTIVE DELTA K CORPESPiFr•NING TO EACH INPUTPOINT ( UNIT : KSI*SORT(INI"H)
"ADN( r :ROWTH RATE DA/DN CORRESPONDING TO EACH DELTA , OR EFFECTIVEDELTA K ( UNIT : MICROINCHES
l,.1 ONSTANT Mf" USED IN WALKER'S EQ.!ATION.
CU -T~OFF OF THE MINIMUM APPLIED STRES',. RPATIO, I.E. IF RKRC, R=PC
N'ICFNF COPTION TO !NPUT EITHER ( DELTA K Z, DA/D1N ) PAIRS OR ( CF ,. NFPAIRS FOR FORMAN"$ EQUATION.IF INCFNF = O- INPUT ( DELTA K & DAiDN ) PAIRS,
= I, INPUT ( CF & NF ) PAIRS.NOTE : 'CF ' 'NF' ARE CONSTANTS OF FORMAN'S EQLIATION.
FCtI) CONSTANT 'C' USED IN FORMAN"S EOUATION.FOR DELTA ý' IN UNIT KSI*SQRT(INCH)
FN( I) C'ON'-STANT "N USED IN FORMAN'S EQUATION.FO:R DELTA K IN UNIT KSI*SORT(INCH)
KC VALUE TO BE USED IN THE FORMAN'S EQUATION.
( UNIT : KE'1-ýISQRT(INCH) )
FR R-RATIO OF CONSTANT AMPLITUDE OF INPUT DA/DN DATA.
1MFINCP OPTION TO INPUT EITHER ( DELTA K & DA/DN ) PAIRS OR CF & NFPAIRS FOR PARIS' EQUATION.IF INCPNP = 0, INPUT ( DELTA K " DA/DN ) PAIRS,
= 1, INPUT ( CF & NF ) PAIRS.NOTE : "':F' & 'NF" ARE CONSTANTS OF PARIS' EQUATION.
PC (I CONS.TANT 'C * USED IN PARISI EQUATION.i-,R DELTA K IN UNIT KSI*SRT(INCH)
PN(I I i-lN:::T•i7,NT -N-* USED IN PARIS' EOUATION.4 FOR DELTA i IN UNIT KSI*SQRT(IN'H)
17
TABLE 2-2. (CONTINUED)
THREKO : THRESHOLD DELTA K OF THE MATERIAL USED. WHEN CALCULATEDDELTA K IS LESS THAN OR EQUAL TO THREKO, NO CRACK GROWTHWILL BE CONSIDERED. ( UNIT : KSI*SQRT(INCH)
CRITI<C : CRITICAL STRESS INTENSITY FACTOR OR FRACTURE TOUGHNESSOF THE MATERIAL. ( UNIT : KSI*SQRT(INCH)
FTY : TENSILE YIELD STRENGTH OF THE MATERIAL. ( UNIT : KSI
IRETAR : OPTION TO CONSIDER SPECTRUM RETARDATION EFFECTS.IF IRETAR = 0, NO RETARDATION EFFECT WILL BE CONSIDERED,
= 1, SPECTRUM RETARDATION EFFECTS WILL BE CONSIDERED.
IMODEL OPTICNS TO USE VARIOUS RETARDATION MODELS.IF IMODEL = I, WILLENBORG MODEL WILL BE USED,'IF IMODEL = 2, GENERALIZED WILLENBORG MODEL WILL BE USED,
Wj= 3, HSU MODEL WILL BE--USED,Yl= 4, WHEELER-MODEL WILL BE USED.
IPLANE OPTIONS TO USE PLANE STRESS OR PLANE STRAIN IN THE CALCULATIONOF YIELD ZONE.IF IPLANE = 1, PLANE STRESS IS USED,
z 2, PLANE STRAIN IS USED.
EXPM WHEELER'S RETARDATION MODEL EXPONENT M.
XKMXTH : MAXIMUM THRESHOLD STRESS- INTENSITY FACTOR ( UNIT I KSI*SQRT(INCH)(ONLY FOR GENERALIZED WILLENBORO MODEL)
SOS OVERLOAD SHUT-OFF RATIO(ONLY FOR GENERALIZED WILLENBORG MODEL)
MS : MISSION NUMBER.
IREAD : OPTION FOR INPUTTING THE LOAD SPECTRUM.IF IREAD = 1, READ IN SMAX, R, & CPF
= 2, READ IN SMAX, SMINi & CPF= 3, READ IN SMAX, SMEAN,A& CPP
4, READ IN SMEAN, SALT, & CPF= 5, READ IN SDEL, R, & CPF
ILAYER NUMBER OF LOAD LAYERS IN THE MISSION.
TITLEM MISSION IDENTIFICATION TITLE.
SRATIO SCALE FACTOR OF THE LOADING SPECTRUM.
18
TABLE 2-2. (CONTINUED)
HOURM : EQUIVALENT FLIGHT HOURS TO THIS MISSION ( IN HOURS~II
"SMAX : MAXIMUM AXIAL STRESS OF THE LAYER. ( UNIT KSI )
'-MIN : MINIMUM AXIAL STRESS OF THE LAYER. UNIT KSI )
R : AXIAL STRESS RATIO OF THE LAYER, OR R'=SMIN/SMAX.
i'PF : NUMBER OF CYCLES OF THE LAYER.
"SMEAN : MEAN AXIAL STRESS OF THE LAYER. ( UNIT KSISMEAN = (SMPX+SMIN)/2.0
SALT : ALTERNATING AXIAL STRESS OF THE LAYER. ( UNIT (KSI".ALT = (SMAX-SMIN)/2.0
SDEL : AXIAL STRESS RANGE OF THE LAYER. ( UNIT KSISDEL = SMAX-SMIN
NPASSO : NUMBER OF BLOCKS OF LOAD SPECTRUM TO BE, REPEATED IF FRACTUREDOES NOT OCCUR. IF NOT SURE, SET NPASSO = 0, THEN THE PROGRAMWILL INTERALLY SET NPASSO = 1,000,000.
NSEGT : TOTAL NUMBER OF SEGMENTS IN ONE BLOC:K OF LOAD SPECTRUM.
NFLTS : NUMBER OF CONSECUTIVE FLIGHTS OF SAME MISSION IN ONE SEGMENT.
MISSION : MISSION NUMBER OF THE FLIGHT.
ITHRU : OPTION TO SPECIFY FOR THROUGH-THE-THICKNESS OR PART-THROUGH CRACK.IF ITHRU = 0, FOR CORNER CRACK,
= 1, FOR THROUGH-THE-THICKNESS CRACK.
METHOD : METHOD OF STRESS INTENSITY FACTOR CALCULATION.= 1, usE COMPOUNDING METHOD.= 2, LISE GREEN FLINCTION METHOD, AND STRESS DISTRIBUTION
ALONG CRACK GROWTH PATH WILL BE INPUT=-2, USE GREEN FUNCTION METHOD, -AND AUTOMATICALLY
SCALCULATE STRESS DISTRIBUTION ALONG CRACKGIROWTH PATH FROM THE TABLES STORED IN THE
L PROGRAM, WHICH IS A FUNCTION OF OUTER-TO-INNER RADIUS RATIO OF LUG. IN THE CASE LOFLUGS WITH BUSHINGS, THIS OPTION SHOULD BEEXERCISED ONLY WHEN THE RATIO OF LUG OUTER
rlw RADIUS TO BUSHING INNER RADIUS(=PIN RADIUS)IS 2.25, SINCE THE SUBROUTINE DIRCAL CONTAINSDATA ONLY FOR THIS LUG-BUSHING CONFIGURATION.
ERE ;19
TABLE 2-2. (CONTINUED)
IBETA OPTIO:N TO FI.IFUT BETA FACTORS DIRECTLY.IF iBETA = ,0l, $ IF WILL BE C"OMPUTED BY GREEN FUNCTION ,ETHOLD
OR COMPOUNDING METHOD DEPENDING ON THE VALUE OrTHE PARAMETER " METHO'D
= 1, DIRECT INPUT OF NORMALIZED STRESS INTENSITY FACTOrt.=-1, AUTOMATICALLY COMPUTE NORMALIZED STRESSý INTENSITY
FACTORS FROM THE TABL.S STORED IN THE FRCI:-RAMI, WHICHIS A FUNCTION OF OUTER-TO-INNER RADIULS RATIO OF LUG
IOF'pYP OPT ION TO CHOOSE THE GREEN FUNCTION TYPE ( DEFAULT = I ).IF IOFTYP = 1, UiE MODIFIED GREEN FUNCTION FOR LUGS WITH NO
BUSHINGS )= 2, USE ORIGINAL GREEN FUN.TION ( FOR LUGS WITH
BUSHINGS- )
RADIUS RADIUS OF THE LUG HOLE ( UNIT : INCH
W.DTH WIDTH CF THE LUG (=OUTER DIAMETER OF LUI). ( UNIT : INCH
THICK; THICKNESS' OF THE LUG. ( UNIT : INCH
CRACKO TNITAL CRACK LENGTH 'C'. ( UNIT * INCHNOTE --e REFERS TO THE CRACK LENGTH ON LUG SURFACE.
