residual stress distribution changes during dynamic

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1965-6

Residual Stress Distribution Changes DuringDynamic Unidirectional Tensile LoadingHenry Swan ToddBrigham Young University - Provo

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RESIDUAL STRESS DISTRIBUTION CHANGES

DURING DYNAMIC UNIDIRECTIONAL TENSILE LOADING

i2 0-0 0 2.7 ~ 5 6 &

1 1 ^

A T hesis P resen ted to

The Faculty of the D epartm ent of M echanical Engineering Brigham Young U niversity

In P a rtia l Fulfillm ent

of R equirem ents for the Degree M aster of Science in Engineering

by

Henry Swan Todd

June 1965

T his th esis by Henry Swan Todd, is accepted in i ts p re sen t form by the

D epartm ent of M echanical Engineering of B righam Young U niversity as

satisfy ing the th esis req u irem en ts fo r the degree of M aste r of Science.

Date

Typed by M argare t K luss

ii

ACKNOWLEDGEMENT

The author is s in cere ly g ratefu l to the m em bers of h is G raduate Com m ittee

fo r th e ir patience and many hours of w ork in h is behalf. The author is a lso

deeply g ratefu l to the Education D epartm ent of the In ternational B usiness

M achines C orporation for th e ir generous a ss is tan ce in providing com puter

tim e for the analysis of experim ental data described in th is investigation.

But m ost of a ll the author is g ratefu l to h is wife for h e r encouragem ent and

untiring ass is tan ce .

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TABLE OF CONTENTS

ACKNOWLEDGEMENT.............................................................

LIST OF F I G U R E S ...................... ...........................................

LIST OF T A B L E S ......................................................................

IN T R O D U C T IO N .................................................................. ....

Statem ent of the P r o b l e m ................................................

REVIEW OF THE L IT E R A T U R E .......................................

NonDestructive R esidual S tress D eterm ination M e th o d s ...................................................................................

X-Ray D iffraction M e th o d .............................. . . . .

U ltrasonic M e t h o d .............................................................

D estructive Residual S tress M e th o d s ..........................

L im itation of R esidual S tress Calculating Methods .

Surface Residual S tress Changes Under Fatigue L o a d in g ...................................................................................

TOOL AND EQUIPMENT D ESCRIPTIO N ..........................

Fatigue Testing M a c h i n e ................................................

G r i n d e r ...................................................................................

C urvature G a u g e ..................................................................

C urvature Sign Convention ............................................

THE APPROACH TO THE PROBLEM ..........................

T est Specimen Design, P rep ara tio n and Loading

The D issection M e t h o d .....................................................

CHAPTER

I

II

III

IV

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CHAPTER PAGE

R esidual S tress C alculation Method D erivation . . . . 17

C urvature E q u a t i o n .......................................................................26

C urvature Equation M a t r i x ..........................................................27

C alculation P r o c e d u r e .................................................................. 29

V R E S U L T S ................................................................................................... 30

D iscussion of R e s u l t s ...................................................................30

N onshot-Peened Unloaded Specim ens ....................................30

N onshot-Peened Loaded Specim ens ....................................30

Shot-Peened Specim ens ...................... 32

VI CONCLUSIONS AND RECO M M EN D A TIO N S................................. 33

Conclusions .................................................................................... 33

R e c o m m e n d a tio n s ............................................................................34

APPENDIX

A RESIDUAL STRESS GRINDING........................................................... 36

B DERIVATION OF CURVATURE DISPLACEMENTE Q U A T IO N ............................................................................................. 41

C CURVATURE CORRECTION EQUATION WITHD E R IV A T IO N .........................................................................................42

D COMPUTER PROGRAMS AND COMPUTATION LOGIC , . 44

E SAMPLE COMPUTER CALCULATED R E S U L T S ........................ 64

F EFFEC TS OF POSSIBLE DISSECTION GRINDINGINDUCED S U R F A C E ............................................................. 83

LIST OF REFERENCES ...................................................................86

A B S T R A C T .................................................................. 88

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LIST OF FIGURES

FIGURE PAGE

II I - l Fatigue T esting Machine ......................................................... 8

III-2 G rinder .......................................................................................... 8

II I- 3 C urvature G a u g e ............................................................................. 10

IV - 1 T es t Specimen ............................................................................ 13

IV-2 Fatigue T es t Specimen Drawing ............................................ 14

IV-3 Sectional Drawing D escribing D issection P rep a ra tio n . . 16

IV-4 Layer Removal Beam Section ................................................. 16

IV-5 P ossib le S tress and C urvature P a t t e r n .............................. 19

IV-6 B ar C urvature A fter L ayer R e m o v a l ................................... 19

V - l R esidual S tress V s. Depth ..................................................... 31

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LIST OF TABLES

TABLE PAGE

D -l G eneral Symbol D i r e c t o r y ............................................................ 45

D-2 Flow C hart Symbol C o n v e n t io n s ................................................ 47

CHAPTER I

INTRODUCTION

In recen t y e a rs th e re has been much engineering effo rt channeled tow ard

obtaining h igher s treng th , low er weight and co st product designs. In p u rsu it

of th is goal som e carefu lly designed and te s ted p a r ts have catastroph ically

failed a f te r a long h is to ry of repeated successfu l se rv ice , even though the

load a t the tim e of fa ilu re was no h igher than the p a r t had repeatedly c a r r ie d

previously . T hese m echanical fa ilu re s a re commonly c lass ified a s fatigue

fa ilu re s .

Much w ork has gone into the study of the causes and m eans of prevention of

fatigue fa ilu re . Many d ifferent th eo rie s have been devised fo r p redicting when

and under what conditions fatigue fa ilu re w ill occur. No single com plete de

scrip tion of the m echanism of fatigue fa ilu re has as y e t been verified . Many

re s e a rc h e rs ag ree , however, th a t a key to th is problem is the condition of the

su rface . One investigato r rep o rted su rface sensitiv ity

sufficient tha t under ce rta in conditions, ju s t the placing of tran sp a ren t tape

(21)on the su rface of a specim en a lm ost doubled the fatigue l i f e . ' ’

According to M r. J . J . O brzut, an ed ito r of "Iron Age, " "Fatigue life is

in c reased significantly by im posing a re s id u a l com pressive s t r e s s on the

* N um bers in pa ren th esis re fe r to s im ila rly num bered re fe ren ces in R eferences a t end of paper.

1

T his sta tem en t ag rees with many e a r lie r s tatem entssu rfaces of p a r ts ." ^

m ade by o thers including M r. J .O . Almen, fo rm erly of G eneral M otors

R esearch L a b o ra to ry .(7 ’ 9’ 11 • 12’ 13, 14, 15 >

It is apparen t th e re is a t p re sen t a g re a t need fo r advancem ent of fatigue

re s is ta n t m echanical design technology. The reduction in s ize and weight of

the load carry ing m em bers of a useful design in many designs is p resen tly

lim ited by the knowledge of the fatigue re s is ta n c e of the p a r t. An under

standing of the m agnitude and effect of the re s id u a l s t r e s s s ta te , especially the

su rface , of the load carry in g m em ber appears to be a fru itfu l a re a of study.

STATEMENT OF THE PROBLEM

The problem to be studied can be s ta ted in two p a rts : (1) Develop the

m echanical techniques and com puter-o rien ted p rocedures fo r the determ ina

tion of te s t sam ple in itia l res id u a l s t r e s s conditions; (2) Using the above

techniques, analyze the change in re s id u a l s t r e s s d istribu tion of s tee l tensile

specim ens subjected to various num bers of s t r e s s cycles of a magnitude in

excess of the te s t m a te ria l endurance lim it.

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CHAPTER n

REVIEW OF THE LITERATURE

NONDESTRUCTIVE RESIDUAL STRESS DETERMINATION METHODS

X -ray D iffraction Method

The m ost common method fo r nondestructive re s id u a l s t r e s s m easurem ent

is the X -ray D iffraction Method. ^ This method involves using diffracted

x -ra y s for the m easurem ent of v e ry sm all d istances between successive

c ry s ta l lay ers in an e las tic , homogeneous, and iso trop ic m a te ria l. The

spacing between p a ra lle l c ry s ta l p lanes is a m easu re of the absolute s tre s s

norm al to the m easurem ent plane.

T his method re lie s on accu ra te m easurem ents of the angles of d iffracted

m onochrom atic x -ra y s . T herefo re i t is only successfu l n ea r the su rface

of the p a rt. In o rd e r to determ ine re s id u a l s t r e s s values a t locations

beneath the su rface of the p a rt, successive lay e rs m ust be rem oved in a

m anner such tha t changes in the shape of the p a r t due to re lie f of in te rn a l

s tra in s a re taken into account. The m a te ria l rem oval p ro cess a lso m ust

not induce re s id u a l s tre s s e s . The X -ray D iffraction Method becom es a

destructive method, when it is used to analyze in te rna l s tre s s e s .

T h ere a re many re fe ren ces available to the re a d e r concerning the X -ray

D iffraction Method, a few of which a re item ized. 3’ 5’ 8’ 18 Much work

is p ro g ressin g on the developm ent and perfecting of th is method for fu tu re

(16)use.

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U ltrasonicM ethod

Another nondestructive method fo r the m easurem ent of re s id u a l s t r e s s le ss(91commonly rep o rted in the lite ra tu re m akes use of u ltrason ic sound .v ’ This

method u tilizes the p rincip le tha t the sonic wave velocity in a homogeneous

iso trop ic e lastic m edium is a function of the density and rig id ity of the tra n s -

v e rs in g m a te ria l. It has been shown tha t for 6061-T6 alum inum and C 1018

s tee l th e re is a lin ea r re la tionsh ip between the unid irectional m agnitude of

absolute s tre s s and the change in sh ea r wave velocity divided by the in itia l

velocity (birefringence).

T h erefo re , by s ta rtin g a sh ea r s t r e s s wave through a specim en and m onitoring

the f i r s t derivative of propagation velocity , using a ca lib ra ted s t r e s s velocity

re la tionsh ip fo r the medium , i t is possib le to re c o n stru c t the s t r e s s pa ttern .

DESTRUCTIVE RESIDUAL STRESS METHODS

Several m ethods ex ist fo r the analysis of res id u a l s tre s s magnitudes in

m a te ria ls , if the in teg rity of the p a r t can be sac rificed . A few of th ese a re

the B rittle -L acq u e r, the Trespanning, and the D issection m ethods. 1 If

re liab le com plete inform ation is d e sired of th ese methods the D issection (191method is b e s t .v ’ This method has been used extensively a t G eneral

M otors R esearch L ab o ra to ries . ^

The D issection method involves the carefu l rem oval of thin lay ers of m ate ria l

from a specim en w here re s id u a l s t r e s s values v a ry only with depth. The lay er

rem oval is perform ed in a m anner th a t does not induce re s id u a l s tre s s e s in the

p a rt. At each step in the m a te ria l rem oval operation, the cu rva tu re is carefu lly

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m easured . It is possib le to rem ove m a te ria l f i r s t from one side and then

another providing appropria te accounting of the thickness and cu rva tu re a t

the tim e of the specim en inversion is made.

In the d issection operation, as the lay er rem oval p ro g re s se s , the cu rva tu re as

a function of the specim en th ickness is tabulated. By combining th is in form a

tion appropria te ly , given sufficient tim e, the o rig inal s t r e s s v s. distance

p a tte rn can be reconstructed . ^ ^

LIMITATION OF RESIDUAL STRESS CALCULATING METHODS

As was d iscussed above, the method th a t y ields the m ost com plete p a tte rn of

re s id u a l s tre s s inform ation is the D issection method. One of its shortcom ings

is the ex trem e calculating effort n e ce ssa ry to reduce the data. The job of

m anually going through a ll the many steps tha t a re n e ce ssa ry to re c o n stru c t

the o rig inal s t r e s s p a tte rn fo r each and every sam ple is often uneconom ical.

One of the m ain objectives of th is investigation was to develop a com puter-

orien ted calculation method and to p re p a re a d igital com puter p rog ram that

would perfo rm the tedious p a r t of the cu rv a tu re data analysis . Thus the

com puter would rece iv e the cu rv a tu re th ickness inform ation obtained during

the d issec tion operation and yield the o rig inal s t r e s s p a tte rn .

SURFACE RESIDUAL STRESS CHANGES UNDER FATIGUE LOADING

At the tim e when the investigation described h ere in was perform ed , a li te ra tu re

sea rc h rev ealed no published inform ation concerning the changes of su rface

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re s id u a l s tre s s e s subjected to fatigue loading. P r io r to the com pletion of the

w ritten descrip tion of th is investigation a re p o r t was published in Machine

D esign m agazine in which M r. W. E . L ittm an concluded th a t when a specim en

with su rface re s id u a l s tre s s e s is loaded to a point ** near the fatigue lim it, the

re s id u a l s t r e s s rem ain s p rac tica lly unchanged by fatigue loading." He also

s ta ted th a t " a t s tre s s e s above the fatigue lim it, (surface) re s id u a l s tr e s s e s

m ay re la x as an accom panim ent of the fatigue p ro cess . . . .

in p a ren th esis is added fo r c larity .)

„ (17)(Inform ation

Only the la te r c a se of " above the fatigue l im it" was investigated in th is study.

F o r th is case M r. L ittm an 's re su lts a s s ta ted ag reed with the re su lts of

th is study. (See C hapter V )

CHAPTER HI

TOOL AND EQUIPMENT DESCRIPTION

In o rd e r to g rasp the significance and im pact of a study, an understanding

of not only the investigative p rocedu res, but the m ajo r tools and equipm ent

u sed is indispensable. A descrip tion th e re fo re of the m ajo r tools and equip

m ent used is p resen ted below.

FATIGUE TESTING MACHINE

A six -specim en fatigue testing m achine was designed and bu ilt in the

M echanical Engineering D epartm ent of B righam Young U niversity , fo r the

purpose of generating data fo r th is investigation. T his m achine cycled tensile

specim ens a t the ra te of th ree-hundred cycles p e r m inute. When a fa ilu re

occu rred in a p a rtic u la r channel, a tim e r autom atically stopped, and thus the

num ber of load cycles to which the specim en had been subjected was known.

See F igure EH-1. The re fe ren ced w ork contains a com plete descrip tion of

th is m achine.