CRACKF FINAL CRACK LENGTH DESIRED IF FRACTURE DOES NOT OCCUR.UNIT : INCH
AO2CIN : INITIAL FLAW SHAPE RATIO OF PART-THPOUGH CRACK, A/2C..-'NOTE : 'A" REFERS TO THE CRACK LENGTH ALONG LUG HOLE WALL.
TITLEB : TITLE FOR METHOD OF COMPUTATION OF STRESS INTENSITY FACTORS.
NBPT : NUMBER OF DIRECT NORMALIZED BETA FACTORS TO BE READ IN.
D : VALUE OF SOME CHARACTERISTIC LENGTH WHICH IS USED ( EXAMPLE LUGS41OLE RADIUS ) TO NORMALIZE THE CRACK LENGTH. ( UNIT : INCH;,IC;Z : DEFAULT = 1.0 'INCH.
C C'%VERB : VALUE OF C/B FOR WHICH THE BETA FACTOR IS BEING PROVIDED.
_d:T-A Tit ', ALL'E CF BETA FAC7TR FOR THE ABOVE COVERB VALUE.9ETA7B =KIRGROSS SECTION STRESS*5;.'RT(PIE"C))
tJ'-. : NUMBER OF F-_'INTS AT WHICH THE ST.'E.ZS DISTRIBUITION IS 7NF'.IT.A NEGATIVE VALUE F'CF' 'NSIGý MEANS THE SAMiE AS METHOD = -2.
1"J WHICH CASE THE VAL'tE OF "NSIGO II :'Ec7AULTED TO A VALUEL ".F -EE NOTE A)
20
TABLE 2-2. (CONTINUED)
SIRS.IG OPTI:DI TO INCLUDE RESID1UAL STRES'E-ES .SEE NOTE B).
lF IRSIG = 0, NO RESIDUAL STRESSE.,= , RESIDUAL STRESSES ARE ALSO PPESENT.=-I, AUTOMATICALLY C:ALCULLATE THE RESIDUAL STRESSES
USING THE INPUTS TBR, EL, EBEL,DELL,,POL AND R'OB("I'I. 1I" IS DEFLAULTED TO A VALUE OF ii IN THISiCASE ALSO - SEE NOTE A)
I WRITEA OPTION TO WRITE INTERPOLATED GREEN FUNCTTION..F IWRITEA = 0. INTERPOLATED GREEN FUNCTION WILL NOT BE PRINTED?
= 1, INTERPOLATED GREEN FU1!CTION WILL BE PRINTED.
TER BUE::HIN3 THICKNESS DIVIDED BY LOADING FPIN RADIUS= BUSHING THICKNESS/I(LUG INNER RA IUS-BU'SHING THICKNESS)
EL YOUNG'S MODULUS OF LLIG MATERIAL ( UNIT : KSIS
EPEL BEJSHING-TO-LUG MATERIAL YOUNG'S MODULUS RATIO
DELD : DIAMETRICAL INTERFERENCE LEVEL ( UNIT : INCH
PCL : POI'B".ION"S RATIO OF LUG MATERIAL
FOB : POISSION'S RATIO OF BUSHING MATERIAL
YO : LOCATION AT WHIC:H THE STRESS IS BEING INPUT. YO (Y-RI)/RI.
S._ : STRESS AT LOCATION YO NORMALIZED BY GROSS SECTION STRESS.
XS•G = STRESS/GROSS' SECTION STRESS.GROSS SECTION STRESS = P/(.0O*RObTHICK-'NESS:)
= PI(W*THICKNESS)
R.IG RESIDUAL STRESS VALUE (SEE NOTE B). ( UNIT = KSI
NIOTE A: ThE i POINT'. CORRESPOND TO DIVIDING THE NET-SECTION OF THE LUGBY 1 ' EQUIAL SEGMENTS AND THE 11 "YO= (Y-RI)/F Ii VALUES APEAUTOMATICALLY CALCULATED.
NTE e THE RESIDUAL STRESS CASE IS APPLICABLE TO THROUGH-THE-THICKNESSCRACK PROBLEMS ONLY. HOWEVER FOR CORNER CRACK PROBLEMS INPUT THE-MAXIMUM STRESS DISTRIBUTION AND A STRESS RATIO "SUCH THAT ACONSE'VATIVE LIFE PREDICTION COULD ,TILL BE MADE. (SEE SAMPLE
L PRr'BLEF:'. 7 AND :)
L? 21
SECTION III
SAMPLE PROBLEMS
In this section, several sample inputs and outputs of the crack growth
program LUGRO are provided to aid the user. Each sample problem consists
of problem definition, input and output. Descriptive details are added to
the input and output to explain the input variables and to interpret the
output. All the sample problems illustrated in this section correspond to
specimens tested under this program. Thus, wherever appropriate, the plot
of analytical-experimental correlation data is provided.
• 23
x3
SAMPLE PROBLEM #1
Material : Aluminum
Ro/Ri : 2.25
R. : 0.751
Thickness : 0.50 Inch
0°0 6 Ksi
R : 0.1
Crack Type : Through-the-Thickness
c : 0.025 Inch
Crack growth analysis for the above lug and crack geometries and loading
condition is conducted in this sample problem using Forman's crack growth
rate equation and the following given 4 factors.
No. c/(Ro - Ri43
1 0.0 5.957
2 0.1 3.899
3 0.2 3.126
-4 0.3 2.804
5 0.4 2.500
6 0.5 2.422
7 0.6 2.364
8 0.7 2.463
9 0.8 2.646
10 0.9 3.308
*R 0 R . B 0.9375 Inch
4 Analytical-experimental correlation result is given in Figure 3-1.
2
[ "'4A_ f-JAND AFLC_:'.----:" Line 1: Title
2: -0 0-1-- Line 2: IEQU = 2, Select Forman Equation
4: 40 0.1455. C:) 0,57:S
,-,: 6.0 C 2 . O0 Lines 3,4,5,6: Material Property7.560 data AK vs. da/dN
:.0 t 2.(:)0 AK K andF12.C 1:3. 200 ,(Kthreshold' c ty
I !:20). ") 5:=: '9:001: 15. 0 2,4 00C0
24 : 40. () -::0 0450 X--- 5Q. (:: C)C
15., 45. C) 6520. C,0017: 60. 1 0. 1 -0. 117' -) .'.,,74 -
C0 -- Line 7: IRETAR 0, no retardation19 1 1
Lines 9,10,11,10: -ONTANT AMPLITUDE WITH SIGMA(MAX)= 6. K.z=;I AND R=1.1. 1 12, 13:-
1. 0 1Constant2:6. C) 1 10)0.C) Amplitude LOadin,
0 - Line 16: ITHRU = IBETA 1 1 Spectrum ef initi: 1 Through-the-Thickness crack,
"-.5: -Direct input of 6 factors
i7: . 72500 .':-:.75 .Lines 17, 18: Lug and Crack Geometries"0''" (.025o, .=,77Y.:72 'kDIREC:T INPUT OF BETA FACETOR::*: 10 0. '5 75-10: 0.) 5. '957
"4J.. .. -• : . :3 .-. :-
3:2::0. "2"-:.126.-
•.:4: 0. : 2:Lines 20,21, 22: Input of a factors5="- "-. 2500
:--:7:0.5 .. 36
-P :: . 92.4"-:.4390: 0.: =,:':::
25
I41
(C C .(4 0' N ic 0 I) 0
IL
Ln (1 0 C
a C N, w 4 N 0 C' 0
(C.OC A. t
2 Z
w~ Cw
CC N 0 0 0. o C'Ly
C z Ft. N U) C) to U
,A
3
V.
b. 26
C- c
CC- C r
C -l
Q W,
C 2
C:VQ
22
. ' .t .~ . . . . .. . . 0.. . .4 ' . . .C. . . .ceC. w 0;0C0
(f, 0LC.' 000 4~
(%.~
o~ o N co 40 -- --- NN NN t r:N C M i1 o N
..J n, 1" I-
(f. I. OrccIt w' Ci I-
0 Z N X : *ucr .' - ' C. C . C ... . C.( . . .
C LI
Z ~ Q" -OOOOC 0 ZI P, 000000000;,L( 0Q '''0 CCC .1) w U:-1 w L' 0c ý . .. . .C..C.
== j r)z CI-C 01.(C' (.0~~.N C C' 0 N v((".'0 C'.if) ()I.oo oo N ---4 - . T
IL '-IV.m % ,-
L , o w J z m N N 0 v 0 0 1.8
45
ýY-I C4 0
(4 (N ?6 0
-00 '-. 0-
, N N
0 wL
0z 0
0.ý ~ I a- r-,
D zz
0 0 C,
C. : C 0 cC
I Q-
~ (429
*10
00 - COMPOUNDING ................
.................. ...... ............. ...................GENSF CTO
.......................................U
ALUMINUM
THOU AND
OF CYCLS R
M`30
w
SAMPLE PROBLEM #2
This sample problem is identical to the previous sample problem,
except that the .8 factors are obtained from an already-available table in
the program, instead of providing them as input. This is accomplished by
specifying the value of 'IBETA' as -1 in the input.