GRINDER

A model D-10 DoAll Denver G rinder w as used fo r the specim en dissection

w ork (see F igure IH-2). T his g rinder was equipped with a m agnetic chuck,

autom atic c ro s s feed, and tab le tra v e l action which m ade i t ideal fo r th is

investigation. The grinding wheel was a m edium soft lype, v itr ified bonded

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Figure m -1 Fatigue T esting M&chine

Figure in - f DeAU Model I>*10 Grinder

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No. 46 s ize g ra in , m anufactured by the N orton Company and labeled 32A46-

H8VBE. T his type of grinding wheel produces a m inim um change in re s id u a l

s t r e s s e s . (See recom m endations Appendix A).

CURVATURE GAUGE

The cu rv a tu re gauge used was designed to m easu re specim en deflection between

a p a ir of level fu lcrum s two inches ap art. By the use of an ohm m eter and a

m ic ro m ete r e lec trica lly iso la ted from the m etal gauge b ase , v e ry accu ra te

m easurem ents of specim en deflection w ere possib le , (see F igu re HI-3). F o r

the cu rv a tu re gauge used, which had a fu lcrum spacing of a 2 -in .f cu rv a tu re

is re la te d to deflection by th is form ula:

C = 2D / (1 + D2 ) (HI-1)

w here

C = cu rv a tu re

D = deflection as m easu red between the tw o-inch sep ara ted

fu lcrum s

A com plete derivation of Equation (HI-1) fo r any fu lcrum spacing is availab le

in Appendix B. Since,for the la rg e s t deflection m easured , D < 0 .1 bymax

use of Equation (IH-1) then,

Cm ax < 0 - 2 / ( 1 + 0 .0 1 ) = 0.198

th e re fo re ,

C = 2D (D3-2)

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T h eu ae o f £q. (in -2 ) Instead of Eq. {HI-1) introduces a sim plification error

of lo ss than 1 percent. The 2-tn , fulcrum spacing wan chosen for com patibil

ity and accuracy la unn with the te st specim en. Maximum accuracy in obtained

with maximum fulcrum sparing. T his width must be le e s than the length o f the

specim en te st section .T

Amero curvature calibration is obtained by using any thick, fla t, e lectrica l

conductive m aterial. However, if double curvature data is taken by reading

curvature with both sid es o f the specim en in contact with tee curvature gauge

fulcrum s, an accurate curvature calibration i s act necessary .

Figure in -3 Curvature Gauge

C urvature Sign Convention

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The side of the specim en w here m a te ria l is cu rren tly being rem oved is placed

next to the fu lcrum s of the cu rva tu re gauge. When the specim en is in this

orientation, if the cen te r of the specim en is low er than the line between the

top of the fu lcrum s, th is is defined as positive cu rv a tu re . The sign convention

is such tha t the common rep resen ta tio n of positive m om ents induces positive

cu rva tu re .

CHAPTER IV

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THE APPROACH TO THE PROBLEM

TEST SPECIMEN DESIGN, PREPARATION AND LOADING

The m ain fac to rs in the design of the te s t specim en w ere:

o A vailability of quality s tee l m ate ria l© C ost and ease of specim en m anufacture into a s ize com patible

with the fatigue m achine

o The m atch of specim en s tren g th to availab le fatigue m achine loading

o A specim en te s t section sufficiently long enough for the ex istence of a unidirectional re s id u a l s t r e s s p a tte rn

To ensu re tha t s tee l of known com position was used in the specim en fabrication ,

governm ent-surp lus a irc ra f t m a s te r- ro d bolts w ere obtained from A irw ork

C orporation, M illville, New Je rse y . T hese bolts w ere designed by P ra t t &

Whitney A irc ra ft, a D ivision of United A irc ra ft C orporation, E as t H artfo rd ,

Connecticut (P ra tt & Whitney Drawing No. 43659). The bolts w ere fab rica ted

from AMS (A ircraft M ateria ls Specification) 6322 s tee l, which is the sam e as

SAE 8740. The alloying agents in the s tee l w ere:

P r io r to using th ese bolts for specim en fab rica tion they w ere s tre s s - re lie v e d

for one-half hour a t 1200°F, then a ir cooled. A p ic tu re of th ese bolts, before

and a fte r fabrication is shown in F igu re IV -1.

CarbonNickel

Chrom ium

MolybdenumM anganese

0. 40 percen t0. 50 percen t0. 50 percen t

0. 25 percen t0.75—1.00 percen t

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Flguro rv-1 { Loft - Taat ^pooima* Hoatdoe Alter maaoetioe coater - Toat ^poaimon Hlgbt - Matter Hod Bolt

N O T E S :

1. MAKE FROM P /N 43659 MASTEROD BOLT

2. ROUND EDGES . 0 1 - . 02 R

FAIR INTO FLAT SECTIONSSECTION A-A

F igure IV-2 Fatigue T est Specimen

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The te s t specim ens w ere fab rica ted according to the drawing of F igure IV-2.

In itially the bolts w ere m illed; final dim ensions w ere obtained by light grinding.

By testing sev e ra l of the fab rica ted specim ens in tension i t was found tha t the

approxim ate yield and u ltim ate s tren g th s w ere 5500 and 8400 lbs respec tive ly .

It was d esired to subject the specim ens to cyclic loading high enough so tha t the

specim en would fa il eventually a fte r sev e ra l m illion cycles. With the fatigue

m achine se t to induce a m axim um load of ju s t under 5000 lbs, the f i r s t sp ec i- •

m en failed a fte r 2. 3 m illion cycles. This sam e approxim ate load level was

used throughout the r e s t of the investigation. Half of the specim ens had in itia l

re s id u a l com pressive s t r e s s induced into the su rface by satu ra tio n shot peening

a t approxim ately 80 psig with m edium size shot. Shot-peened and nonshot-

peened specim ens w ere then subjected to the following num bers of load cycles:

0, 1, 10, 100, and 11,100 .

THE DISSECTION METHOD

Specim ens th a t had rece iv ed the d esired num ber of load cycles w ere carefu lly

p rep a red for d issec tion grinding by use of a m illing m achine. The specim en

was f i r s t cut in half and then the cen te r te s t section of the rem ain ing half was

reduced to a width of one-eighth inch, (see F ig u res IV-1 and IV -3). I t was

d esired to have only a one-dim ensional re s id u a l s t r e s s p a tte rn in the specim en

te s t section , fo r th is re a so n opposite sides w ere trim m ed with the m illing

m achine, leaving only a one-eighth inch wide specim en te s t section.

The d issec tion m ethod fo r the re s id u a l s t r e s s determ ination involves the r e

moving of sm all sections of the specim en and reco rd in g the corresponding

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125 0875 -

DISSECTION

SECTION

t

150

y

A R E A R E M O V E D

F igure IV-3 Sectional Drawing D escrib ing D issection P rep ara tio n

F igure IV-4 L ayer Removal Beam Section

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values of curvature . In th is m anner a h is to ry of cu rva tu re v e rsu s specim en

thickness is obtained.* In th is investigation the high grad ian t of changes in

residual s tre s s with d istance through the specim en occu rred close to the surface;

th e re fo re , in itia l sections of the specim en w ere rem oved s ta rtin g w ith the cen te r.

A fter reducing the th ickness in steps down to about 30 m ils , the specim en was

turned over and v ery thin cuts w ere m ade on the outside until the th ickness of

the specim en was reduced to about 25 m ils . At a th ickness of le ss than 25 m ils

the specim en becam e too thin to w ork with on the grinding tab le . F o r a detailed

descrip tion of the grinding method see Appendix A.

RESIDUAL STRESS CALCULATION METHOD DERIVATION

One of the m ore tim e consuming and certa in ly the m ost difficult p a r t of th is

study was the detailed m athem atical derivation of the cu rva tu re to orig inal re s id

ual s t r e s s calculation method. The hand p rocedure developed by L. G. Johnson

was used as a g u id e /23)

The following sections co nsist of a derivation of the m athem atical equations

used fo r com puter solution of the o rig inal s tre s s pa ttern .

Given a long e las tic , homogeneous and iso trop ic rec tangu lar b a r with a re s id u a l

s t r e s s p a tte rn that is only a function of depth x , (See F igure IV-4). L et the

in itia l s tre s s a t x = 0 be S , and the in itia l cu rva tu re when x = 0 be C . ,o o

*When the specim en becom es thin a cu rva tu re m easurem ent co rrec tion m ust be introduced to com pensate fo r specim en weight-induced m easu red curvature .One co rrec tion m ethod that can be used consists of taking two readings of cu rv a tu re for each observed th ickness. One of these cu rva tu re readings would be with the specim en in the norm al position (cutting side next to cu rva tu re gauge fulcrum s) and the o ther with the specim en inverted . In the analysis of the cu rv a tu re data e ith e r both values of cu rva tu re o r the m ean would be used. Another method involves the use of the co rrec tio n equation derived in Appendix C.

18

Suppose the th ickness x is rem oved leaving a stock th ickness t - x , thus

m aking an in te rn a l su rface the exposed su rface . Let the new s tr e s s a t th is

su rface be . The te rm Q x is defined as the s t r e s s on the cut su rface

a fte r a cutting depth of x inches.

By definition, positive s t r e s s e s a re ten sile , positive cu rv a tu re is convex on the

side of the cut, and positive m om ents (M) induce positive cu rv a tu re . F o r s im

plification, the width of the b a r is assum ed to be unity. No generality is lo s t by

m aking th is assum ption. A possib le s t r e s s and cu rv a tu re d is tribu tion p a tte rn

is given in F igure IV-5 w ith a re su ltan t cu rv a tu re of the b a r in F ig u re IV-6.

C onsider a b a r with cu rv a tu re CQ , iden tical to tha t of F igure IV -6, except

absen t of a ll re s id u a l s t r e s s ; assum e th a t M is the ex ternally applied m om ent

th a t would e s tab lish the cu rv a tu re C a fte r a cut of depth x .X

Providing C is sm all ^ x

c - c =x oM _x_

E Ix(1)

W here I is the a re a m om ent of in e r tia (in4 ) and E = m odulas of e la s tic ity 2

(lb /in ). The change in cu rv a tu re C - C in the specim en without an ex te rn a lX o

m om ent is the cu rv a tu re due to in te rn a l m om ents equal to M induced byX

re s id u a l s tr e s s e s re liev ed in the d issec tion p ro c e ss .

F o r any cut of depth x , if a sm a lle r cut dx was made:

dM = (1 ) dx (V x>2 (2)

19

F igure IV-5 P ossib le S tress and C urvature P a tte rn

F igure IV-6 B ar C urvature A fter L ayer Removal

From Equation (1)

20

dCxdMx

E Ix

Substituting Equation (2) into Equation (3) and noting tha t

<*0 - x >3 *x 12

(3)

(4 )

we obtain

dCx 6 Q X

T ~ ■ K ( t - x ) :: ■ C * <5>X ' o '

Let us now exam ine the change in s t r e s s a t an a rb itra ry depth x = x^ as

the cut p ro g resse s from x = o to x = x 1 . T he s t r e s s a t x = x-^

w ill change because of

1. rem oval of s tre s s lay ers allowing the bar to change length, and

2. because a new cu rva tu re equilibrium is estab lished due to se lfbending of the bar.

Let dS^Q re p re se n t the change in d ire c t s tre s s a t the depth x = x^ and d S ^

re p re se n t the change in s t r e s s a t x = x^ due to bending as m ate ria l is rem oved.

In o rd e r for s tre s s equilibrium to ex ist a c ro ss the bar

( t Q - x) dS1D = Q x dx (6)

S = residual s tre s s a t x = x ^

Q x = su rface res id u a l s t r e s s a t cut depth x ^

where

F rom Equation (5)

21

q x = i E <‘ 0 - x >2 c i

T herefo re , combining Equations (6) and (7) and solving for dS1D

dSlD = 6 E ( t o " X>

(7)

( 8)

The change in s t r e s s a t x = x^ because of additional bending due to rem oval

of lay er dx can be thus rep resen ted

-dM y1dSIB

w here y^ is the d istance from x = x^ to the neu tra l axis

F rom F igure IV-6t - x

and

' i = <xi - x> - ("V - )

T h erefo re , combining Equations (4), (9), (10), and (11)

- 6 Q,dS 'x

IB dx( t Q - x ) 2

and substitu ting Equation (7) fo r Q letting t = t - x- yieldsX 1 O 1

(9)

( 10)

( 11)

( 12)

dSIB = E C ' dx’ t + x r t - x ‘[ - 2 — - x i j - ^ u v - v - J dx

but ^ 1 dSlB + ^ l D (13)

therefore, combining Equations (8) and (13)

22

d s i - e c ; ‘ i - ( ‘- V 1 ) . ^ (14)

When the cut r e a d ie s x = x^ , the to ta l change in s t r e s s

- Sx], = J dS1 dx (15)

w here Sx^ = orig inal re s id u a l s t r e s s a t x = x ^ p r io r to any specim en

d issec tion . T h ere fo re , substitu ting Eq. (14) into Eq. 15)

X1 x 1

Q x 1 - Sx1 = E t x j C* dx - E to J CT d x + - J x C ' d x (16)

butX1 X1

C dx x

dCxdx dx = C - C

Xj. O(17)

and

j x ^ d x

X1

xdG = xCX X

X1 X1 X1

- | c d = XlC - I Cj X X 1 X J 0 0 1 o

C dx x (18)

{

23

Combining Equations (16, (17), (18), and substitu ting ( t + x ^ ) fo r t

sX l - B t l (°X1 - c o) + T T - c o ) - hi \* ifa

■ \- l E *1 (%-° o ) + f i r c o(19)

Substituting Eq. (7) into Eq. (19) and changing a rb itra ry depth x 1 to x

S = E3

’ 2 x- C ' - 2t (C - C ) + [ C dx - 2 x x o ' I x x C (20)

F ro m Equation (19)

x !Q - S = | 2 t , C - C ■ f C dx + x , C ^Xj^ x 1 3 1 \ X2 o / J x 1 o (21)

Q - S ] i s the change in s t r e s s su rface x , has experienced in the X1 X1 / 1

cutting operation as x went from o to x ^ . If a t th is point an ex ternal

m om ent (M ^ ) w ere applied of such a m agnitude to r e s to re the cu rv a tu re

Ov to Cn from Equation (1) and F ig u re IV-6

M -MC_ = C„ + ^Tt— th e re fo re C - C =

x 1 ' o

X1 E I i 'O E l , ( 22 )

o r

M, = - EL. / c - C \ 1 1 [ x x oj (23)

24

The new s tre s s on the su rface x^ would be

q :x i

= Q x +x iMl t l 2 1 1

and substituting Eq. (23) into Eq. (24) y ields

Q ' = Q - - E t , / C - C \^ x 1 2 1 1 x i °j

and likew ise

<4 - « t + 5 E t i { % - c o)

(24)

(25)

(26)

With the b ar in the position of cu rva tu re CQ both the x = x ^ and the

x = t su rface have experienced the sam e change in s t r e s s since cutting

began. T herefore

Q ' - S = Q ' - S +x 1 x- ^ t t (27)

substituting Eqs.(25) and (26) into Eq. (27)

- S t - Q X.- S - E t, /c - C

1 X1 1 I X1 o j(28)

Substituting Eq. (21)

Q t - St= -E3 (% 'C°)+I

X1C dx - X.. C x 1 o (29)

F rom E q . (28)

Sxx - % - < Q t - S t > - E t l ( % - Co) (30)

but

S t = < V

25

(31)

If now the b a r is inverted and layer rem oval is begun anew from the opposite

side, Eq. (20) w ill y ield for the new cu rva tu re v e rsu s cutting distance p a tte rn ,

the s tre s s p a tte rn that existed in the specim en a fte r the f i r s t cut was finished

and p rio r to the beginning of the second.

T herefo re , to obtain the orig inal s t r e s s values of the specim en p r io r to the

f i r s t cut using the coordinates of the second: F rom Equations (30) and (31)

Sx = S2 x - < « t - S t> Co)

= S2 x - < Qt - S t > - x E ( CX l - Co ) <32>

w here

S = O riginal s t r e s s value in bar of cut 2 (coordinates of cut 2)X

S2x = S tress values obtained fo r cut 2 by repeating the sam e procedure as cut 1 with specim en inverted

(Q t - Sp = S tress change the su rface x = x . (outside surface) experienced during cut 1 calcu lated according to

Eq. (29).

x = Cutting coordinate of second c u t , o < x < t ^ (of f i r s t cut)

(CXl - Co> Total change in cu rva tu re of b a r during cut 1 as x of

f i r s t cut o < x < x ,

26

C urvature Equation

In o rd e r to use Equation (20) to de term ine S = F ( x ) , an equation of theX z

form C = F„ (x ) m ust be known. Let F„ (x ) be a general polynom ial withX o o

constant coefficients.

During the cutting operation, specific values fo r cu rv a tu re and th ickness w ere

m easu red . Let th ese be C. and T. , w here i takes on values from 1 to nl l ’

( i = 1 , n ) . n is the to ta l num ber of cu rva tu re and th ickness m easurem ents.

F rom F igure IV-5

By m aking use of Equation (33) to convert the th ickness data to cutting depth,

C = F„ ( x ) can now be w ritten in the formX O

X . = T - T. 1 o 1 (33)

Cx = A 1 + A2x + A3x2 + + A , ,x m + 1m (34)

m+ 1

E A ,* 11- 1 (35)

k = 1

w here the A 's re p re se n t constants to be determ ined from the cu rv a tu re data

and m is the o rd e r of the cu rv a tu re f it equation. F rom Eq. (35)

m+ 1dCx/d x = 2 ( k - l ) A k x k “ 2 (36)

/ cx dx = 2 ¥ Ak x ko k = 1

X m + 1and (37)

C = A o 1also

Substituting the above equations into Equation (20)

27

m +1s = V Ix 3k = 1

( k - 1 ) | 2 Ak x k " 2 - 2 T Ak x k " 1 + ^ A k x k + ( 2 T - x ) Ax ]

m+ 1

- 2k = 2

E A3 k -• ( k - 1 ) T2 x k " 2 - 2 T x k " 1 ^ 1_ k l

K x J (39)

since when k = 1 , a ll te rm s cancel. T here fo re

C x = A2 x + A3 x"5 +n - 1

+ A x + A 1 x + Am m +1m

m + 1

- Z Ak xk = 2

k - 1(40)

w ill y ield the sam e re su lt as Equation (34)

C urvature Equation M atrix

From Equation (35)m + 1

Cx - t Ak x k = l

k -1 w here m equals the

o rd e r of curve fitting equation. Let Cj and x. re p re se n t the i^1 m easured

data point, and le t n equal to ta l num ber of data points.

n / m + 1

2 2 'd = l ' k= 1

Let Z f Ak x ^ k 1 - C .J [ com pare with Eq. (35)] (41)

28

The cu rvatu re equation that is the c lo sest data fit occurs when Z is a

minimum. * T herefore

dZa A i

j ~ 1 , m + 1 [ j takes values from 1 to

(m + 1)]

F rom Equation (41)

3Z3Aj

n2 S

'm + 1

Ek = 1

k -1 Ak x i - C i) x i _1 0 j = 1 , m + 1

th ere fo re

n m + 1 n

Ei= 1 k = 1

£ A k x ^ + k - 2 - £ c ^ V 1i = 1

or

j = l , m + 1

k = l 2 m + 1

j = 1 n A l + 2 x i A 2 ...........A m + 1 I C.

2 m +1j = 2 V x . A + Y x . A y x. A S C. x. i = 1, nj ^ i 1 ^ i ^ i m + 1 ^ i i

, i v m . v m +1.j = m + 1 Z x . A ^ Z x . A . 2m2 *i Am +1 2 c i x i

m

* NOTE: In p rac tice m , the cu rvatu re equation o rd er, is se lec ted such that the b est smooth curve of the orig inal data is obtained.

w here

(43)

and

H.J

and

N = Number of experim ental points to be fitted

M = O rder of polynom ial fitting equation

C alculation P rocedu re

C alculation p ro cedu re fo r obtaining m a trix A and cu rva tu re equation:.

1. C alculate each te rm of "G" square m a trix according to Equation (43).

2. Calculate "HH column m a trix according to Equation (44).

3. Calculate "G" m a trix invert.

4. F orm m atrix "A" according to Equation (45)

5. F orm cu rva tu re equation according to Equations (35) o r (40)

The detail com puter logic and p ro g ram s which im plem ent the above a re

n ( j + k - 2 )

~ S C. x .( 3 - 1 )i = l l i

\ = G. , 1 H.* Jk j

(44)

(45)

availab le in Appendix D.

G j k \ - H j (42)

29

° jk

o r

CHAPTER V

RESULTS

F igure V -l re p re se n ts p lo ts of su rface specim en residual s tre s s as a function

of position for specim ens in itia lly nonshot-peened and shot-peened subjected

to num bers of applied load cycles varying from 0 to 11,100. (See Appendix E

for com puter output.)

DISCUSSION OF RESULTS

Nonshot-peened Unloaded Specimen

R eferring to F igure V - l , the nonshot-peened, unloaded specim en exhibited a

ten sile s tre s s lay er on the surface with low in tensity com pensating com pressive

s tre s s e s in ternal. Since th e re was only one unloaded, non-shot peened sp ec i

men analyzed, verification is not possib le . The evidence, though, suggests

that in the specim en p rep ara tio n a su rface re s id u a l tensile s tre s s w as induced

in the final grinding operation.

Nonshot-peened Loaded Specimens

All the nonshot-peened specim ens that had been loaded p r io r to d issection

exhibit a residual com pressive s t r e s s on the surface. This seem s to indicate

tha t even though the average specim en s tre s s was below the 3d eld point, the

su rface yielded in tension resu lting in com pressive su rface s tre s s a fte r rem oval

of the load. These su rface s tre s s e s do not appear to appreciably change with

loading cycles up to 11,100 cycles.

30

LOADCYCLES 0 1 10 100 11,100

20-

o - / .... / 1 . / // / / r r j

I / / V / \ / /- /

/v y /

/

V

r- 2 0 -

/

/

/

/ /

RESIDUAL 1 / 1/

STRESS- 1 /(ksi)

1 i/

i-40 - 1 i / i1

1 i / 1

1 i i 11 i 1 1

-60 - 1 i 1 11 i 1 1

- 1ii

1 i1 | j

-80 - 1I

i

i

1

-1 i

0 5 0 5 0 5 0 5 0 5DEPTH (mils)

F igu re V - l R esidual S tress v s . Depth for Shot-Peened (Dashed Line) and NonShot-Peened (Solid Line) Samples A fter Given N um bers of Load Cycles (Positive S tress is tensile)

31

Shot-peened Specimens

In the case of the shot-peened specim ens the re su lts indicate that the in itia lly

high res id u a l com pressive s tre s s e s a re re liev ed by the repe titive high ten sile

loading. The in itia lly shot-peened specim en subjected to 11,100 cycles has a

su rface s tre s s p a tte rn resem bling very much the nonshot-peened specim en

subjected to 100 cycles.

The re su lts of th is study tend to vindicate the la te r work of W. E. Liftm an as

(17)re la ted in Chapter II .

In o rd e r to com pare the accuracy of the com puter calculation method a hand

s tre s s calculation of the cu rvatu re data from the unloaded shot-peened sp ec i

men was m anipulated according to the s tep -by -step p rocedu re outlined in the

re fe ren ce by L. G. Johnson It was found tha t the resu lting re s id u a l s tre s s

p a tte rn was v irtually identical with tha t calculated using the com puter p rog ram

h ere in described.

32

CONCLUSIONS AND RECOMMENDATIONS

33

CONCLUSIONS

1. T ensile fatigue loading of the specim ens to a maximum load s tre s s below

the yield point of the m a te ria l induced local yielding a t the su rface . This

local su rface yielding induced com pressive res id u a l s tre s s e s at the s u r

face and low m agnitude ten sile s tre s s e s in te rn a l to the te s t sam ple.

2. Subjected to the fatigue loading of magnitude sufficient to produce eventual

fa ilu re , the in itia l su rface com pressive re s id u a l s tre s s e s decreased in

magnitude with cum ulative num bers of load cycles.

3. Within the conditions of th is study, (load s t r e s s below the y ield point of

the specim en m a te ria l but above the endurance l im it) ,i t appears tha t the

shot-peened specim ens would have a longer fatigue life.

4. The com puter based calculation method developed in th is work demon

s tra te d autom atic capability for obtaining orig inal residual s t r e s s vs.

depth p a tte rn s from curva tu re vs. specim en th ickness data.

RECOMMENDATIONS

34

1. U nless the te s t sam ple is to be annealed a fte r final p rep ara tio n , the final

m echanical operations should be such as to not induce re s id u a l s tre s s e s .

One m ethod to accom plish th is is to follow the sam e d issec tion grinding

techniques, (outlined in Appendix A) for the final specim en su rface

p rep ara tio n .

2. In the grinding operation c lo se r adherence to the grinding p ro ced u re of

Appendix A should be used. It is noted tha t th e re is a significant amount

of sc a tte r in som e of the data, and, what is even m ore im portan t, when

the specim en was inverted fo r grinding on the opposite side of the specim en,

the cu rv a tu re data taken on the second cut did not always f it the final c u rv

a tu re of the f i r s t cut. This d isplacem ent in cu rv a tu re was alw ays a

negative sh ift signifying tha t the grinding induced re s id u a l ten s ile s tre s s e s

in the su rface . Appendix F is a m athem atical trea tm en t of effects of

grinding induced re s id u a l su rface s t r e s s on final calcu lated s t r e s s values.

3. In o rd e r to fully verify the conclusions, it is fe lt tha t m ore data should be

taken. Some of the conclusions a re based on the re su lts of one o r two

sam ples ra th e r than a consisten t tren d of many. This th e s is , th e re fo re ,

outlines the method, develops the equipm ent, and defines a re a s for

fu tu re study.

35

a p p e n d i x

36

APPENDIX A

RESIDUAL STRESS GRINDING

by

C arm in G u rre ra , Shop Technician,

a t Request of J . O. Almen

Forw ard

In res id u a l s tre s s grinding of the O. D. and I. D. of a ring o r fla t su rfaces ,

the condition of the wheel and depth of cut w ill determ ine whether s tre s s e s

w ill be im parted onto the su rface o r not by grinding. For sa tisfac to ry re su lts ,

the wheel m ust be kept clean and sharp , (em phasis on sharp), and the depth of

cut m ust be d ra s tica lly reduced for conventional grinding p ra c tice for the la s t

few thousandths inch of stock to be rem oved.

The following describes the p rocedure of s tre s s grinding as p rac ticed by the

ME-1 D epartm ent of the R esearch L abora to ries Division of G eneral M otors

C orporation fo r re s id u a l s tre s s analysis.

P ro cedu re _ F la t Surfaces (surface grinder):

Let us say, for exam ple, tha t a . 030 inch layer has to be ground off to some

p rede term ined dimension. F ir s t , d re ss the wheel. P roceed to rem ove the

f ir s t . 020 inch in the somewhat conventional m aim er of . 001 to . 0015 inch

depth of cut, depending upon the size of the w ork specim en. At no tim e shall

the surface becom e d iscolored o r overheated to such an extent as to make it

unbearable to touch.

The rem aining . 010 inch lay e r should be rem oved as follows:

D ress wheel - rem ove . 005 inch lay er with cuts . 0003 inch deep

D ress wheel - rem ove . 003 inch lay er with cuts . 0002 inch deep

D ress wheel - rem ove . 002 inch lay er with cuts . 001 inch deep.

For rem oval of lay ers of . 010 inch thick o r le ss , p roceed as outlined.

The afo re m entioned schedule is based on experim ental work done on steel

specim ens of 50 R hardness with a su rface a re a of approxim ately 2 sq. in.

(3 /4" x 3"). A fter making five com plete p a sse s over the specim en with cuts

of . 0001 inch deep (. 0005 inch to tal th ickness of layer rem oved), the wheel

req u ired red ress in g . F or proportionally la rg e r a re a s , say 10 sq. in. (5" x 2,r)

the wheel would req u ire d ressing a fte r one com plete p a ss with a cut of . 0001

inch deep.