Since the f factors input in the sample problem #1 are essentially the
same as those stored in the table, the results of crack growth history are
also the same. The slight difference in che solutions (<.15%) is due to
computational round-offs.
1
31
R?3_5
1 ABPLi:.,46 AND ABPLC'Z,32: 0 0 1
" ":: 12 01
4: 4.0 0.1455: 5.0 0.57:-,
S1.20 2. 0507: :_. C) 7. 5008: 0C). 0 12. 900
1 2.0 1:3. 20010: 15.C(.) ":300r11: 20.0 53. 900
:25 0 134. 000K-:: '230. 0 353. 00014: 40. 0 2'350. 00015: 45.0 6520.000!6: 60.9 0. 1 -0. 117: 0.0 60.9 74..:918•: 0 019: 1 1 120:: c.NN'$TAI\T_ _ AMPFLITU!DE WITH 8=IciMA(IMAX )= 6K.81" AND R=O. 1
- 1: 1.0 1.02: .0 C)C. 1 100).0
22":: C)11
241: 1. 01.
25: 1 t
l) @Line 16: IBETA =-1, Calculate27: 0. 7500 ._-:75 0. 500C) factors from the tables
""2-'::,,'5 .9375 stored in the program2:-: 0.,. :. ....
'N
oc. ' 0 N 0 ev a N N 0 N? 4 N- 0 ~o) O .004C' 0 4N ' I
4 4 N - - N N ~ t,
a-.
z 0 0 ts Eel~ ? '0 O t00 -' C ' C' C ' C C ' -
i a Iý a 0 S I I~ C' 4 N N N Id? - C -
II0xN I' ' ' C
: -f. Q wC w -)
c w (LZ 0..=
U. WU 0' 0 0Z'F' d 0 C' C' C ' C' C ' C . =I * r-
GO)~~~~~~~~~~ z' I ? C ' C C C ' C ' C
(f 0IS -L L)C d ' ( ' 0 C ~ C ' 4 Cw- 2........................-
2 IC.) N N N 000' C') '33
4 zr
f6 .(r, x. C
*I V C'
iLi
0 If C .
CICt
1, 20S
- (64
(C.
'-C. to
40 34
0 If).
1, 0r ~ ~~ =.
Z <C~- .~i~I-owar m 0i 0~~'-~' x~
C- -. l1 -r 0 - L
CI , " ( f o r,1 C.oLL' W 'h 000
I- Iz -- - - - -- - - - -
z ri Q ()a ~ f) = IC
C <E ZZ0 _ OC 0. x -r l cT1
1: -1 Mý x WZtIi- NO C? xw wc -. 0 w ýO -. ec( W co
n L. I u ie j ' 0 Ci-U. . 3 cc 2 i I.J - I-a. U~a
Xf.J 0Q W1, 0 C1j2 z 161 i-NC I,
-i z - UC 0- C
xC .= W0a ;5C FiI eI -0 00000000000-.-.. LL0 - 'C ZZ 0 00000000000000000 i
LL .LC . . . . . . . .000t)1a.r. .Q
a-Ci Q . . 00000-C00--
35
I~-
IQ I
t
p ThO )OU)0NOU)
0 .00 IW 'Cc CK C 0) t N 'C
- -NN-t4-Joo
C)CeI00-CQ 0'-N
l~t' -. 'O )0W 0) 0 U
N00
I! 0
''0 C. VyIr -. e1 - T 0.' 0 C , N ;N PIN(1 N 0''OP)00v'OO (41
) (1) 00
0'f, ONo--Ct 'tNN CC
.a .'( .4 .4 .) .4 ' ..( .4 .L' 0 d -OO O C f40fl,- X
c00C. 5C00c, 0 00 c-5 0.5v...~~~~~~~ rWWr r C .C 5 L
Qat~I
C) LO36
SAMPLE PROBLEM #3
This sample problem also analyzes the same lug and crack geometries
and loading condition as the two previous sample problems. However, in
this case, the Green's function method is used for computation of stress
intensity factors. The following stress distribution (normalized by the
gross-section stress, %o) is input as a function of (y - Ri)/Ri:
No. Cy - Ri)/Ri a/ao
1 0.0000 5.3190
2 0.0625 4.2390
3 0.1875 3.0938
4 0.3125 2.3490
5 0.4375 1.9395
6 0.5625 1.6268
7 0.6875 1.3950
8 0.8125 1.1700
9 0.9375 0.9720
10 1.0625 0.7200
11 1.1875 0.4073
No input is provided for the parameter 'IGFTYP'. The program thus
6 defaults the value of 'IGFTYP' to 1, selecting the modified Green's func-
tion to calculate the stress intensity factors. Comparison of results of
this sample problem with the previous two sample problems shows a crack
growth life difference of about 2%, which arises from slight differences in
r the stress intensity factors in the two cases.
37
1: ABPLC:46 AND ABPLC9:3"2• 2 C) 0 13: 12 04: 4.0 C '0. 1455: 5.0 0. 57.:/.. 6.0 ) 2. 0 5 0
: :8. (1 7. 50010.0 12. 900
9: 12.0 1 . 20010: 15.0 .30011: 20.0 58. 90012: 2-5. 0 134. 00012': .0. C) 353.00014: 40.) 2850.00015: 45. 0 652.C0. 00014: 60.9 0.1 -0. 117: 0.0 60.9 74. 9- .- 0 019: 1 1 120: CONSTANT AMPLITUDE WITH SA-T-M.(MX)= 6 K-I AND R=0.121: 1.0 i.022: 6.0 C. 1 100. 0
24: W-- Line 16: METHOD = 2, IGFTYP blank,"2: 1Use Green's function method,25:1 select modified- Green's26: 1 ® C Q function.27: 0. 7500 ---.375 0.50002*z: 0. 0250 .937529: 11 0 C)--0: 0. 0000 5.3190
31 : 0. 0625 4. 239002: .01c75 3. 0938
32: 0.:3125 2. .2.49034: 0. 4Z375 1 .9395-,S:"0.5625 1 Lines 23, 25: Stress distribution--:6: 0.6:::75 1 :-'503-:7: 0.8125 1. 1700-'.: 0. 9375 0. 9720
1. 0625 0. 7200* 40: i. 18-75 0. 407ý3
4I 38
- 6 c 0 ON In U) o V) tfl 0
0 ~ ~ f N N N N 0 U 0 0),Z 0 n 0 N N 0ý 0 :., .0 N
- j (1 (4 ' C. (1 0 -T LO
z
f0 VC 0L ce 2'. 10 ' U) C 00 N rC E 0 c 0 0000L' 0 0 NC,4 U N - -
U. 0) 0 '
z
w Q~11 0 0o
0 Nl tU) : 0 0 0. 0 0 0 0 0 0 0Lr Lmu - i 0 0 ! U) 0' N l0 0 '40 2
N 1 0 D-: D R M C .-
-1 - eq V ) 0 ) 1P ) N 1
3 0 CD ID (
Z.0
L)l0 2W0
NE aCc~Cc 00 1
0 O4z -13
0 0 .oIo o w.Z Z0 C .c 0 0O CN C.0 0 0 0 c- 0 c 0 0 0 0 -jCZ)
ZCC~~kl v U) 'C 0 z)0 0 0 0 UV, C, zl - r~
W00V-00 o
39
fl.
Czz- 0
CP C
Q~ w
Cj z
wx
rut- -
Z 40
VI L
t ~~z
0,0 0 0
0 LQ-JL r r - 0c 4. .. . .z o- v ' NN , qNC
C,' Lo 1 1 4
2( 1r) 02C :0L
0-- U)LoI.-.r,0 V) 9- -jt
tkt0 LL 0 C a0 ~ 0 0 . s f x' '- N .. o .1a CA 01*.- M Q ' ~ N~ 0 cc W ~ 0 0 ( - . .o 0 0 q q ~
-,0= 0C 00 -.41t*. LI(At.-' =1.4W.. . D- 0 00-.'(0 C. - *j c *as() 0n : (0C)4 -. -.. 20-
C c 0 2 0 OC (0C (
L u (h1 *.4-~~ 2 CZ' 01 -. z. gz vO Q 0 a, L
E P0 N e) =, -i C C'J
D. Z- D *) C' -I- 0 02-vN0 00NNN n0Luw 00 vn) C)0 E(( u4L .&M. . ..0 .t .0* .O C 0 W . . . . . . . . ... N 0I 0 00 0* 0 C.c.c. o o* C' . .z -'C 'IxL w0* 00w'N D O o 1C 0 4 0 ~ ) o 4 O o'u on cu N-aCL (0: 3 1C--LL J- e 0 v J ~ ~ l Q. - 0 4I -N 4. ClN 0)
9 2 CC..4 Z j 0 (
C ( 4 a ( Z L W.
- ~ 0 w CC4Lu ': ~.~ 41I(0 2
x. r
-4 C,
CD 0 N ,0 C o000n0 0 M'
* - -
N0
(ro 00
P- CC. C.