It m ust be borne in m ind that ex trem ely light cuts will tend to dull the wheel

sooner than heav ier cuts. T herefore , the opera to r m ust be very observing in

detecting p rem a tu re dulling of the wheel, generally seen as a bright or g laring

su rface finish.

37

38

The tab le trav e l ra te should be medium , although a fa s te r ra te is p re fe rre d

over a slow er trav e l. The slow er ra te will quicken wheel dullness

C ross feed of the w ork is generally from . 015 to . 020 inch p e r p a ss . For

specim ens . 010 to . 020 inch thick, it req u ired g re a te r caution.

Consecutive cuts (down feed of the wheel) a re m ade a fte r each full coverage

of the wheel over the w ork is made. No sparking out is n ecessa ry except for

very final cut if a sm oother finish is desired .

Grinding Wheel:

To d re ss the wheel, cuts of . 001 inch deep with a sharp diamond a re found

to be m ost sa tisfac to ry .

The diamond should be rap id ly p assed under the wheel in o rd er to produce a

free cutting wheel. A fter making the la s t p a ss with a . 001 inch depth cu t, do

not re p a ss the diamond under the wheel before c learing the wheel from the

diamond; o therw ise the diamond will only dull the sharp edges of the ab rasive

g ra ins on the face of the wheel.

The point of the diamond should be on cen ter line of the wheel and the nib tilted

in the sam e d irection as the ro tation of the wheel. The r i l t o r drag angle should

be 10 to 15 deg from the ve rtica l.

39

The wheel is of the m edium soft type, with a v itr ified bonded No. 46 size grain,

and of m edium s tru c tu re . It is m anufactured by the Norton Company, and is

labeled 32A46-H8VBE. Symbol 32A stands fo r Alundum abrasive; No. 46 grain

s ize (medium); H grade (soft); No. 8 s tru c tu re (medium spacing); V bond

(vitrified); and BE fo r type of bond.

The width of the wheel is l / 4 inch instead of the conventional 1/2 inch width of

reduce drag. The range of wheel speed is 3300 -3500 rpm . Ail w ork is

ground dry.

O. D. Grinding:

The sam e ra te of stock rem oval as outlined for su rface grinding is recom m ended,

w henever possib le to apply, depending upon the s ize of the work, rig id ity of the

work, and m achine. G eneral p rac tice is to p rac tica lly sp ark out before applying

additional in -feed of the wheel to the work.

Not much thought o r concern is given a s to w hether to g rind wet o r dry, since

the depth of the cuts a re very light.

On the two un iversal grinding m achines used for s t r e s s grinding, one employs

a l / 2 " x 12” wheel a t 1700 -1800 rpm and the o ther has a 1 /2 " x 10" wheel

running a t 2600 -2700 rpm .

Again only about 1 /4 inch width (by dressing) of the wheel is used fo r both

m achines. The grade of both wheels is p rac tica lly the sam e as fo r the su rface

g rinder, 32A46-18VBE.

I. D. Grinding:

40

Exactly the sam e recom m endations and specifications as those for O. D.

grinding, except that the wheel speeds used a re as recom m ended by the

m anufacturer.

The depth of cuts will v a ry with the s ize of work, rig id ity of the quill, and

m achines, e t c . , invariably le ss than those specified for su rface grinding.

APPENDIX B

41

DERIVATION OF CURVATURE DISPLACEMENT

EQUATION (m -I)

Symbol Definitions:

D = Deflection from 2-inch cen te rs

p = Radius of cu rva tu re

C = C urvature

r = one-half fu lcrum spacing

F rom the F igure:

r = P sin 9 and D + P cos 9 = P

2 2 sin 9 + cos 9 = 1 , th e re fo re

( * ) 2 * mSolving fo r P : P = r 2 + D2

2D

Since r = 1 and C = —

C = 2D 1 + D5

(m-i)

s

APPENDIX C

CURVATURE CORRECTION EQUATION DERIVATION

Assum ption: Weight of specim en te s t section between pivots of cu rv a tu re

gauge can be neglected.

The re s id u a l s t r e s s te s t section used in th is study was cut to one-eighth inch

p r io r to d issection. It is felt that the contribution to m easu red cu rv a tu re due

to the weight of th is thin section is v e ry sm all com pared to the weight of the

specim en ends, (see F igu res m -3 and IV-1).

Let M be the in te rn a l b a r mom ent. T herefo re M = M ,t ( M, is a x x 1 1

co n stan t) - 1< x < 1

From streng th of m a te ria ls considerations:

y =M1 t

~e T

I = _1_12 w t'

w here w = width of te s t section

42

y = f y dx + k2

= —i— x + k, E l 1

43

When x = 0 , the slope (y ) of the b a r = 0 . T herefore = 0

J ydx+ k.

M ft x2E l 2 kr

y = 0 when x = - 1 , th e re fo re k9 = -M t "2 EI

M ,t 9Combining y = (xz - l ) = 0 (x2 - l )

2EI WEt

C urvature is m easu red a t the cen ter position w here deflection is maximum ,

(x = 0 ) th e re fo re }

- 6 M,y = ------- = D

max WE t A

F rom Chapter in , Equation (III-2) C = 2D , w here C = cu rva tu re ,

th e re fo re CC = w here CC = the co rrec tion cu rvatu re value whicht z

added to the m easured cu rva tu re will com pensate for the end weight of the

te s t specim en.

For the specim ens used in th is study it was found that a value of

_ 7CC = 12. 5 x 1 0 agreed well with the mean cu rva tu re obtained by m e asu r

ing on both sides of the sam ple.

APPENDIX D

44

COMPUTER PROGRAM AND COMPUTATION LOGIC

The following is a flow ch art descrip tion of the s tep -by -step com puter

calculation logic fo r the determ ination of re s id u a l s tre s s p a tte rn s from

specim en curvatu re and th ickness data. See Table DV-1 fo r the definition

of sym bols used and Table DV-2 for the flow ch art symbol conventions.

Table D -l

45

CC

T

D

NIP

NRP

DI

NP

NRP1

C

X

NCUT

NPP

XINT

E

CURV

THICK

GENERAL SYMBOL TABLE DIRECTORY

C orrection Constant (used to c o rre c t specim en curvatu re due to weight of ends of specimen)

Thickness of specim en

D istance cen te r of specim en is deflected below the line connecting top of two-inch cen te rs on cu rvatu re m easuring instrum ents

Number of data values taken with specim en in inverted position

Number of data values taken with outside su rface of specim en which is reg u la r position

Data identification card (can contain 72 ch a rac te rs of any alphanum eric inform ation)

Total num ber of points (NP = NIP + NRP)

NRP + 1

C urvature of specim en

D istance of cut

Cut num ber (has value of e ither 1 o r 2 depending on w hether data is from f ir s t o r second cut of specim en)

Number of points to be used in cu rv a tu re equation plotting

C urvature equation calculation in te rva l

Modulus of e lastic ity

Curve fitted cu rva tu re value

Curve fitted specim en th ickness value

46

M O rder of curve fitting polynom ial

NM Number of curve fitting polynom ials to be used

H Summation location (see F o rtran P rogram )

Z An accuracy m easurem ent for the cu rva tu re equation fit of the o rig inal cu rva tu re data

DIST Cut d istance used in plotting fitted cu rva tu re vs. X .

DCTJRV d C /d X

CURVEI / c d X

DFINAL Final cu rv a tu re value fo r f i r s t cut

CFINI Final value of the in tergal of cu rva tu re for f i r s t cut

ORIGT Original th ickness of specim en p r io r to d issection

i Index in teger

j Index in tegeri

k Index in teger

Table D-2

47

FLOW CHART SYMBOL CONVENTIONS

Symbol Meaning

''50 Input Statem ent

D ata is inputted to die com puter a t s ta tem en t num ber 5.0.

A rithm etic Statem ent

The com putation d escribed m athem atically inside the rec tang le tak es p lace . Com puter p ro g ram sta tem en t num ber 100 applies to th is p a r t of the p ro g ram .

Output Statem ent

The values of the v a riab le s lis ted inside the sym bol a re p rin ted out.

Linkage Symbol

The logic a t the tw o -o r-m o re linkage sym bols a re h e re connected.

M odification Statem ent

An ite ra tio n is m ade, j taking on values from 1 to n .

< 1

* 1

Conditional Statem ent

The p ro g ram takes one of th re e ro u tes depending on value of enclosed v a ria b le .

RESIDUAL STRESS DATA ANALYSIS LOGIC

48

0

CALL ' SUBROUTINE

MATINV ,GIV, M P1, A,

1. DETERM ]

DI, G, H GIV, A, j DETERM

150

z = 0

50

52

400C FINAL = O CFINI = O

------------------ ^ - 1 , M +l^>

4 1 0 i - 1 . C FIN A L = C FIN A L + A , X N P J

C FINE * C FINI + A . X N p5 / )

CHOLD = Q TM IST = -

+ IQ H O LD - Q T ^

C FIN A L ( T N P * c f i n a l

2 F IN I) E / 3h s t

D I, C FINAL, QTMIST, CFINI

550

S. = ( ( T- DI ST ^) 2 D CURVE

/ 2 - 2 ( T - D I S T . ) CURVE. + CURVEI^ ) E /3

- DIST • E • C FINAL -

QTMIST

D I, I , DI ST . , S THICK 4i = 1 , NPP C H O L D , QHOLD,C FIN A L, QTMIST

C FINAL = O Q TM3ST = O

NM - I COUNT)

I COUNT «I COUNT+1

DATA ORDER AND USE DESCRIPTION*

53

Data Identification C ard (DI)

Specimen Cut Number (NCUT)

C orrection Coefficient (CC)

’ NRP

Thickness and Deflection D istance Data ( T , D)

NIP

Thickness and Deflection D istance Data ( T , D )

N PP INTE

ORIGT

NM

P rovision is m ade for a value of one or tw o.

If m easurem ents of deflection on both sides of the specim en a re obtained, th is coefficient can be equal to zero .

Each ca rd w ill handle 72 c h a rac te rs of num erical inform ation in the form of 12 s ix -c h a ra c te r fie lds. Specimen th ickness m ust appear before the corresponding deflection.

Thickness and deflection data for the specim en in the inverted position .

This c a rd contains th re e fie lds of inform ation. F ir s t , N PP is the num ber of re su ltan t calcu lated points to be plotted. Next, INT is the in te rva l used between each calcu lated s t r e s s and deflection value. L astly , E is the modulus of e lastic ity .

O riginal o r f i r s t value of th ickness to be u sed in plotting the re su lts .

* Com pare w ith Table D - l .

If NM is la rg e r than one, the p rogram w ill look for additional curve fitting o rd e r ca rd s a fte r th is one. The calcu lations m ade on the second cut data u se cu rv atu re data from the f i r s t cut. It is th e re fo re im portan t tha t the curve fitting o rd e r tha t is b est be p laced la s t if m ore than one M is used . T h ere is provision built into the p rog ram whereby second cut inform ation can be p ro cessed independently of f i r s t cut data.

CFI stands for CFINAL and QTM re p re se n ts Qj. - S . . It is with th is c a rd tha t prov ision for p ro cessin g 2nd cut data independently of f i r s t cut data is provided. This ca rd m ust appear a fte r the f i r s t curve fitting o rd e r (M) ca rd in each 2nd cut data se t. If m ultiple curve fitting o rd e rs a re used, the r e s t follow th is c a rd . In p ro cessin g in the s tandard m anner w here final cu rv a tu re values from the f i r s t cut a re u sed with the second, p lace ze ro s in each of th ese 15 c h a rac te r fie lds.

54

M

CFI QTM

APPENDIX D

c APPENDIX D 0002cc

COMPUTER PROGRAMS AND DATA DESCRIPTION 0 00 40006

c RESIDUAL STRESS DATA ANALYSIS 0010c 0 02 0

DIMENSION T ( 30 )» D ( 30 ) » X ( 3 0 ) , H i 10 ) , G (10 »10 ) » GIV(20 , 2 0 ) , A (20 ) , 00301 CURVE ( 50 )» DCUR VE ( 50 )» CURVE I ( 50 ) » D I S T I 5 0 ) , S<50 3 , D I ( 1 2 3 , C (303 , 00402 THICK(50 ) 0050

WRITE( 6 , 1) 00831 FORMATI 1H1 / / / / / 1 0 X 10HAPPENDIX E 17X 27HCOMPUTER CALCULATED RE 0085

1SULTS) 0086c 0090c READ DATA IDENTIFICATION CARD AND DISSECTING CUT NUMBER 0100c 0110

50 READ ( 5» 10 ) ( D I ( I ) t 1=1, 12 ) 012010 FORMAT ( 1 2A6) 0130

READ ( 5 , 14 ) NCUT, CC 014014 FORMAT ( 15 / ( E 1 5 • 0 ) ) 0150

c 0160c READ THICKNESS AND CURVATURE DISTANCE - OUTSIDE OF SPECIMEN -UP 0170c 0180

READ ( 5 , 1 1 ) NRP, ( T ( I ) , D ( I ) , I = 1 , N R P 3 019011 FORMAT ( 15 / ( 1 2 F 6 . 0 33 0200

c 0210c COMPUTE CORRECTED CURVATURE 0220c 0230

DO 100 I = 1, NRP 0240100 C( I 3 = 2 . 0 * D( I 3 + CC / T(I 3 ** 2 0250

c 0260c READ NO. OF DATA POINTS TAKEN WITH SPECIMEN INVERTED 02 70c 0280

READ ( 5 , 1 2 3 NIP 029012 FORMAT ( 15 3 0300

NP = NRP + NIP 0310

cNRP 1 = NRP + 1 0 32 0

0330c READ DATA POINTS TAKEN WITH SPECIMEN INVERTED 0 34 0

c 0350READ (5* 1 3 ) ( T i l ) , D ( I ) . I = NRP1, NP ) 0360

13 FORMAT ( 1 2 F 6 »0 ) 0370C 0380C COMPUTE CORRECTED CURVATURE 0390C 0400

DO 110 I * NRPlt NP 0410110 C(I ) = 2 . 0 * D( I ) - CC / T( I ) ** 2 0420

C 0430C COMPUTATION OF CUTTING DISTANCE AND CHANGE IN CURVATURE 0440C 0450

TEMP = c m 0455DO 120 I = 1, NP 0460X ( I ) = T( 1) - T i l ) 0470

120 C I I ) = C( I ) - TEMP 0475C 0480C PRINT OUT CALCULATED DATA 0490C 0500

WRITE ( 6 , 1 5 ) DI , NCUT, CC, ( I , T ( I ) , X ( I 5, D (I ) , C ( I ) , 1=1 05101, NP ) 0511

15 FORMAT( / / 10X 12A6, / / 10X 6HNCUT = 1 3 , 5X 4HCC = El 05201 5 . 5 / / 11X 1HI 18X 4 H T I I ) 16X 4HX (I ) 16X 4 H D ( I ) 16X 4 H C ( I ) / / ( 7X 05252 1 5 , 3X 4 F 2 0 . 8 )) 0530