1* -o N0 1olN0V
C* W
Ix0 I-I- 4
Jww
... ( 0CC.00C C 0))" . N-. '0 0 0 ,00c00
w w U 0 0C:ý1)0 00000000000 .0 0.Z0000.08 ax C O I f - ,C cNvz 0 0 0 0 0 0 0 00 I.0 tr00C'00 - 0 0 00 LZ~ - w
= 42
SAMPLE PROBLEM #4
Instead of inputting the normalized stress distribution as in the
previous sample problem, it can also be obtained from an already-available
table in the program. This can be accomplished by specifying 'METHOD' = -2
or using a negative value for 'NSIG'. This is illustrated in the two sets
of input data provided for this sample problem. The output data for the
two sets of input data will be identical.
44
-•o 434i
1: ABPLC46 AND ABPLC932: 2 0 0 1
3: 12 C)4: 4. 0 0. 145
5 . 0.5786:- .: *') 2 * C)9-),: 6,. 0 2. 0'50
7: 3. 7. 500c10.)0 12. 900
9" 12.0 18.20010 Of. 0 28.30011 X0. 0 58. 90012: 25. (. 134. 0001 -:: :30. 0 3513. 0CC)014: 40. 0 2850.09015: 45.0 6520. 00016: 60.9 0.1 -0.117: 0.0 60. 9' 74.91i: 0 019: 1 1 120: CONSTANT AMPLITUDE WITH SIGMA(MAX)= 6 KSI AND R=O.I
21: 1.0 1.06.. 0.1 100. 0
2-3-: 0
24: 0 1-15:1
,1: ' C Line 16: METHOD = -2, use Green's
27: 0. 7500 3.375 0. 5000 function method and
28: C. 0250 .9375 calculate stress distribu-S29: 11 C) C) tion from the table stored
in the program.
F
44
1: ABPLC:46. AND ABPLC932: 2 ) 0 1
:" 12 0
4: 4.0 0.1455: 5.0 0. 578Z.: 6.o 2.; 05'07: -3. 0 7. 500A :: 10.0 12.900"": 12.0 18.200
10: 15.0 28. 30011: 2-0. ) 58. 90012: -.5. 6) 1:34. 0001 *3:0. 0 35-:-. 00014: 40.0 2850.00015 : 45.0 6'520. 00016: 60.9 0. 1 -0.117: 0.0 610.9 74. '7P1 ) 019: 1 1 120: CONSTANT AMPLITUDE WITH SIGMA(MAX)= 6 K:I AND R=0.121: 1.0 1.022: 6.0 0.1 100.023: 024: C) 125: 126: 1 © 0 - Line 16: METHOD = 2, use Green's27: 0. 7500 3. :375 0. 5000 function method2i E: 0. 0250 .p.375
*1 2 : C) C) Line 23: NSIG = -8, calculate stress distribution
from the tables stored in the program
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SAMPLE PROBLEM #5
Material : SteelRo/Ri : 3.0
R. : 0.75 InchS~1Thickness : U.5 Inch
o0: 14 Ksi
R : 0.1
Crack Type : Corner
c 0: 0.025 Inch.•'• 0
ao/2 co : 0.5
This sample problem analyzes and pre-iicts the growth behavior of a
corner crack using the Green's function method. 'ITHRU' = 0 specifies that
this is a corner crack problem. A value of 0.5 is input for 'AO2CIN' to
specify that the shape of the initial corner crack is quarter-circular.
The output contains three regions of crack growth, namely corner crack
growth until the crack breaks through the thickness, transitional crack
growth to through-the-thickness crack shape, and subsequent through-the-
thickness crack growth until failure.
Analytical-experimental correlation result for this sample problem is
given in Figure 3--2.
N5
I: SBPLCS5 AND SBPLC792: 2 0 0 1
4: 6.0 0.09115: 8.0 e). 19206: 12.0 0.74007: 16.0 1. 6600
20.0 2..99009: 24.0 4.7700
10: 28 • 6. 970011: 32.0 9.480.012': -21. 0 13. 5000•i 13: 56.0 26. 8)00014: 74.0 50. 000015: 88.0 9::. 500016: 98. 0 159. 000017: 224.7 0.1 -0.118:: 0. 0- 224.7 179.719: 0 -020: 1 1 121: CONSTANr AMPLITUDE WITH SIGMA(MAX)= 14 KSI AND R=O.122: 1.0 1.02:':' 14.0 0. 1(.0.024" C)2'-5 0 126: 1 127: @ 2 0 0 Line 16: ITHRU = 0, corner crack2:-, 0. 750.0 4. 500 0. 500029;: 0. 0.2!5, 0 1.50
0.5 Line 19: AOZCIN 0.5, a /2c 0.500.
31 : 11 0 '32 : 0.0 5.14533: 0.1 4. 10134: 0. 3 2.634.35: 0.5 1.854
0.7" 1.4973-0. 09 1.248
1.1 1.065139: 1.3 0.897
40: 1.5 0.74441: 1.7 0.55842: 1.9 0.3:93
51
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SAMPLE PROBLEM #6
This sample problem illustrates the use of compounding method to
analyze a crack problem by specifying 'METHOD' 1. The lug and crack geo-
metries and loading condition are the same as the sample problem #5. In
the output, only one crack length (thc front surface crack length c) is
printed. Since a/c ratio is assumed as constant in the compounding method,
the crack length along the lug hole wall or the back surface crack length
can be calculated using the front surface crack length, a/c ratio and the
thickness of the lug.
The computed solution using the compounding method is also included in
Figure 3-2 (sample problem #5).
V
.5
[ 57
I 8BPLC55 AND SBPLC792: 2 0 0 13: 13 0
4: 6.0 0.09115: 8.0 0. 19206: 12.0 0.74007: 16.0 1.66008: 20.0 2.99009: 24.0 4.7700
10: 28.0 6.9700i1: 32.0 9.480012: 38. Ck 13. 500013: 5-5.0 26.800014: 74.0 50.000015: 88.0 93.500016: 98.0 159.000017: 224.7 0.1 -0.118: 0.0 224.7 179.719: 0 020: 1 1 121: CONSTANT AMPLITUDE WITH SIGMA(MAX)= 14 KSI AND R=0.122: 1.0 1.023: 14.0 0.1 100.024: 025: 0 126: 1 I27: Q C' Line 16: ITHRU = 0, METHOD 1,
28: 0. 7500 4. 500 0.5000 corner crack, use29: C0. 0250 1.50 compounding method30: 0.5
58
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62
SAMPLE PROBLEM #7
Material : AlumnumRo/Ri : 2.25
Ri : 0.75 Inch
Thickness : 0.5 Inch
Crack Type : Through-the-Thickness
c 0 : 0.025 Inch
Loading : As Described Below
This sample problem illustrates the analysis of a through-the-thick-
ness crack problem with residual stress. In this case, the lug is loaded
with a far-field stress (ao) of 15 ksi and a stress ratio (R) of 0... For
this loading condition, the uncracked lug undergoes plastic yielding. An
elasto-plastic stress analysis was conducted tc obtain the stress distribu-
tion at the maximum and minimum (corresponding to R = 0.5) stress levels.
The resulting stress distributions are presented in Figure 3-3. The stress
distribution at the minimum stress level is considered as the residual
stress and the difference in the stress distributions between maximum and
minimum stress levels is considered as the alterating stress. This stress
distribution, without normalizing by the far-field stress (a ), is speci-0
fied as shown in the input data. Since the stress distribution is not
normalized, values of 1.0 and 0.0 are input for 'SMAX' and 'R' in the
spectrum layer input.
Comparison of analytical and experimental results is presented in
Figure 3-4. The present output data correspond to the curve labelled
PLASTIC STRESS.
63
7075-T651 ALUMINUMRdR. = 2.25
R 0.75 INCH= 15 KSI
60 aO 0
0mcx
S~ AaR = 0.5S• 40f m rin, R=0.5
.1z
t 20I-"U
amin, R 0. 1
00 .5
(y- -
i Figure 3-3. Stress Distribution Along y.AxiSfor an Alumlinum Lug with Ro/Ri 2.25
64w
i: ABPLC49 AND AB*'LC792 0 ' 1
-: 12 04: 1.5 0.04155: 92.0 0. 1256: 3.0 0.2497. 4.0 0.8768: 5.0 2.650': 7.0 9.190
10: 9.0 15.90011: 11.0 25.10012: 13.0 45.10013: 15.0 95.90014: 19.0 53:3.00015: 23.,) 2080.000016: 60.9 0.5 -0.117: C. 0- 60.9 74.9183: 0 019: 1 1 120: CONSTANT AMPLITUDE WITH SIGMA(MAX)= 15 KSI AND R=0.521: 1.0 1.022: 1.0 0.0 100.0-. Line 12: SMAX = 1.0, R 0.02-3: C)
24: 0 125: 1 126: @ 2 0 - Line 16: ITHRU = 1, through-the-
27: 0. 7500 3. 375 0. 5000 thickness crack
.08':00250 0. 937529: 11 C) _ _ 0 _ Line 23: IRSIG = 1, residual stressQ present
30- 0. 0000 3:4.70 3pen.10.1 ,: 0.0625 .30.97 28.2232-- 0.1875 22.84 22.54
: 0.3125 17.70 18.2-.634: 0. 4375 14.79 15.40.54 0. 5625- 12.46 12.86
0. 6.275 10.73 11.06 Line 25*: Stress distribution
S031 •5 9.02 015 (cyclic and residual
),8. 0.9375 7.53 7.80 stresses)1..- 1 -0.25 5.66 5. 51
40: 1. 1875 3.31 3.61
65
4
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V*l N. -o LAl N . N0 - . '0CK.0N'0m V,0 VV0-o onNLAL LA0LA0 N0 4o, N-0 00
-i = v-, 00 0 LAOV 00M N0O0LF AQ"N O
0 C-1 *N N N MM0 00
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.o ............. ELASTIC STRESS ::............................... ;......... I.. ........... .........] ...................... ... ... ... .. " .... .......... ... ....... :............. ............................................................ !..... . .. .... .... .......... ....... !...................