C 0540C READ IN MODULUS OF ELASTICITY, NO. OF PLOTING POINTS AND INTERVAL 0550C 0560

READ ( 5, 16 ) NPP, XINT, E 057016 FORMAT( 1 5 , 2 F 1 5 . 0 ) 0580

C 0590C READ ORIGINAL SPECIMEN THICKNESS VALUE 0600C 0610

READ ( 5 , 1 3 ) ORIGT 0620C 0630C INITIALIZE CURVE FITTING EQUATION COUNTER 0640C 0650

ICOUNT = 1 0660C 0670

05

C READ NUMBER OF EQUATION ORDERS USED AND' EQUATION ORDER 0680C 0690

READ ( 5 , 1 2 ) NM 0700130 READ ( 5 , 12 1 M 0710

MP1 = M + 1 0720C 0730C COMPUTATION OF CURVE FITTING MATRIX 0740C 0750

DO 132 J = 1, MP1 0760131 H{ J ) = 0 . 0 0770

DO 132 K = 1, MP1 0780132 G ( J , K) = 0 . 0 0790

DO 137 J = 1, MP1 0800DO 137 I = 1, NP 0810I F ( J - l ) 135 , 133, 135 0812

133 H ( J ) = H ( J ) + C ( I ) 0814GO TO 1351 0816

135 H ( J ) = H ( J ) + C ( I ) * X ( I ) ** U - l ) 08201351 CONTINUE 0825

DO 137 K = 1, MP1 0830I F U + K-2) 136, 1353 , 136 0832

1353 G( J , K) = G I J , K) + 1. 0834GO TO 137 0836

136 G ( J , K) = G U , K ) + X ( I ) ** ( J + K-2 ) 0840137 CONTINUE 0850

DO 140 J = 1, MP1 0860A U I = H ( J ) 0870DO 140 K = 1, M P 1 0880

140 G I V U , K) = G ( J , K) 0890C 0900C INVERT COMPUTED MATRIX 0910C 0920

CALL MATINV ( GI V ( 1 , 1 ) »MP 1 , A (1 ) , 1 , DETERM) 0930C 0940C WRITE OUT COMPUTED FUNCTIONS 0950c - 0960

WRITE ( 6 , 1 7 ) DETERM, { K,K= 1 , MP1 ) 0970Oi-a

17 FORMAT! / / 10X 9HDETERM = , 1 P E 1 5 . 8 , / / 20X 4HH ( J > 9X 09801 6HG( J , K) / / 10X 3HK = ,23X 7 ( 1 2 , 11X )) 0990

WRITE ( 6 , 171) 0992171 FORMAT ( / ) 0994

DO 150 J = 1, MP1 1000WRITE ( 6 , 18 ) J ,H( J ) , ( G ( J , K ) , K=1 , MP1 ) 1010

18 FORM ATI 10X 3H J = I 2, 2X(8E 1 3 . 4 ) ) 1020150 CONTINUE 1030

WRITE ( 6 , 181) DI 1035181 FORMAT ( 1H 1 / / / / / 1 0 X 1 2 A 6 ) 1036

WRITE ( 6 , 19 ) ( K» K= 1, MP1 ) 104019 FORMATt / 20X 4HA(J) 9X 8 H G I V ( J , K ) / / 10X 3HK = ,23X 7 ( 1 2 , 1 1 X ) ) 1050

WRITE ( 6 , 171) 1052DO 200 J = 1, MP1 1060WRITE ( 6 , 18 ) J , A ( J ) , ( G I V ( J »K ) » K=1,MP1) 10 70

200 CONTINUE 1080C 1090C COMPUTATION OF PARAMETER Z (A MEASURE OF CURVE FITTING ERROR) 1100C 1110

Z * 0 . 0 1120DO 300 I = 1, NP 1130SUM = 0 . 0 1140DO 250 J = 1, MP1 1150I F ( J - l ) 2 4 0 , 230, 240 1152

230 SUM = SUM + A< J) 1154GO TO 250 1156

240 SUM = SUM + A( J ) * X ( I ) ** ( J - l ) 1160250 CONTINUE 1165300 Z = Z + ( SUM - C ( I ) ) ** 2 1170

C 1180C COMPUTATION OF DISTANCE AND FITTED CURVATURE FUNCTIONS 1190C 1200

DO 350 I = 1, NPP 1210CURVE( 1 ) = 0 . 0 1220DCURVE( I ) = 0 . 0 1230CURVE I ( I ) = 0 . 0 1240D I S T ( I ) = FLOAT( I ) * XINT 1250

Cnoo

THI CK( I ) = ORIGT - D I S K I ) 1260DO 350 J = 1, MP1 1270CURVE ( I ) = CURVE ( I ) + A( J ) * D I S T ( I ) ** ( J - l ) 1280DCURVE( I ) = DCURVE( I ) + F L O AT ! J - l ) * A( J ) * DI ST ( I ) ** ( J - 2 ) 1290CURVEI ( I ) = CURVEI(I ) + A( J ) * D I S T ( I ) ** J / FLOAT(J) 1300

350 CONTINUE 1310C 1320C WRITE OUT COMPUTED FUNCTIONS 1330C 1340

WRITE ( 6 , 2 0 ) NPP, M, Z, E , ORIGT, ( I , D I S T ( I ) , THI 13501 CK( I ) , D CURVE 1 I ) ♦ CURVE ( I ) , CURVEI ( I ) , 1=1 , NPP) 1360

20 FORMAT ( / 10X 6HNPP = , 1 3 , 7X 4HM = , 12 , 7X 3HZ = E 1 2 . 5 , 6X 13701 3HE = E 1 2 . 5 , 6X 13752 7H0RIGT = F 7 . 4 , / / 11X 1HI 5X 7 H D IS T ( I ) 1 0 X 8 H T H I C M I ) 9X 9HDCURVE 13803 8X 8HCURVE( I ) 9X 9HCURVE1 ( 1 ) / / ( 9X 1 3 , F 1 5 . 8 , 4 F 1 7 . 8 ) ) 1400

I F ( NCUT - 1 ) 9 9 8 , 4 0 0 , 4 5 0 1410998 WRITE ( 6 , 2 1 ) 1420

21 FORMAT! 10X 43H CAL LED EXIT AT 998 DUE TO ERROR CONDITION ) 1430CALL EXIT 1440

C 1450C CALCULATION OF MEAN STRESS FOR 2ND CUT STRESS COMPUTATION 1460C 1470

400 CFINAL = 0 . 0 1480CFINI = 0 . 0 1482DO 410 J = 1, MP1 1484CFINAL = CFINAL + A( J ) * X( NP) ** ( J - l ) 1486

410 CFINI = CFINI + A( J ) * X(NP) ** J / FLOAT(J ) 1488CHOLD = CFINAL 1490QTMIST = - ( T(NP) * CFINAL + CFINI ) * E / 3 . 0 1500QHOLD = QTMIST 1510WRITE ( 6 , 211) DI 1512

211 FORMAT ( 1H 1 / / / / / / / 10X 12A6) 1513WRITE ( 6 , 2 2 ) CFINAL, QTMIST, CFINI 1520

22 FORMAT ( / 10X 8HCFINAL =, E 14 .5 , 10X 8HQTM1ST =, E 1 4 . 5 , 10X 15301 7HCFINI =, E 1 4 . 5 ) 1540

CFINAL = 0 . 0 1550QTMIST = 0 . 0 1560

GO TO 5 0 0 15 704 5 0 W R I T E ( 6 , 2 1 1 ) D I 15 72

I F ( I C OU NT - 1 ) 9 9 7 , 4 5 2 , 4 5 4 1 5 8 09 9 7 W R I T E ( 6 , 9 7 ) 1 5 9 0

9 7 F O R M A T ( 10X 3 1HCAL L ED E X I T AT 9 9 7 DUE TO E R RO R ) 1 6 0 0CALL E X I T 1 6 1 0

4 5 2 READ ( 5 , 4 5 3 ) C F I N A L , Q T M I S T 1 6 2 04 5 3 F O R M A T ( 2 E 1 5 . 0 ) 1 6 3 04 5 4 I F ( C F I N A L ) 5 0 0 , 4 6 0 , 5 0 0 1 6 4 04 6 0 C F I N AL = CHOLD 1 6 5 0

Q T M I S T = QHOLD 1 6 6 0C 16 70C O R I G I N A L S T R E S S V S . D I S T A N C E BELOW S P E C I M E N S U R F A C E C O M P U T A T I O N 1 6 8 0C 1 6 9 0

5 0 0 DO 5 5 0 I = 1, NP P 1 7 0 05 5 0 S ( I ) = ( ( T ( l ) - D I S T ( I ) ) * * 2 * D CURVE (I ) / 2 . 0 - 2 . 0 * (T (1 )-' D I S 1 7 1 0

1 T ( I )) * C U R V E ( I ) + CURVE I ( I ) ) * E / 3 . 0 - D I S T U ) * E * C F I N A L - Q T M I S 1 7 2 02T 1 7 3 0

C 1 7 4 0C W R I T E O U T C OMPUTED F U N C T I O N S 1 7 5 0C 1 7 6 0

W R I T E ( 6 , 2 3 ) C HO LD , Q H O L D , C F I N A L , Q T M I S T , ( I , D I S T U ), 1 7 701 THI CK( I ) , S( I ) , 1 = 1 , N P P ) 1 7 8 0

2 3 F ORMAT ( / 10X 8 H C H 0 L D = E 1 4 . 5 , 10X 8 H Q H 0 L D = E 1 4 . 5 , / / 1 0X 1 7 9 01 8 H C F I N A L = E 1 4 . 5 , 10X 8 H Q T M I S T = E 1 4 . 5 , / / 11X 1H I 9X 1 8 0 02 7 H D I S T U ) 14X 8 H T H I C K U ) 17X 4 H S ( I ) / (9X 1 3 , F 1 9 . 8 , F 2 1 . 8 , 1 8 1 03 F 2 5 . 8 ) ) 1 8 1 1W R I T E ( 6 , 2 3 1 ) 1 8 1 4

2 3 1 F ORMAT ( 1 H 1 / / / / / ) 1 8 1 6I F ( NM - I C OUNT ) 5 6 0 , 5 0 , 6 0 0 1 8 2 0

5 6 0 W R I T E ( 6 , 2 4 ) NM , I C O U N T 1 8 3 024 F ORMAT ( 10X 4HNM = , 1 5 , 8 H I C OU NT = , 1 5 , 5X 2 1 H E R R0 R C O N D I T I O N AT 1 8 4 0

1 5 5 0 , ) 1 8 5 0CALL EX I T 1 8 6 0

6 0 0 I C O U N T = I C O U N T + 1 1 8 7 0GO TO 1 30 1 8 8 0END 1 8 9 0

c*o

C MATRIX INVERSION WITH ACCOMPANYING SOLUTION OF LINEAR EQUATIONS MAOOIOC ~ MA0020

SUBROUTINE M ATI NV t A, N, B, M,DETERM ) ________________________• MAOQ3QC MA0040

DIMENSION, _IPIVOT( 20), A(20, 20), B (20,1 ), INDEX{20,2), PIV0T(20)_ ____MA0050C DIMENSION IPI VOT(20 ) » A(20, 20), B ( 20 , I ) , INDEX (20 ,2 ) , PIVOT (20) MA0060

EQUIVALENCE (IROWtJROW), ( I COLUM » JCOLUM ) * (AMAX , T, SWAP).________ MA0070C MA0080C INITIALIZATION MA0090C '...... ~ ....... .................. '. " ' MAO 100

10 DE TERM= 1.0 _ _ _ _ - MA011015 DO 20 J=1,N MAO 12020 IP I VO T ( J ) = 0 _ _ _ _ _ _ _ ____ MAO 13030 DO 550 1= 1,N MAO 140

C _ _ _____________________________ ______________________________ MAO 150C SEARCH FOR PIVOT ELEMENT MA0160C ________ _________________________________________________________________ __________ MAO 170

40 AMAX=0.0 MAO 18045 DO 105 J= 1»N MAO 19050 IF (IPI VO T( J ) - l ) 60» 105, 60 MA0200

____60 D0_100 K= 1, N ___ MA021070 IF ( IP IVOT(K)- i) 80, 100, 740 MA0220

___ _80 1F ( ABS( AMAX ) ~ABSJ A( J , K) ) ) 85 , 100, 100 __________________________________________MA023085 I ROW = J MA024090 1 COLUM= K_ _ _ _ _ _ _ __ ________ _ _ ____ _ MA025095 AM AX = A ( J,K) MA0260

100 CONTINUE_________________________________________________________ ;______________________________MA02 70105 CONTINUE MA0280110 I PI VO T ( I COLUM ) = I PI VOT( I COLUM.) + 1_____________________________________________________ MA0290

C MA0300C INTERCHANGE ROWS TO PUT PIVOT ELEMENT ON DIAGONAL___________________________ MA0310C " MAO320

130 IF ! IROW-I COLUM )_ 140, 260, 140 __MA0330140 DE TERM= -DETERM ...... ......... - “ ' MA0340150 DO 200 L= 1, N _ _ _ _____ _ _ _ _ _ _ _ _ _ _ _ _ _ MA0350160 SW AP = A( I ROW, L ) MA03/ >170 A( IROW,L) = A(ICOLUM,L) MA03 70

05h-4

200 A( ICOLUM, L ) = SWAP _______ __ __ _ MA0380205 I F (M) 260» 260, 210 MA0390

___210 DO 250 L= 1,__M___________________________________ .MA0400220 SW AP= B ( I ROW » L ) MA0410230 B( IROW, L ) = B( I COLUM* L ) ____________________________ MA0420250 B( ICOLUM,L) = SWAP MA0430260 INDEX ( I , 1) = I ROW _ _ _ _ MA0440270 INDEX( I , 2 )= ICOLUM MA0450310 PIVOT! I ) = A( ICOLUM, I COLUM )_ _ _ _ _______ _____ _____________ MA0460320 DE T£RM= DETERM*PIVOT! I ) MA0470

C MA0480C DIVIDE PIVOT ROW BY PIVOT ELEMENT MA0490C MA0500

330 A! ICOLUM, I COLUM) = 1.0 MA0510340 DO 350 L=1»N ■ _ ________ MA0520

'350 A( ICOLUM, L) = A! I COLUM, L) /PIVOT! I) ....~ " ' MA0530355 I F (M ) 380, 380, 360 _ _ _ _ _ MA0540360 DO 370 L= 1, M MA0550370 Bt ICOLUM, L) = B( I COLUM, L)/PIVOT! I ) MA0560

C .. .. ...MAO5 70C REDUCE NON-PIVOT ROWS______________ MA0580C ‘ " " " ” MAO590

380 DO 550 L 1= 1, N __ __ __ MA0600390 I F (L1-1COLUM) 400, 550, 400 MA0610400 T=A(L1, ICOLUM) _ __ _ MA0620

' 420 A! L 1, I CO LUM ) = 0.0 MAO6304 30 DO 450 L = 1, N ________________________________ ‘_______________________________MAO640450 A!LI, L ) = A(L1, L )-A!ICOLUM, L )* T MA0650455 IF (H) 550, 550, 460 __ _ MA0660460 DO 500 L=1, M MAO670500 B!L1,L) = B(L1,L)-B!IC0LUM,L)*T _ _ _ _ _ _ __ __ MA0630550 CONTINUE MA0690

C _ ___________ __ ________ _____________________ MAO 700C ' INTERCHANGE COLUMNS “ ' ' ' “ MAO710C MAO 720

600 DO 710 1 = 1, N '..... ..MAO 7306 10 L = N+1-I __________________________________ MAO 740

<jiN)

620 IF ( INDEX ( L, 1 ) -INDEX! L, 2) ) 630 , 7 1 0 , 6 30 MA07506 30" JR0W = INDEX ( L, 1) " " MAO 76064-0 JCOLUM=INDEX( L, 2) MA0770650 DO 705 K= 1 , N ... “ " ' MAO780660 SWAP=A( K, JROW) MA0790670 At K» JRO W ) = A( K, JCOLUM) " ' ~ ““ " " ' MAO300700 A( K, JCO LUM ) = SWAP MA081070S' CONTINUE" “ " " ” MA08207 10 CONTINUE MA0830740 RETURN “ " ' ' ' ‘ ' * MAO840750 END MA0850

05co

APPENDIX E

SAMPLE COMPUTER CALCULATED RESULTS

64

APPENDIX E COMPUTER CALCULATED RESULTS

SPECIMEN NO. OUSP, CUT I

NCUT = I CC = 0 . 1 2 500E- 05

i T i n " xm d ( i ) c mI 0 . 1 4 6 0 0 0 0 0 0 . 0 . 0 0 0 7 0 0 0 0 0 .

_2________________ 0 . 1 3 2 0 0 0 0 0 _____________ 0 . 0 1 4 0 0 0 0 0 ______________ 0 . 0 0 1 7 0 0 0 0 ________ 0 . 0 0 2 0 1 3 0 93 0 . 1 2 4 5 9 9 9 9 0 . 0 2 1 4 0 0 0 0 0 . 0 0 1 7 0 0 0 0 0 . 0 0 2 0 2 1 8 74 0 . 1 1 5 6 0 0 0 0 ___ 0 . 0 3 0 4 0 0 0 0 ________ 0 . 0 0 2 0 0 0 0 0 0 . 0 0 2 6 3 4 9 05 0 . 1 0 5 4 0 0 0 0 ~ ~ 0 . 0 4 0 5 9 9 9 9 ' 0 . 0 0 3 1 9 9 9 9 0 . 0 0 5 0 5 3 8 86 0 . 0 9 5 0 0 0 0 0 0 . 0 5 1 0 0 0 0 0 ________ 0 . 0 0 3 3 0 0 0 0 0 . 0 0 5 2 7 9 8 67 0 . 0 8 4 7 0 0 0 0 0 . 0 6 1 2 9 9 9 9 0 . 0 0 4 4 9 9 9 9 0 . 0 0 7 7 1 5 5 98 0 . 0 7 5 2 0 0 0 0 0 . 0 7 0 8 0 0 0 0 0 . 0 0 5 7 9 9 9 9 0 . 0 1 0 3 6 2 3 9y 0 . 0 6 6 3 0 0 0 0 ' ~ 0 . 0 7 9 7 0 0 0 0 0 . 0 0 5 2 9 9 9 9 ' ' 0 . 0 0 9 4 2 5 7 2

10 0 . 0 5 5 4 0 0 0 0 0 . 0 9 0 6 0 0 0 0 0 . 0 0 7 7 0 0 0 0 0 . 0 1 4 3 4 8 6 311 0 . 0 4 3 0 0 0 0 0 0 . 1 0 3 0 0 0 0 0 0 . 0 0 6 8 0 0 0 0 0 . 0 1 2 8 1 7 4 012 0 . 0 3 7 8 0 0 0 0 0 . 1 0 8 2 0 0 0 0 0 . 0 0 6 6 9 9 9 9 0 . 0 1 2 8 1 6 1 913 0 . 0 3 0 8 0 0 0 0 0 . 1 1 5 2 0 0 0 0 0 . 0 0 5 7 0 0 0 0 0 . 0 1 1 2 5 9 0 3

DETERM = . 8 . 5 962 0 2 1 4 E - 25

H( J ) ____________ G ( J , K)

K =________________ ___________ __1 ________________ 2 3 _________________ 4____________ _____ 5

J = 1 0 . 9 5 7 5 E - 0 1 0 . 1 3 0 0 E 02 0 . 7 8 6 2 E 00 0 . 6 4 7 5 E - 0 1 0 . 5 9 6 4 E - 0 2 0 . 5 8 3 3 E - 0 3J = 2 0 . 7 8 8 8 E - 0 2 0 . 7 8 6 2 E 00 0 . 6 4 7 5 E - 0 1 0 . 5 9 6 4 E - 0 2 0 . 5 8 3 3 E - 0 3 0 . 5 9 1 6 E - 0 4J = 3 0 . 7 1 9 8 E - 0 3 0 . 6 4 7 5 E - 0 1 0 . 5 9 6 4 E - 0 2 0 . 5 8 3 3 E - 0 3 0 . 5 9 1 6 E - 0 4 0 . 6 1 4 7 E - 0 5J = 4 0 . 6 9 4 9 E — 0 4 0 . 5 9 6 4 E- 0 2 0 . 5 8 3 3 E - 0 3 0 . 5 9 1 6 E - 0 4 0 . 6 1 4 7 E - 0 5 0 . 6 4 9 7 E - 0 6J =_5 _ 0 . 6 9 5 1 E - 0 5 0 . 5 8 3 3 E - 0 3 0 . 5 9 1 6 E - 0 4 0 . 6 1 4 7 E - 0 5 __ 0 . 6 4 9 7 E - 0 6 ____0 . 6 9 5 2 E - 0 7

GiCl

SPECIMEN NO. OUSP, CUT 1

A{J ) GI V( J , K)

K = 1 2 3 4 5

J = 1 0 . 4 2 1 3 E- 04 Q.9445E 00 - 0 . 8 3 1 2 E 02 0 . 2 2 7 5 E 04 - 0 . 2 4 4 2 E 05 0 .8 98 6 E 05J = 2 0 . 1 6 0 7E - 0 0 - 0 . 8 3 1 2 E 02 0 . 1 4 2 6 E 05 - 0 . 5 1 1 0 E 06 0 .6 3 77 E 07 - 0 . 2 5 8 4 E 08J = 3 - 0 . 4 2 8 3 E 01 0 . 2 2 7 5 E 04 - 0 . 5 1 1 0 E 06 0 . 2 0 3 3 E 08 - 0 . 2 6 9 3 E 09 0 . U 3 4 E 10J = 4 0 . 9 1 4 8 E 02 - 0 . 2 4 4 2 E 05 0 . 6 3 7 7 E 07 - 0 . 2 6 9 3 E 09 0 . 3 6 9 5 E 10 - 0 . 1 5 9 5 E 11J = 5 - 0 . 5 1 3 2 E 03 0 . 8 9 8 6 E 05 - 0 . 2 5 8 4 E 08 0 . 1 1 3 4 E 10 - 0 . 1 5 9 5 E 11 0 . 7 0 0 IE 11

NPP = 24 M = 4 Z = 0 . 7 7 5 3 4 E - 0 5 E = 0 . 29500E 08 ORIGT = 0 . 1 4 6 0

I D I S K I ) THI CK! I ) DCURVE CURVE( I ) CURVE I ( I )

1 0 . 0 0 5 0 0 0 0 0 0 . 1 4 1 0 0 0 0 0 0 . 1 2 4 4 3 3 3 1 0 . 0 0 0 7 4 9 4 5 0 . 0 0 0 0 0 2 0 52 0 . 0 1 0 0 0 0 0 0 0 . 1 3 5 9 9 9 9 9 0 . 1 0 0 3 9 2 7 8 0 . 0 0 1 3 0 6 7 6 0 . 0 0 0 0 0 7 2 43 0 . 0 1 4 9 9 9 9 9 0 . 1 3 1 0 0 0 0 0 0 . 0 8 6 9 9 4 5 4 0 . 0 0 1 7 7 1 1 1 0 . 0 0 0 0 1 4 9 64 0 . 0 2 0 0 0 0 0 0 0 . 1 2 5 9 9 9 9 9 0 . 0 8 2 6 9 8 8 3 0 . 0 0 2 1 9 1 8 8 0 . 0 0 0 0 2 4 8 85 0 . 0 2 5 0 0 0 0 0 0 . 1 2 1 0 0 0 0 0 0 . 0 8 5 9 6 5 9 6 0 . 0 0 2 6 1 0 7 1 0 . 0 0 0 0 3 6 8 86 0 . 0 2 9 9 9 9 9 9 0 . 1 1 6 0 0 0 0 0 0 . 0 9 5 2 5 6 1 9 0 . 0 0 3 0 6 1 5 7 0 . 0 0 0 0 5 1 0 47 0 . 0 3 5 0 0 0 0 0 0 . 11099999 0 . 1 0 9 0 2 9 8 0 0 . 0 0 3 5 7 0 7 4 0 . 0 0 0 0 6 7 5 98 0 . 0 4 0 0 0 0 0 0 0 . 1 0 6 0 0 0 0 0 0 . 1 2 5 7 4 7 0 6 0 . 0 0 4 1 5 6 7 8 0 . 0 0 0 0 8 6 8 79 0 . 0 4 4 9 9 9 9 9 0 . 1 0 1 0 0 0 0 0 0 . 1 4 3 8 6 8 2 5 0 . 0 0 4 8 3 0 5 5 0 . 0 0 0 1 0 9 3 1

10 0 . 0 5 0 0 0 0 0 0 0 . 0 9 5 9 9 9 9 9 0 . 1 6 1 8 5 3 6 5 0 . 0 0 5 5 9 5 2 4 0 . 0 0 0 1 3 5 3 311 0 . 0 5 4 9 9 9 9 9 0 . 0 9 1 0 0 0 0 0 ' 0 . 1 7 8 1 6 3 5 1 0 . 0 0 6 4 4 6 2 9 0 . 0 0 0 1 6 5 4 012 0 . 0 5 9 9 9 9 9 9 0 . 0 8 6 0 0 0 0 0 0 . 1 9 1 2 5 8 1 4 0 . 0 0 7 3 7 1 5 1 0 . 0 0 0 1 9 9 9 213 0 . 0 6 5 0 0 0 0 0 0 . 0 8 1 0 0 0 0 0 0 . 1 9 9 5 9 7 7 9 0 . 0 0 8 3 5 0 9 5 0 . 0 0 0 2 3 9 2 114 0 . 0 6 9 9 9 9 9 9 0 . 0 7 6 0 0 0 0 0 0 . 2 0 1 6 4 2 7 4 0 . 0 0 9 3 5 7 0 0 0 . 0 0 0 2 8 3 4 715 0 . 0 7 5 0 0 0 0 0 0 . 0 7 0 9 9 9 9 9 0 . 1 9 5 8 5 3 2 6 0 . 0 1 0 3 5 4 3 3 0 . 0 0 0 3 3 2 7 716 0 . 0 8 0 0 0 0 0 0 0 . 0 6 6 0 0 0 0 0 0 . 1 8 0 6 8 9 6 6 0 . 0 1 1 2 9 9 9 1 0 . 0 0 0 3 8 6 9 317 0 . 0 8 4 9 9 9 9 9 0 . 0 6 1 0 0 0 0 0 0 . 1 5 4 6 1 2 1 8 0 . 0 1 2 1 4 3 0 3 0 . 0 0 0 4 4 5 6 018 0 . 0 9 0 0 0 0 0 0 0 . 0 5 5 9 9 9 9 9 0 . 1 1608110 0 . 0 1 2 8 2 5 2 7 0 . 0 0 0 5 0 8 0 919 0 . 0 9 5 0 0 0 0 0 0 . 0 5 1000G0 0 . 0 6 3 5 5 6 6 7 0 . 0 1 3 2 8 0 5 2 0 . 0 0 0 5 7 3 4 720 0 . 0 9 9 9 9 9 9 9 0 . 0 4 6 0 0 0 0 0 - 0 . 0 0 4 5 0 0 7 5 0 . 0 1 3 4 3 4 9 5 0 . 0 0 0 6 4 0 4 021 0 . 1 0 5 0 0 0 0 0 0 . 0 4 1 0 0 0 0 0 - 0 . 0 8 9 6 3 0 9 6 0 . 0 1 3 2 0 7 0 6 0 . 0 0 0 7 0 7 1 822 0 . 1 0 9 9 9 9 9 9 0 . 0 3 6 0 0 0 0 0 - 0 . 1 9 3 3 7 3 7 1 0 . 0 1 2 5 0 7 6 2 0 . 0 0 0 7 7 1 6 923 0 . 1 1 4 9 9 9 9 9 0 . 0 3 1 0 0 0 0 0 - 0 . 3 1 7 2 6 8 6 7 0 . 0 1 1 2 3 9 7 3 0 . 0 0 0 8 3 1 3 124 0 . 1 2 0 0 0 0 0 0 0 . 0 2 6 0 0 0 0 0 - 0 . 4 6 2 8 5 5 5 5 0 . 0 0 9 2 9 8 7 8 0 . 0 0 0 8 8 2 9 6