.................... !•• ....... .... ................
U
b
P~~~~i~ --. ................... & ......... " .... ' 7 . .P AS C ST E "PLAS"C.S/ES
... . . ..... .. . PL A PL 4
. R0/R~ =.2......... .....
- "' ::::::::• ::............:.......... .... ...i. . . . . . . .:.,,..•,,ov ~~ .............o .. ....... ......... . • .z< ....... ........................= :Uj .. .. .......... ° o° °°° °
S..............;.. ..... R - ,R .. 25... .............................
G = 5 KSi
* 0 1 2 34
•V THOUSANDS OF CYCLES
Figure 3-4. Through-the-Thickness Crack Growth Data and Pr:ediction,[IA.uminum L~ug, Ro/Ri=2.25, O"° 15 ksi, R,=0.5
* 70
. . . . . . . .. . . . . . . . .. . . . . . .
SAMPLE PROBLEM #8
In the input instruction (Section II), Note B states that the residual
stress case is applicable to the through-the-thickness crack problem only.
Sample problem #7 illustrated the analysis of a through-the-thickness crack
problem with residual streos. Note B also states that, for analyzing cor-
ner crack problems with residual stress, input the maximum stress distribu-
tion and a stress ratio such that a conservative life prediction can still
be made. Using the data of sample problem #7, the maximum stress distribu-
tion and a conservative R are calculated as follows:
ares(Y-Ri)/Ri Ualt ares Cmax ( •alt. + "res) Reff - -max
(KSI) (KSI) (KSI)0.0000 34,70 32.10 66.80 0.48054
0.0625 30.97 28.22 59.19 0.47677
0.1875 22.84 22.54 45.38 0.49669
0.3125 17.70 18.26 35.96 0.50779
0.4375 14.79 15.40 30.19 0.51010
0.5625 12.46 12.86 25.32 0.50790
0.6875 10.73 11.06 21.79 0.50757
0.8125 9.02 9.30 18.32 0.50764
0.9375 7.53 7.80 15.33 0.50881
1.0625 5.66 5.95 11.61 0.51249
1.1875 3.31 3.61 6.92 0.52168
A conservative R will be the minimum value of Reff in the above table.
The maximum stress distribution and the conservative R are then specified
as shown in the input data.
Also note in the output data of sample problems 1 through 6, the
failures are due to net-section yielding. In sample problems 7 and 8, the
failures are due to the exceedence of critical stress intensity factor
(fracture toughness) values.
Predicted and experimental data are compared in Figure 3-5. The curve
labelled PLASTIC STRESS corresponds to present output data.
71
1: ABPLC:35 ABD ABPLC372: 2 0 0 1-: 12 04: 1.5 0.04155: X. 0.1256-: 3.0 0. 2497: 4.0 0. 876
5. 0 2.650?: 7.0 9.190
10 9.0 15.90011: 11.0 25.10012: 13.0 45.10013: 15.0 95. 90014: 19.0 533.00015: 23.0 C200.00016: 60.9 0.5 -0.117: 0. 0 60.9 74.918: 0 C-
19: 1 1 120: CONSTANT AMPLITUDE WITH SIGMA(MAX)= 15 1..I AND R=0.521: 1.0 1.0
1.0 0.47677 100.0---- Line 12: SM4AX = 1.0, R 0.4767723: C)24: 0 12 25: 1 1
,: © 2 0 Line 16: ITHRU 0, corner crack27: 0. 7500 3. 375 C. 50002S: 0. 0250 .9375
S29: 0.5.0: 11 0 0,:1: 0. C)000 6.6. 80
0.0625 59.190.1875 45.38
':4: 0.3125 35.96::5: 0. 4375 30.19
C-0. 5625 25.32 Lines 23, 25: Stress distribution
37: 0. 6875 21.79 (no residual stress)
0. '-125 1. 32"9: 0. •9:2:75 15.33
40: 1.0625 11.61* 41: 1. 1-:75 6.92
72
-N ' q 0 N C) '0 N 0 N
V) - r, 41 N r LO N O OD 0- O'- N 'C N C, 0 C. 0 0 0 0
LL C ' f- C' C C N C' U) C
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LL L)
UC S 00 C' 0 C* 0 a' 0 0lb N V Is 0, 0 0 0
x 0r 00 00 0. ' N
'C - C 0 ' N - 4 0) Ur) M -
U. N < ( 0 0 U) 0 - ' -
C
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~~ a'
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41 0 9-' -( 0. ' O 000 00 *C'C C' N ' C .0' . 0 0 C. 0 0 0
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- 0 2 0 (A' (. W -j 4- w'1) O= .0 *Cr 0 M ;~I)'II'', 2
D0 IL w - (Ii -N f- 00 0 0 0zc N
.4 = C .O W /4 _j owILý . 0 . U-I- CL - LQi, 22 *0 V O cCCICZ
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~ o~ -z ~C'IXjJ 014 0 0000000000 ZC 0(.r ( OI44) IfI' I*ONt 0140-470I 6*z n -Z0 r, -~ u- 00'M-.C'0 00'N '-' -Ur 0 ~ ' -. ' 0 C' O I
r 1 14''. O w 2 = ..0.0.).0.I.-. ~ .Lu ...... .- '-.
X v wWCInLQ t- WLIL C..o- CZ ft i-C - C J-' Z2Cr Xi
c, L CU X- 3 Cr.0 - 2 I
Cr L C) CILO 2-W
.4 (' u' ILIL W~w r - -004r~).oe04C'0CP75O I
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P. 0W (0p~ 0 o0 0 0,-~ M Qs 0 1- mcNNNNN t 1 T- 44 0 C2 .0 N - Q ic L
CLL 0000*C O0~O~ O Of.0 0,-. a 0 c-ý Xi 0000 0 000000000 0c C, 0 a0 0
L2r . . 1* (L 0
2U W( 0-03~
L' &Z W r00 0 N t0-.00U0' N 0CK N 0: N4~0 4U ...
x1 00 V n4Z.f- 0 :N 0000000000-00-0~0 N e20 0 00. 00=C 0.00
LO - =/ ~ O .- N "0.W0 0. 4 z 0 00- IL ~2c W :90~q w0 0 000 . .W .N' 0 .O --. .2 . =
a0 2(' 0 ~0 g 2* *N
42 F. IX-m
0 ,N 0 N N ~, -4 00. w 0 N44,0 OoW 4ON4OO NNI CZ=0Oý000-0.0 MO Ix~ ~ C0 ~00-C a: WE NLU
Z ~ t, -,I 00('C~ 0NN x.0'Ux'N00 ~0V 0 -0 O N 0 01IJ 01 ?0 0: LI W ~ C 2 L L
4r 0 4 -T 000 4 00C0-T00 -40aaw 00ý O Oo- N c ý LC 01, C, 0 - C.. f-
IxC r 0 .' 0 1 , Nf,0 '01 0 .. 6N 2 r ) 1C eN0 - wN I N (-. C4C4-
Z -LO 11 0 *I W . .U. .-.. z
NC O CO f 0-- 004 0 1 N4.-0 00000 0,00 U) W Ir t0rN--
;Lý6 N("ý C
V) 76 ýV -,N0 C C)N(i WI
10' ELAS.TIC STRESS ...........
~. . . . . . . . . . . . . . . ............. . ... ...... ............. .................
U PLASTIC STRESS
U 0THOUSANDS..... OF......... CYLE .............
I 0-/R -22
Q .......................... .... . .............. b...............R18O.........2
100STREUSANS OCYLESTI TES
Almiu Lug =/.2.5 17 5 KSI, =
. ....... ..........7 7= .
r'S
SAMPLE PROBLEM #9
In all the sample problems presented thus far, only simple constant
amplitude loading is illustrated. This sample shows the input for a
slightly complex block spectrum loading. The schematic and details of
block spectrum loading are given in Figure 3-6 and Table 3-1. The method
of inputting the block spectrum is shown in the input data.
The above block spectrum will introduce spectrum retardation effects.
The Generalized Willenborg model ('IRETAR' = 1 and 1IMODEL' = 2) is used in
this sample problem to account for the crack growth retardation effect.
Values of 0.0 and 3.5 are used in the input for the parameters 'XKMXTH'
(maximum threshold stress intensity factor) and 'SOS' (overload shut off
ratio), respectively. These values correspond to a value of 0.4 for the
factor 0 of the Generalized Willenborg equation. The plastic zone is cal-
Sculated assuming a plane stress condition ('IPLANE' 1 1).
Figure 3-7 shows the analytical-experimental data correlation for this
sample problem. The labels mean the following.
[A] - Hsu retardation model is used
[B] - Generalized Willenborg model is used (Present output data)
[C] - Willenborg model is used
[D] - No retardation effect is considered.
4.7'
g4"
•- 78
=SIRESS RATIO, 1? 0.1 NN51.00
LOADFACTOR
0.50 AN
N1 N2 N344
U) . 0. • I.
NUMBER OF CYCLES
Figure 3-6. Schematic of Block Spectrum Loading.
TABLE 3.1. DETAILS OF BLOCK SPECTRUM LOADING
STRESS DATA CYCLE DATALOAD FACTOR MAX. STRESS NO. OF
SYMBOL VALUE LEVEL (KSI) SYMBOL CYCLES
a1 0.45 2.7 N 950
02 0.55 3.3 N2 650
30.65 3.9 N3 450(33
040.75 4.5 N4 250(44
05 0.85 5.1 N5 136•55
a6 0.95 5.7 N6 44
a 7 1.05 6.3 N7 15
08 1.15 6.9 N8 4
09 1.25 7.5 N9 1
NOTE: UNIT LOAD FACTOR 6 KSI; R =0.1
79
_• ~1" ABPF_:76
20 2 0i
4: 4. ,C 0. 1455: 5C) 0 . 57-6., 6.0 "-o5c)
7 ,0 7. 5!.Q
10. 0 1S/12: 12.0 1C., .2,00
: 1.0 2-3. 300:0.0 5. *-00 Line 7: IRETAR 1, IMODEL 2,
12: 25. 0 3,-:4. 000 Account retardation effect1.3* ._--:0. 353. 000) with Generalized Wilienborg14. 40.0 2,,850. 000 .... model15: 45. 0 50. 00odel16: 60.94 C). 1 -0.117: 60.94 74. '91 : _ - -19-'- O) 3. 5 Line 8: IPLANE = 1,20: T' XKMXTH = 0.0,21:BLOCK SPFECTRUM CEFINITI:N SOS = 3.522:1.C0 1,023: 2.7 0.1 950.0
0.1 650.0•. i 0.1 450.0 '4.5 0. 250.0 Line 12: Block Spectrum Loading
27: 5.1 . 13-6.02 5.7 0.1 44.0
6.3 0.1 15.0:-0: 6. 0. I. 4.0:31: 7.5 0.1 1.0
:-1 .3 ).3 15"' .. 3 5 0 O34: ! 1
:'• 1 C' C).- 6 .... 7.5000"
"4': 0. 16C)0 . :1
4: . 625 4.2-'?041: 0. 1 -7_ -:.42: ',3125 2. 34904: 3: 0. 4.375 . 939544: 0. 5625 1.62, 8
C 45: 0. 6875 1 395504,. : 0. '-'125 1.17047: C. 9.-375 0. 972(,13 1 0 i. 2,•25 0. 72,0 C
iV ; ý41 1 `.• .: -7 C % / K0 7 -
80
Is 0 m 1 0 t- I' 0 -. 0 N' 0O '0 (1, CA Qi 4 0 0,C. 00 0
r - 0 0 N . 00 0~ 0 Y 0
ir0 )C l 0 r, 0, r l W
0
0 0 '0 ~~ 0 0 0 0c tr C 1 0 000 0 0 0 0-0
0:W0 V 0. 04 1 K - - 0 0 ý300 MN 000 NO 16-;
C. -- z 0 0 N . I-
0 N -x~00
W CWQ o.-i
0 ) coCL W3. 0
a O F; 1'0 0 0 0 0 0- 0
Q - C. 0 If C. 0 Q 0. 0 0 0 0 D 0 1
0 C,2 c - N .0 0 0 0 0 N
0 r.* 4 L 00 N' 0' 14 0v -z
-U02
w w--I
I- C81
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0-82
In
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c .z i 0 Ix xiC al S. Li. w I.W0 0 0W W0Cl.C*ff) n 0 If-1 wr( _3W NC.: ciNýC
z -j .0-1I. t(>1.09-N 0 00 (1) 0 0 ,0) t'eC.0< 00NaC Cf - EO 9-.. X i = 0C- (1)9Q.0 a. CI) 0ý -0' C. ' ,0NIr t!q r )0v
CI D0 - 0l it If,CN. u ~ ko -o r' 0/ 0 - 0 0 00 z 2ý ) , w 0 Q- .- cc0 CIOZ (4O C4 (i. o-3 -7 tr 3,0P C)
ZU CLI a4 ZW -4 a.-J 9/ . . .........
(r'C~~~ tiZ' Li 3.LC 0Cr -
LL - 3i10 I) LiC/~, .9.W
(Ll ,0 C~ W i
Li i~u - 3 CW~9-.W 9-2 83
-0-NP CON--ON-0-~0
N 0 e -0 m-cD ;; f,1E a# ~ r-0 -. U)C')'O-.- .0 -
YN 'IL
ix z
>. N N0
0 , ' N N. N 0 010t ' I I 0- L 0.00V000.0.0-0IOU NO M
co Z NNNNNNNNC0000' 0 aI0 - . .f 00 .....
0 W 4 2
08V 1-q0O N004 'DNO',NO
0 Wu. 9 .0l4c - 0 00000r:1;0 0'~ N~ 2* 0 l 00 0
m L (A) N~
W. W I.
0o us. o. 0ý . . .1. 0-W A 00 CI Mk)C l 1 0 rium
C . zr . ~ -t . . ..
k ( - e'Xo 0 u
L~ I84
S.. -IJ [a A
109 D [B 1A .................. . .... (C ] ........1 ' ...................
- ..I . fB ..A . . .... .......................s . .. .. . ........ ... .. .. .. .. ..................
s . . . .N.... i..... ... .. . . . . i......... ........ ...................
4 .. . .... ........ i............... ... i................... i....................-u= /:.0M -ABPLS76
.:•) .. ... . ........................ .....?:•- • "Ro/Ri = 2.2,5
U
•"• •[• Oomax = 7.5 KSIS•/ co = 0. 1136 INCH
,•:•-•;::•,• fBLOCK SRCTRUM
SI-
;i 0 100 200 300 400
PASSES
Figure 3-7. Through-the-Thickness Crack Growth Data and Prediction, Aluminumlug, -Ro-/P,=2.25, Block Spectrum Loading, oa=7.KI
870
SAMPLE PROBLEM #10
This example corresponds to prediction of corner crack growth behavior
in a lug subjected to a much more complex spectrum of flight-by-flight
lkading. This spectrum is typical for a cargo aircraft (C-5). This spec-
trum inclqdes thirteen different missions (0, 1 through 12). The details
of the missions are provided in Table 3-2. In this table, a special load-
ing cycle is defined in terms of N/FLT = 0.1, for example in Mission 1.
This simply means that the particular load is applied once in ten
occurrences of this mission. When Mission 1 includes this load it is
referred to as Mission 1*. In the input for this problem, Mission 1 and
Mission 1 are treated as separate missions. The sequence of missions in
one pass (mission mix) of the spectrum is given in Table 3-3. One pass
consists of 120 missions and one mission has the same meaning as a flight.
In this sample problem, the Hsu retardation model ('IRETAR' = 1 and
'IMODEL' = 3) is used and the yield zone is calculated using the plane
strain condition ('IPLANE' = 2).
Analytical and experimental results are compared in Figure 3-8.
Labels [A], [B], [C] and ED] mean the same models as given in sample
problem #9.
86
TABLE 3-2. MISSIONS DEFINITION FOR CARGO SPECTRUM
NMAXT1STRESS STFESS
1-3I KSCI W:/FLT
INES 118.o83 -1.808 1.o04.423 2.423 19,98.00
13.L92 9.492 193.0015. 106 9.1o6 24.0015.863 7.363 4.0016.909 5.572 1.0018.083 2.602 .10 *
-MS 217-987 -1.799 1.00
5.080 3.080 2273.0013.824 9.824 204.0015.189 9.'189 25.0015.908 7.908 5.0016.899 5.494 1.0017.987 2.384 .10
NES 316.751 -1.675 1.004.888 2.888 2891. 00
14.139 10.139 227.0015.30o 9.304 25.0015.918 7.918 4.0016.751 5.302 1.0o
MIS 416.695 -1.669 1.006.157 4.157 2827.C0
14.755 10.755 209.0015.562 9.562 23. C016.o65 8.o65 .oc16. 695 5.536 1oO
M'• 517.952 -1.795 .C00I..737 2.737 2099.00
10.329 1 75.001 I.20 9.420 21.0016.101 8.101 LL.CO, .,,6 5.964 i.00S7.952 2.988 .10
* N/-MLT = 0. 1-Means the application of this load once in. -,n occu'rencesof this mission (refer -o sequence cf missions table).