G>Ci

11581E 05 CF INI 0 . 83356E- 03

. 1158 IE 05

S ( I )1 0 1 0 5 . 1 0 7 1 7 7 73

5 7 0 5 . 6 7 2 6 0 7 4 22 9 2 4 . 3 4 7 5 9 5 2 11 2 6 8 . 4 3 7 9 2 7 2 5

3 3 8 . 3 1 9 4 6 9 4 5- 1 8 0 . 5 1 4 5 3 5 9 0— 5 2 5 . 3 9 8 6 3 5 8 6- 8 6 4 . 4 4 6 8 9 9 4 1

- 1 3 0 4 . 4 9 3 0 9 2 6 5 - 1 8 9 9 . 0 6 9 0 6 1 2 8 - 2 6 5 6 . 3 0 1 6 0 5 2 2 - 3 5 4 6 . 9 0 8 0 8 1 0 5 - 4 5 1 2 . 1 2 5 4 8 8 2 8 - 5 4 7 1 . 6 6 2 1 7 0 4 1 - 6 3 3 1 . 6 4 6 1 1 8 1 6 - 6 9 9 2 . 5 7 1 5 3 3 2 0 —7 3 5 7 . 2 5 3 7 8 4 1 8 - 7 3 3 8 . 7 7 3 8 0 3 7 1 - 6 8 6 8 . 4 2 803955 - 5 9 0 3 . 6 7 3 5 8 3 9 8 - 4 4 3 6 . 0 8 5 0 8 3 0 1 - 2 4 9 9 . 2 9 9 1 9 4 3 4

1 7 6 . 9 5 8 2 7 4 8 42 3 8 9 . 3 3 2 6 4 1 6 0

Ci-q

SPECIMEN NO. OUSP, CUT I

CFINAL = 0 . 1 1 1 7 6 E - 0 1

C HOLD =____ 0 . I l l 7 6 E - 0 1 ____

CFINAL = 0.

QTMIST = - 0 .

QHOLO__=__ - 0 .

QTMIST = 0 .

I1

_ 2345 6_78 . 9

10 1 1

J. 2_13141516 17 18_1920 21 2 22324

D I S T ( I )_______0 . 0 0 5 0 0 0 0 0 0 . 0 1 0 0 0 0 0 0 0 . 0 1 4 9 9 9 9 9 0.02000000 0 . 0 2 5 0 0 0 0 0

__0.0 2 9 9 9 9 9 9 0 . 0 3 5 0 0 0 0 0 0 . 0 4 0 0 0 0 0 0 0 . 0 4 4 9 9 9 9 9 0 . 0 5 0 0 0 0 0 0 0 . 0 5 4 9 9 9 9 9 0 . 0 5 9 9 9 9 9 9 _ 0 . 0 6 5 0 0 0 0 0 0 . 0 6 9 9 9 9 9 9 0 . 0 7 5 0 0 0 0 0 0 . 0 8 0 0 0 0 0 0 0 . 0 8 4 9 9 9 9 9 0 . 0 9 0 0 0 0 0 0 0 . 0 9 5 0 0 0 0 0 0 . 0 9 9 9 9 9 9 9 0 . 1 0 5 0 0 0 0 0 0 . 1 0 9 9 9 9 9 9 0 . 1 1 4 9 9 9 9 9 0 . 1 2 0 0 0 0 0 0

THI CK( I ) 0 . 1 6 1 0 0 000

^ .1 3 5 9 ^ 9 9 9 0 . 1 3 1 0 0 0 0 0 0 . 1 2 5 9 9 9 9 9 0 . 12100000 0 . 1 1600000 0 . 1 1099999 0 . 10600000 0 . 1 0 1 0 0 0 0 0 0 . 0 9 5 9 9 9 9 9 0 . 0 9 1 0 0 0 0 0 0 . 0 8 6 0 0 0 0 0 0 . 0 8 1 0 0 0 0 0 0 . 0 7 6 0 0 0 0 0 0 . 0 7 0 9 9 9 9 9 0 . 0 6 6 0 0 0 0 0 0 . 0 6 1 0 0 0 0 0 0 . 0 5 5 9 9 9 9 9 0 . 0 5 1 0 0 0 0 0 0 . 0 4 6 0 0 0 0 0 0 . 0 4 1 0 0 0 0 0 0 . 0 3 6 0 0 0 0 0 0 . 0 3 1 0 0 0 0 0 0 . 0 2 6 0 0 0 0 0

DETERM = 5 . 4 4 6 5 0 6 86 E - 3 1

H( J ) _G( J » K)

K = 1 2

JJJJ

= 1= 2 = 3

0 . 4 2 3 6 E - 0 1 0 . 1564E- 03 0 . 56 4 2 E- 06 0 . 2 1 1 2 E- 0 8

0 . 1 2 0 0 E 02 0 . 2 8 2 0 E - 0 1 0 . 9 6 7 8 E - 0 4 6 . 3 6 0 2 E - 0 6

0 . 2 8 2 0 E - 0 1 O'."'9 67 8 E - 04 0 . 3 602 E —06 0 . 1 3 9 7 E- 0 84

D ( I ) C( I )

- 0 . 0 1 2 2 0 0 0 0- 0 . 0 1 3 4 0 0 0 0- 0 . 0 0 9 7 9 9 9 9- 0 . 0 0 8 2 0 0 0 0- 0 . 0 1 0 8 0 0 0 0- 0 . 0 0 8 8 0 0 0 0- 0 . 0 1 1 3 0 0 0 0- 0 . 0 1 1 8 0 0 0 0- 0 . 0 0 7 5 9 9 9 9- 0 . 0 0 7 2 0 0 0 0- 0 . 0 0 8 3 0 0 0 0- 0 . 0 0 7 2 0 0 0 0

3 , 4

0 . 9 6 7 8 E - 0 4 0 . 3 6 0 2 E - 0 60 . 3 6 0 2 E- 0 6 0 . 1 3 9 7 E - 0 80 . 1 397E- 08 0 . 5 5 5 6 E - 110 . 5 5 5 6 E - 11 ' 0 . 2 2 4 6 E - 13

0 .0 . 0 0 2 3 2 9 3 30 . 0 0 5 0 2 8 6 10 . 0 0 8 3 4 3 6 20 . 0 0 3 2 8 5 9 70 . 0 0 7 3 3 2 0 00 . 0 0 1 0 7 2 7 30 . 0 0 2 1 4 3 4 10 . 0 0 6 0 9 8 6 50 . 0 0 6 7 8 3 6 30 . 0 0 4 4 4 1 2 90 . 0 0 6 5 9 5 2 5

NCUT = 2 CC = 0 . 1 2 5 0 0 E - 0 5

SPECIMEN NO. 0 USP, CUT 2

X( I )T ( I )I

12345678 9

101112

0 . 0 2 9 4 9 9 9 9 0 . 0 2 8 8 0 0 0 0 0 . 0 2 7 3 9 9 9 9 0 . 0 2 6 4 9 9 9 9 0 . 0 2 5 5 0 0 0 0 0 . 0 2 5 1 9 9 9 9 0 . 0 2 9 4 9 9 9 9 0 . 0 2 8 8 0 0 0 0 0 . 0 2 7 3 9 9 9 9 0 . 0 2 6 4 9 9 9 9 0 . 0 2 5 5 0 0 0 0

' 0 . 0 2 519999

0 .0 . 0 0 0 7 0 0 0 00 . 0 0 2 1 0 0 0 00 . 0 0 3 0 0 0 0 00 . 0 0 3 9 9 9 9 90 . 0 0 4 3 0 0 0 00 .0 . 0 0 0 7 0 0 0 00 . 0 0 2 1 0 0 0 00 . 0 0 3 0 0 0 0 00 . 0 0 3 9 9 9 9 90 . 0 0 4 3 0 0 0 0

2 3 4

SPECIMEN NO. 0 USP, CUT 2

______________ M J ) GI V { J » K )

K =__________ _______________________1

I - 0 . 1 2 0 2 E - 0 2 0 . 4 7 4 0 E - 0 0 - 0 . 8 2 9 5 E 03 0 . 3720E 06 - 0 . 4 8 0 0 E 082 - 0 . I 3 1 7 E 01 - 0 . 8 2 9 5 E 03 0 . 3446E 07 - 0 . 1927E 10 0 . 2756E 123 0 . 3 0 7 3 E 04 0 . 3 7 2 0 E 06 - 0 . 1927E 10 0 . 1152E 13 - 0 . 1711E 154 - 0 . 5 6 4 8 E 06 - 0 . 4 8 0 0 E 08 0 . 2 7 5 6 E 12 - 0 . 1711E 15 0 . 2 5 9 9 E 17

NPP = 18 M = 3 Z = 0 . 3 3 1 5 7 E - 0 4 E = 0 . 2 9 5 0 0 E 08 ORIGT = 0 . 0 3 0 8

I D I S T U ) THI CK( I ) DCURVE CURVE{ I ) CURVE I { I )

1 0 . 0 0 0 4 9 9 9 9 0 . 0 3 0 3 0 0 0 0 1 . 3 3 2 4 1 8 9 2 - 0 . 0 0 1 1 6 3 0 6 - 0 . 0 0 0 0 0 0 6 42 0 . 0 0 0 9 9 9 9 9 0 . 0 2 9 8 0 0 0 0 3 . 1 3 4 3 0 9 6 2 - 0 . 0 0 0 0 1 1 0 7 - 0 . 0 0 0 0 0 0 9 83 0 . 0 0 1 5 0 0 0 0 0 . 0 2 9 3 0 0 0 0 4 . 0 8 8 9 9 7 3 6 0 . 0 0 1 8 3 0 0 5 — 0 . 0 0 0 0 0 0 5 44 0 . 0 0 2 0 0 0 0 0 0 . 0 2 8 3 0 0 0 0 4 . 1 9 6 4 8 2 3 0 0 . 0 0 3 9 3 6 7 2 0 . 0 0 0 0 0 0 8 95 0 . 0 0 2 5 0 0 0 0 0 . 0 2 8 2 9 9 9 9 3 . 4 5 6 7 6 4 2 2 0 . 0 0 5 8 8 5 3 3 0 . 0 0 0 0 0 3 3 66 0 . 0 0 3 0 0 0 0 0 0 . 0 2 7 7 9 9 9 9 1 . 8 6 9 8 4 3 3 6 0 . 0 0 7 2 5 2 2 8 0 . 0 0 0 0 0 6 6 87 0 . 0 0 3 5 0 0 0 0 0 . 0 2 7 2 9 9 9 9 - 0 . 5 6 4 2 8 0 2 7 0 . 0 0 7 6 1 3 9 7 0 . 0 0 0 0 1 0 4 58 0 . 0 0 3 9 9 9 9 9 0 . 0 2 6 8 0 0 0 0 - 3 . 8 4 5 6 0 6 3 0 0 . 0 0 6 5 4 6 8 0 0 . 0 0 0 0 1 4 0 69 0 . 0 0 4 4 9 9 9 9 0 . 0 2 6 3 0 0 0 0 - 7 . 9 7 4 1 3 5 8 8 0 . 0 0 3 6 2 7 1 7 0 . 0 0 0 0 1 6 6 9

10 0 . 0 0 5 0 0 0 0 0 0 . 0 2 5 8 0 0 0 0 - 1 2 . 9 4 9 8 6 9 1 6 - 0 . 0 0 1 5 6 8 5 3 0 . 0 0 0 0 1 7 3 111 0 . 0 0 5 5 0 0 0 0 0 . 0 2 5 3 0 0 0 0 - 1 8 . 7 7 2 8 0 3 7 8 - 0 . 0 0 9 4 6 3 9 0 0 . 0 0 0 0 1 4 6 712 0 . 0 0 6 0 0 0 0 0 0 . 0 2 4 8 0 0 0 0 - 2 5 . 4 4 2 9 4 2 6 2 - 0 . 0 2 0 4 8 2 5 3 0 . 0 0 0 0 0 7 3 213 0 . 0 0 6 5 0 0 0 0 0 . 0 2 4 2 9 9 9 9 - 3 2 . 9 6 0 2 8 2 8 0 - 0 . 0 3 5 0 4 8 0 5 - 0 . 0 0 0 0 0 6 4 014 0 . 0 0 7 0 0 0 0 0 0 . 0 2 3 7 9 9 9 9 - 4 1 . 3 2 4 8 2 7 1 9 - 0 . 0 5 3 5 8 4 0 2 - 0 . 0 0 0 0 2 8 3 815 0 . 0 0 7 4 9 9 9 9 0 . 0 2 3 3 0 0 0 0 - 5 0 . 5 3 6 5 7 3 4 1 - 0 . 0 7 6 5 1 4 0 7 - 0 . 0 0 0 0 6 0 7 116 0 . 0 0 7 9 9 9 9 9 0 . 0 2 2 8 0 0 0 0 - 6 0 . 5 9 5 5 2 3 3 6 - 0 . 1 0 4 2 6 1 7 9 - 0 . 0 0 0 1 0 5 7 017 0 . 0 0 8 4 9 9 9 9 0 . 0 2 2 3 0 0 0 0 - 7 1 . 5 0 1 6 7 4 6 5 - 0 . 1 3 7 2 5 0 7 9 - 0 . 0 0 0 1 6 5 8 518 0 . 0 0 9 0 0 0 0 0 0 . 0 2 1 8 0 0 0 0 - 8 3 . 2 5 5 0 2 8 7 2 - 0 . 1 7 5 9 0 4 6 7 - 0 . 0 0 0 2 4 3 8 9