87
TABLE 3-2. MISSIONS DEFINITION FOR CARGO SPECTRUM (CONTINUED)
STRESS STRESSKSI TN/_PLT
MIS 616.778 -1.678 1.006.313 4.313 ?082.oo
15.372 11.372 204.0015.904 ý.004 21.0016.321 2 3.0016.778 6.50o I1.00
•INS 717.861 -1.786 1.005.628 3.628 2100.00
11L.6 34 I0.634 164.0015.592 9.592 19.0016.232 8.232 3.0016.916 6.358 1.0017.861 3.335 .10
,us 817.518 -1.752 1.006.414 4.414 2714.o0
15.4o1 i1.4o0 187.0015.941 9.941 19.0016.373 8.373 3.0016.820 6.253 1.0017.518 2.991 .10
mrrs 917.761 -1.776 1.006.r44 I.544 2260.00
15.197 11.197 161.0015.858 9.858 17.0016.406 8.406 2.C016,913 6.694 1.0017.761 3.686 .10
HlS 1017. o01 -1.700 -.006.S06 4.806 1989.00
! 15.273 11.273 151.0015.918 9.918 18.0016. ZL7 5 8. !75 2.0017.001 6.760 1.00
88.-4
TABLE 3-2. MISSIONS DEFINITION FOR CARGO SPECTRUM (CONTINUED)
MAY, mMISTRESS STRESS
.ES 114.5=46 -1..808 1.00
15.523 . 0o0 1.0015.523 .000 i.00""5.523 .000 1.D018.083 .000 1.0015.523 .coo 1.0015.523 .000 1.0015.523 .000 1.0016.191 .000 1.0016.191 .000 1.O03.774 1.774 5`08.O00
12.842 8.842 419.0014.5:46 8.546 51.0015.523 7.523 9.0016.191 6.191 2.0016.913 4.425 1.0018.083 1.151 .10
v..S 1215.650 -1.849 1.0015.650 .$000 .0015.650 .000 1.0015.650 .000 1.0018.487 -1.849 1.0015.650 .000 1.0016.323 .000 1.0016.323 .000 1.016.323 .000 1.00
3.848 1.848 6512.0013.11,2 9.112 55-10.00
14.771 8.771 69.O05.6550 7.650 12.00
16.323 6.323 5.=0017.267 4.096 i.0018.287 .919 .10
89
TABLE 3-3. ONE PASS OF SEQUENCE OF MISSIONS OF CARGO SPECTRUM
SEQUENCE MISSION SEQUENCE MISSION SEQUENCE MISSIOMNO. NO. NO. NO. NO. NO.
1 7 41 2 81 72 8 42 5 82 123 1 43 12 83 114 2 44 7 84 95 12* 45 2* 85 76 7 46 8 86 8*7 5 47 1 87 28 11 48 9 88 59 8 49 4 89 1
10 9 50 7 90 12Ii 7 51 12 91 712 1 52 8 92 1013 12 53 11 93 814 2 54 5 94 1115 7* 55 7* 95 316 8 56 1 96 7*17 11 57 2 97 213 5 58 12 98 119 1 59 8 99 1220 7 60 7 100 521 12 61 0 101 722 4 62 3 102 823 2 63 5 103 924 7 64 1 104 225 8* 65 7 105 726 6 66 12* 106 11*27 11 67 8 107 1228 1 68 2 108 129 12 69 11 109 830 7 70 9 110 531 3 71 7 ill 732 2 72 1 112 233 5 73 12 113 1234 7 74 3 114 835 1* 75 7 115 736 9 76 5* 116 9*37 12 77 2 117 138 3 78 4 118 1139 11 79 1 119 41.O 7 80 8 120 12
*Missions with application of once in ten occurrances loads (i.e., loadswith N/FLT = 0.1)
90
1: SBPLS56 AND SBBPLS542: 2 0 0 0
13 04: 4.0 0.05375: 5. 0 0. 106
6: 7. 0 0. 2477: 9.0 0.482 Line 7: IRETAR = 1, IMODEL = 3,
11.0 0. --33 Account retardation
13.0 1.310 effect with Hsu model10: 16.0 2.25011: 20.0 3. 93012: 24.0 6. 010
14: :35.0 12.8:0015: 50.0 29.000 Line 8: IPLANE = 216: 58. 0 57. 70017. 224.7 0.5 -0. 10: 0.C) 2247 179.7•'20: Z
21: 2S,•~22.- MIS:SION 02• MISSION 0 Lines 9,10,11, 12*, 13:22-=: 1.0 1.0
24: 19.108 -1.184 1.0 Flight-by-flight25: 2 Acargo spectrum;•25: 2 2 626: MI=SION 1 definition beginninj
27: 1.0 1.028: 18.:•03 - 1.-0 1. C)29:.• 4. 423 2.42... 19918. 0,0: 13.492 9.492 193.031: 15.106 9.106 24.0:32: 15.863 7.8636 4.0*33: 16.909 5.572 1.034: 3 2 7
-.235: MISSION 1*36: 1.0 1.0:37: 18.08: -1. ,,S0o. 1.0
.8: 4. 423 2.423 1998.039: 13.492 9.492 193.040: 15. 106 9. 106 24.041: 15.' -3 7.:363 4.042: 16.909 5.572 1.0E 4:3: -. 0'.3 62.602 1.044: 4 2 645 M... I S N 2
41 4.: 1.0 1.047: 17.987 -1.7959 1.048: 5.080 3. 080 227.3. 049: 1:- 824 9.'24 204.0
h50: 15. 1.819 25.0
1 ý91
51: 15.90:=: 7.909 5.052: 16.899 5.494 1.053: 5 2 7-54: MISSION 2*55: 1. 0 i. Q•56: 17.987 -1.79-5 1.057: 5. 080 3.080 2273.058: 1i3. 824 9.824 204.059: 15.189 9.189 25.060: 15. 908 7.908 5.061: 16.85199 5.494 1.062: 17.987 2. 384 1.063: 6 2 664: MISSION 365: 1.0 1.066: 16.751 -1.675 1.06: 4. 2.888 2891.068: 14.139 39 227.069: 15. 304 9.304 25.070: 15.918 7.918 4.071: 16.751 5.302 1.072: 7 2 673: MISSION 474: 1.0 1.075: 16.695 -1.669 1.076: 6.157 4.157 2827.077: 14.755 10.755 209.078: 15.562 9.562 23.079: 16.065 8.065 4.080: 16.6-95 5.536 1.081: 682: MISSION 583: 1.0 1.034: 17.952 -1.795 1.085: 4.737 2.737 2099.086: 14.:329 10.329 175.087: 15.420 9.420 21.08:. 16. 101 8. 101 4.089: 16.936 5.964 1.0
90: 9 2 7S91: MISSION 5*92: 1.0 1.093: 17.952 -1.7795 1.094: 4.737 2.737 209':. 0*95: 14.329 10.329 175.096: 15.420 9.420 21.097: 16. 101 8. 101 4.0
...16.936 .51.964 1.099: 17.9.52 2. 1.0100): 10 2
92
101: MiSBION 61. C) 1.0
S10: 16. 778 "-1.67: 1.0104: 6.31" 4..31 3082.0L 05: 1 ... 72 T 2 .. 3727- 204. 0106.: 15. 904 ".904 21.0
SC) 17 16... :321 : ". :'21 0
16. 778 6. 050 1.o1037 11 2 6
10: MISSION 71 1.0 1.•0" 17.6i -71.78- 1.0'1 5. 62. '.628 " 100.'! !Ii;: 14. ,634 10.6.34 164.0
115 15.5 9'=- *-P. 592 19. Y.0!11b: 16. 232 :-.2"32 3.0.C117: -. 916 .35: 1.0 811 : 12 2 7115r: MIS'S'ION 7*
S20: 1.0 1.021: 17. I6 -1.7. .5.6.- 1.T-5 .... 62G.. 21 .0
14. 64•_ 10 1. 634 16-1. 01.24: 15. 5,.2 . 5.-" 19.01..... .. 9 -" 1 :.0C
125: 11. 23127 17.861 3. '2535 1.0
,29: M ISI ON 8:1.1:3=0 : 1. -: 1.0
1.0 .1: 17.518 -1.752 1.0
13 6.414 4.414 2714.015.401 11.401 187.0
1:34: 15.941 9.941 19.C1 5: 16. 373 3. '73 3.0""!36-: 16. CE2O 6. 253 1.0
. 1:7: 14 2 7E--': MISSION 8*
1.0 1. 0140: 17.518-D -1.752 1. 0141: 6.414 4.414 2714.0142: i5.401 t1. 401 18.7.014_-:: 15. 941 '.941 19.-/'0144: 16.373 0..73 3.145' 16. /-' . .253.146: 17.518 1.0147: 15 - /148-_: MISSION 9
K -s -s I LC ) 1 .150: 17. 761 -1. 776 I.0
93
K27
151 : 6. 544 4. 544 2760.C
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-I 0-t -
SAMPL" PROBLEM #11
Analysis of a lug with an interference-fit bushing is illustrated in
this sample problem. Details of the material and geometric parameters are:
"Lug Material : Steel
Bushing Material : Steel
IP Lug Outer Radius, R : 1.6875 Inch
Lug Inner Radius, R . : 0.84 Inch
Lug Thickness : 0.5 Inch
Bushing Thickness, tB : 0.09 Inch
Young's Modulus of Lug Material, EL : 3 x 10 Ksi
Young's Modulus of Bushing Material, EB : 3 x 10 KsiPoiPoisson's Ratio of Lug Material, 3L : 0.3
SPoisson's Ratio of Bushing Material, VB : 6.3B
Loading Pin Radius (: Lug Inner Radius-
Bushing Thickness), ri : 0.75 Inch
tB/ri : 0.12
EB/E : 1B L
Diametrical Interference, 0
: 14 Ksi
R : 0.1
Crack Type : Through-the-Thickness
c : 0.025 Inch
Four sets of input data are presented for this problem. In the first
"data set, the residual stress and the normalized stress distribution across
the net section are calculated from the already-available tables in the
prog,-avt by specifying 'METHOD' -2 and 'IRSIG' = -1. In the second data
set, the residual stress and the normalized stress distribution (obtained
rT using the concentric cylinder equations and the finite element method) are
input directly. In the third data set, the residual stress is calculated
automatically ('IRSIG' = -1) and the normalized stress distribution is
input directly. In the fourth data set, the residual stress is input
directly and the normalized stress distribution is obtain-J from the
112
already-available tables ('METHOD' -2). In the fourth data set, note
that only tB/ri ('TBR') and E B/EL ('EBEL') are needed to interpolate the
da:a from the tables. Values for parameters 'EL', 'DELD', 'POL' and 'POB'
are not needed for such an interpolation, and will be ignored by the
program if specified, without influencing the output results.
The above four input data sets show the flexibility with which the
stress data can be input. All the four input data sets are equivalent and
thus only one set of output data is included for this sample problem. The
* other three sets of output data would be the same, except for slight
differences in the results due to computational round-offs.
The far-field loading is applied with a stress ratio of 0.1. However,
"the operating stress ratio across the net section of the lug will be dif-
ferent due to the presence of residual stress. In this case, the operating
stress ratio ranges from 0.32 at the inner radius location to 0.64 at the
outer radius location. Thus, for this problem, crack growth rate data
corresponding to a stress ratio 0.5 are input, although the applied far-
field stress ratio is 0.1.
A value of 2 has been input for parameter 'IGFTYP', selecting the
original (unmodified) Green's function for the computation of stress
intensity factors in this problem. The use of the original (unmodified)
Green's function ('IGFTYP' = 2) is recommended for lugs with interference-
fit bushings. The modified Green's function ('IGFTYP' = 1, the default
value) should be used for lugs with no bushing, since the modification of
Green's function accounts for the pin bearing pressure distribution
variation with respect to crack length.
Comparison of experimental and analytical data of this sample problem
is given in Figure 3-9.
113
S:VIER42: AND SVLR442 2 ) 0 13: 13 04: 4.0 0. 05375: 5.0 O. 1066: 7. 0 0. 2477: 9.0 C O. 48-28:. 10 -- 339: 13.0 I. 310
10: 16.0 2. 25011: 20.0 3. 9:30
12: 24.0 6. 01013 : 2.0 :--,. 35014: 35.0 12. 80015: 50.o0 29. 00016: 58.0 57.70017: 250.5 0.5 -0.11$: 0.0 250.5 179.71,':9: 0 020: 1 121: CONSTANT AMPLITUDE WITH SIO13A(MAX)= 14 KSI AND R=0. I22: 1.0 1.023: 14.0 0. 1 100. 0 Line 16: METHOD = -2, IGFTYP 2,24: use Green's function .- method calculating (cyclic)25 0 1 stress distribution using26: 1 1 tables stored in the27: 1 0 o program. Also use2:C: 0. I:40000 E.375 kO.60 unmodified Green's-29: O. 3750 functions29 -0250 0). :=4750)30: 11 03 1: . 12i C) :-. OE.4 i. 0 0.00:0 0.3
Line 23: IRSIG -1 Line 24: TBR, EL, EBEL,Calculate residual stress ! Lie 4:TB, EL, EOBE
using concentric cylinder DELD, POL, POBequation
- -114
1 :!.VLR42 ANDE SVLR442 2 0 0 1•.:: 1_-3• 0
4: 4.0 0. 053:75: 5.0 0. 106
7. 0 0. 2477:: 1.0 0. 4328-:: 11. 0 0.8339: 13. 0 1.310
10: 16. 0 2.25011: 20.0 3. 93012: 24.0 6.01013: 28.0 8. 35014: :35.0 12.80015: 50.0 29. 00016: 58.0 57.70017: 250.5 0.5 -0.1I::1.: 0. 0 250.5 179.719: C) 020: 1 1 121: CO0NSTANT AMPLITUDE WITH SIGMA(MAX)- 14 KNSI AND R=O.122: 1. 0 1. 023: 14.0 0.1 100.024: 029: C) I
-7: 1 2 C) © Line 16: IGFTYP = 2, use unfnodified
28:: 0. 8406000 3. 375 0. 5000- Green's function
29: 0. 0250 0. :3:475030: 11 1 031: .000 3.418 22. .5 2"-32: .050 3.100 20. 833
.151 2.517 18.09134: .252 2. 041 15. 98535:-.... 1.752 1A4.332 Lines 23, 25*: Stress distribution
*3 36: .454 1. 491 13. 012 (cyclic and- residual
.555 1.2?9 11.939 stresses)3-.: .656 1.C0l8 11. 05739: .757 0. 906 10. 32340: 8 5:-5- 0. 655 9. 70441: .958 0. :368 9.179
115
- - ..-F.•- .~-
I:SVLR42 AND SVLR442: 2 0 0 I
4: 4.0 1. 057, 75 : ,. 0 0. 1066: 7.0 0.2477: 9.0 0.4828: 11.0 0. 82:a39: 13.0 1.310
10: 16.0 2. 25011 , 20.0Q 3. 930
12: 24.0 6.01013: 28.0 8. 35014: 35.0 12.,$00
15: 50.0 29,00016: 58 .0 57. 70017: 250.5 0.5 -0.113: 0.C 25'0.5 179.719: 0 020: 1 1 121: CONSTANT AMPLITUDE WITH SIGMA(MAX)= i4 K:3I AND R=O.I22: 1.0 1.023: 14.0 0.1 100.024: 025: 0 126: 1 1 0 _.__.... Line 16: IGFTYP = 2, use unmodified27:' 1 2 0 2ren6fcto28: 0. 840000 3.375 0.05000 Green'• fun29: 0. 0250 C.8475030: 11 G 0 -) , , . ."-1: .12000 3.0E4 1.0 0. 008 0.3 Z, 0.32: 3.4183132 3.1 00334: 2.517I Linen2: isG---":" 2.041 Calculate residual36: 1.752 stress using37: 14 Leyi concentric cylinder
.29 Line 25**: Cyclicequation39: 1. 0 B stress distribution40: 0. 90641: V.65542: 0.368
116
I: SVLR42 AND SVLR442: 2 0 0 1
., 13 04: 4.0 0.05375: 5.0 0. 106
6I 7.0 0.2477: 9.0 0.48211.0 0.:33
9: 13.0 1.310.Q 16. 0 2.250
11: 20.0 3. 93012: 24.0 6. 01013: 28.0 3. 35014: 35.0 12.80015: 50.0 29.00016: 58.0 57.70017: 250.5 0.5 -0.118: 0. E 250.5 179.719: 0 020: 1 1 121: CONSTANT AMPLITUDE WITH SIGMA(MAX)= 14 KSI AND R=0.122: 1.0 1.023: 14.0 0.1 100.0 Line 16: METHOD = -2, IGFTYP 2,24: 0u Green's function method2 05 4 1 calculating (cyclic) stress26: 1 1 distribution using tables21: 1 0 © stored in the program. Also28: 0. 840000 0 use unmodified Green's functio,"X-: 0. 0250 0. 8475030: 11 1 031: .12000 0. C) .0 0. 000 0. 0 0. -,-S,2: 0. 0::2 : 22. 525
--34: 20. 83318.091 Line 24: Only
S36: 15. 985 TBR (= 0.12) al
37: 14. 332 EBEL (- 1.0) ai13.012 Line 25***: input.11.939 Residual stress
N 39: 11. 057 distribution40:: 10. 32341i: 9. 70442: 9. 179
117
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-......... CTTT_. GREEN'S FUNCTION. .........................
. ...................................... STEEL
........................ ...... ...... ... ............................ 0.9E................ .....................................
U" .,.. .... .. .. .. . .. ... .. .. . .. ST E E LO 0 -1 C
:= o i.-.SVLR414KS
". .. .. .. ..... . . . . . ... o . . . . . •.. .•
S...........................
M-• -6DVLR =0.94-NC
...................... ................ e - SVLR42 .:..................I -0I0 INC
0 100 200 040
d THOUSANDS OF CYCLES
Figure 3-9. Through-the-Thickness Crack Growth Data and Prediction, Steel Lugwith Steel Bushing, Ro/ri=2.25, tB-0.09 Inch, a=14 KSI,R=O.1, 8 D.O08 Inch 0 * *
S•US.Government Printing Office: 1985 -- 559.065/2064512
................ 122..................