J = J = J = J =

SPECIMEN NO. 0 USP, CUT 2t

CHOLD = 0 . 1 1 1 7 6 E - 0 1 QHOLD = - 0 . 1 1 5 8 1 E 05

CFINAL = 0 . 1 1 1 7 6 E - 0 1 QTMIST = - 0 . 1 1 5 8 1 E 05

I DI S T ( I ) THI CK{ I ) S ( I )I 0 . 0 0 0 4 9 9 9 9 0 . 0 3 0 3 0 0 0 0 1 7 5 8 2 . 9 7 7 0 5 0 7 82 0 . 0 0 0 9 9 9 9 9 0 . 0 2 9 3 0 0 0 0 2 3 7 6 5 . 3 7 6 4 6 4 8 43 0 . 0 0 1 5 0 0 0 0 0 . 0 2 9 3 0 0 0 0 2 5 8 3 5 . 5 1 4 8 9 2 5 84 0 . 0 0 2 0 0 0 0 0 0 . 0 2 8 8 0 0 0 0 2 4 4 0 5 . 2 2 6 5 6 2 5 05 0 . 0 0 2 5 0 0 0 0 0 . 0 2 8 2 9 9 9 9 2 0 0 5 5 . 1 0 4 2 4 8 0 56 0 . 0 0 3 0 0 0 0 0 0 . 0 2 7 7 9 9 9 9 1 3 3 3 4 . 5 0 2 3 1 9 3 47 0 . 0 0 3 5 0 0 0 0 0 . 0 2 7 2 9 9 9 9 4 7 6 1 . 5 3 2 7 1 4 8 48 0 . 0 0 3 9 9 9 9 9 0 . 0 2 6 8 0 0 0 0 - 5 1 7 6 . 9 3 3 2 2 7 5 49 0 . 0 0 4 4 9 9 9 9 0 . 0 2 6 3 0 0 0 0 - 1 6 0 2 5 . 2 6 4 0 3 8 0 9

10 0 . 0 0 5 0 0 0 0 0 0 . 0 2 5 8 0 0 0 0 - 2 7 3 5 9 . 0 7 2 0 2 1 4 811 0 . 0 0 5 5 0 0 0 0 0 . 0 2 5 3 0 0 0 0 - 3 8 7 8 5 . 2 0 1 1 7 1 8 812 0 . 0 0 6 0 0 0 0 0 0 . 0 2 4 8 0 0 0 0 - 4 9 9 4 1 . 7 5 0 4 8 8 2 813 0 . 0 0 6 5 0 0 0 0 0 . 0 2 4 2 9 9 9 9 - 6 0 4 9 8 . 0 4 1 5 0 3 9 114 0 . 0 0 7 0 0 0 0 0 0 . 0 2 3 7 9 9 9 9 - 7 0 1 5 4 . 6 5 2 3 4 3 7 515 0 . 0 0 7 4 9 9 9 9 0 . 0 2 3 3 0 0 0 0 - 7 8 6 4 3 . 3 9 4 5 3 1 2 516 0 . 0 0 7 9 9 9 9 9 0 . 0 2 2 8 0 0 0 0 - 8 5 7 2 7 . 3 2 4 2 1 8 7 517 0 . 0 0 8 4 9 9 9 9 0 . 0 2 2 3 0 0 0 0 - 9 1 2 0 0 . 7 2 9 4 9 2 1 918 0 . 0 0 9 0 0 0 0 0 0 . 0 2 1 8 0 0 0 0 - 9 4 8 8 9 . 1 4 5 5 0 7 8 1

o

SPECIMEN1

NO. OSP, CUT 1

NCUT = 1 CC = 0 . 1 2 5 0 0 E - 0 5

I T ( I ) X ( I ) D ( I ) c mI 0 . 1 5 0 9 9 9 9 9 0 . 0 . 0 0 0 4 9 9 9 9 0 .23

0 . 1 3 4 0 0 0 0 00 . 1 3 1 0 0 0 0 0

0 . 0 1 7 0 0 0 0 00 . 0 2 0 0 0 0 0 0

-0.- 0 . 0 0 0 4 9 9 9 9

- 0 . 0 0 0 9 8 5 2 1- 0 . 0 0 1 9 8 1 9 8

45

0 . 1 2 0 0 0 0 0 0 0 . 1 0 9 0 0 0 0 0

0.031000000 . 0 4 2 0 0 0 0 0

-0.-0.

- 0 . 0 0 0 9 6 8 0 1- 0 . 0 0 0 9 4 9 6 1

67

0 . 0 9 8 0 0 0 0 00 . 0 8 6 0 0 0 0 0

0 . 0 5 3 0 0 0 0 00 . 0 6 5 0 0 0 0 0

- 0 . 0 0 0 4 9 9 9 9-0.00300000

- 0 . 0 0 1 9 2 4 6 6- 0 . 0 0 6 8 8 5 8 1

89

0 . 0 7 6 0 0 0 0 00 . 0 6 5 0 0 0 0 0

0 . 0 7 5 0 0 0 0 00 . 0 8 6 0 0 0 0 0

- 0 . 0 0 2 0 0 0 0 0- 0 . 0 0 6 0 0 0 0 0

- 0 . 0 0 4 8 3 8 4 1- 0 . 0 1 2 7 5 8 9 6

LOI I

0 . 0 5 4 0 0 0 0 00 . 0 4 4 0 0 0 0 0

0 . 0 9 7 0 0 0 0 00 . 1 0 6 9 9 9 9 9

- 0 . 0 1 0 0 0 0 0 0- 0 . 0 1 7 5 0 0 0 0

- 0 . 0 2 0 6 2 6 1 5 - 0 . 0 3 5 4 0 9 1 6

1213

0 . 0 3 5 0 0 0 0 00 . 0 2 9 9 9 9 9 9

0 . 1 1 6 0 0 0 0 0 0 . 1 2 0 9 9 9 9 9

- 0 . 0 2 1 0 0 0 0 0- 0 . 0 2 9 9 9 9 9 9

- 0 . 0 4 2 0 3 4 4 1- 0 . 0 5 9 6 6 5 9 3

1415

0 . 0 5 4 0 0 0 0 00 . 0 4 4 0 0 0 0 0

0 . 0 9 7 0 0 0 0 00 . 1 0 6 9 9 9 9 9

- 0 . 0 1 0 0 0 0 0 0- 0 . 0 1 8 0 0 0 0 0

- 0 . 0 2 1 4 8 3 4 9- 0 . 0 3 7 7 0 0 4 8

16 0 . 0 2 9 9 9 9 9 9 0 . 1 2 0 9 9 9 9 9 - 0 . 0 3 1 0 0 0 0 0 - 0 . 0 6 4 4 4 3 7 1

DETERM = 7 . 2 9 9 6 6 0 2 I E - 2 4

H ( J ) G ( J » K)

K = 1 2 3 4 5J = 1 - 0 . 3 1 2 7 E - 0 0 0 . 1 6 0 0 E 02 0 . 1 1 5 5 E 01 0 . 1 0 7 9 E - 0 0 0 . 1 0 9 8 E - 0 1 0 . 1 1 6 5 E - 0 2J = 2 J = 3

- 0 . 3 3 9 4 E - 0 1 0 . 1 1 5 5 E 01 - 0 . 3 7 7 6 E - 0 2 0 . 1 0 7 9 E - 0 0

0 . 1 0 7 9 E - 0 0 0 . 1 0 9 8 E - 0 1

0 . 1 0 9 8 E - 0 1 0 . 1 1 6 5 E - 0 2 0 . 1 1 6 5 E - 0 2 0 . 1 2 6 9 E - 0 3

0 . 1 2 6 9 E - 0 3 0 . 1 4 0 7 E - 0 4

J = 4J = 5

- 0 . 4 2 5 9 E - 0 3 0 . 1 0 9 8 E - 0 1 - 0 . 4 8 5 2 E - 0 4 0 . 1 1 6 5 E - 0 2

0 . 1 1 6 5 E - 0 2 0 . 1 2 6 9 E - 0 3

0 . 1 2 6 9 E - 0 3 0 . 1 4 0 7 E - 0 4 0 . 1 4 0 7 E - 0 4 0 . 1 5 7 9 E - 0 5

0 . 1 5 7 9 E - 0 5 0 . 1 7 9 1 E - 0 6

•qI-*

SPECIMEN NO. OSP, CUT 1

AC J )/

G I V ( J t K )

K = 1 2 3 4 5

J = 1 - 0 . 2 0 7 4 E - 0 3 0 . 9 5 8 9 E 00 - 0 . 7 8 1 6 E 02 0 . 1 9 8 0 E 0 4 - 0 . 1967E 05 0 . 6 7 1 0 E 05J = 2 - 0 . 4 2 4 1 E - 0 I - 0 . 7 8 I 6 E 02 0 . U 9 0 E 05 - 0 . 3 9 1 1 E 0 6 0 . 4 4 9 1 E 07 - 0 . 1681E 08J = 3 - 0 . 6 3 6 5 E 00 0 . 1 9 8 0 E 04 - 0 . 3 9 1 1 E 06 0 . 1427E 08 - 0 . 1738E 09 0 . 6 7 5 6 E 09J = 4 0 . 4 1 5 9 E 02 - 0 . 1967E 05 0 . 4 4 9 1 E 07 - 0 . 1738E 0 9 0 . 2 1 9 0 E 10 - 0 . 8 7 1 4 E 10J = 5 - 0 . 5 5 6 2 E 0 3 0 . 6 7 1 0 E 05 - 0 . 1 6 8 1 E 08 0 . 6 7 5 6 E 09 - 0 . 8 7 1 4 E 10 0 . 3 5 2 6 E 11

NPP - 2 4 M = 4 Z = 0 . 1 0 4 6 9 E - 0 3 E = 0 . 29500E 08 ORIGT = 0 . 1 5 1 0

I D I S T C I ) THI CK( I ) DCURVE CURVE( I ) CURVE I ( I )

1 0 . 0 0 5 0 0 0 0 0 0 . 1 4 6 0 0 0 0 0 - 0 . 0 4 5 9 3 7 8 9 - 0 . 0 0 0 4 3 0 5 6 - 0 . 0 0 0 0 0 1 5 92 0 . 0 1 0 0 0 0 0 0 0 . 1 4 1 0 0 0 0 0 - 0 . 0 4 4 8 9 2 3 1 - 0 . 0 0 0 6 5 9 2 0 - 0 . 0 0 0 0 0 4 3 13 0 . 0 1 4 9 9 9 9 9 0 . 1 3 5 9 9 9 9 9 - 0 . 0 4 0 9 4 5 9 1 - 0 . 0 0 0 8 7 4 6 5 - 0 . 0 0 0 0 0 8 1 54 0 . 0 2 0 0 0 0 0 0 0 . 1 3 1 0 0 0 0 0 - 0 . 0 3 5 7 6 7 3 2 - 0 . 0 0 1 0 6 6 6 0 - 0 . 0 0 0 0 1 3 0 25 0 . 0 2 5 0 0 0 0 0 0 . 1 2 5 9 9 9 9 9 - 0 . 0 3 1 0 2 5 1 9 - 0 . 0 0 1 2 3 3 0 6 - 0 . 0 0 0 0 1 8 7 86 0 . 0 2 9 9 9 9 9 9 0 . 1 2 0 9 9 9 9 9 - 0 . 0 2 8 3 8 8 1 6 - 0 . 0 0 1 3 3 0 3 6 - 0 . 0 0 0 0 2 5 3 27 0 . 0 3 5 0 0 0 0 0 0 . 1 1 6 0 0 0 0 0 - 0 . 0 2 9 5 2 4 8 9 - 0 . 0 0 1 5 2 3 2 3 - 0 . 0 0 0 0 3 2 5 78 0 . 0 4 0 0 0 0 0 0 0 . 1 1 0 9 9 9 9 9 - 0 . 0 3 6 1 0 4 0 2 - 0 . 0 0 1 6 8 4 6 8 - 0 . 0 0 0 0 4 0 5 89 0 . 0 4 4 9 9 9 9 9 0 . 1 0 6 0 0 0 0 0 - 0 . 0 4 9 7 9 4 1 8 - 0 . 0 0 1 8 9 6 1 2 - 0 . 0 0 0 0 4 9 5 0

10 0 . 0 5 0 0 0 0 0 0 0 . 1 0 1 0 0 0 0 0 - 0 . 0 7 2 2 6 4 0 2 - 0 . 0 0 2 1 9 7 2 6 - 0 . 0 0 0 0 5 9 6 911 0 . 0 5 4 9 9 9 9 9 0 . 0 9 5 9 9 9 9 9 - 0 . 1 0 5 1 8 2 2 1 - 0 . 0 0 2 6 3 6 1 7 - 0 . 0 0 0 0 7 1 7 012 0 . 0 5 9 9 9 9 9 9 0 . 0 9 1 0 0 0 0 0 - 0 . 1 5 0 2 1 7 3 6 - 0 . 0 0 3 2 6 9 2 8 - 0 . 0 0 0 0 8 6 3 713 0 . 0 6 5 0 0 0 0 0 0 . 0 8 6 0 0 0 0 0 - 0 . 2 0 9 0 3 8 1 2 - 0 . 0 0 4 1 6 1 3 2 - 0 . 0 0 0 1 0 4 8 314 0 . 0 6 9 9 9 9 9 9 0 . 0 8 1 0 0 0 0 0 - 0 . 2 8 3 3 1 3 1 6 - 0 . 0 0 5 3 8 5 4 1 - 0 . 0 0 0 1 2 8 5 415 0 . 0 7 5 0 0 0 0 0 0 . 0 7 6 0 0 0 0 0 - 0 . 3 7 4 7 1 1 1 1 - 0 . 0 0 7 0 2 2 9 9 - 0 . 0 0 0 1 5 9 3 716 0 . 0 8 0 0 0 0 0 0 0 . 0 7 0 9 9 9 9 9 - 0 . 4 8 4 9 0 0 6 2 - 0 . 0 0 9 1 6 3 8 4 - 0 . 0 0 0 1 9 9 6 117 0 . 0 8 4 9 9 9 9 9 0 . 0 6 6 0 0 0 0 0 - 0 . 6 1 5 5 5 0 3 2 - 0 . 0 1 1 9 0 6 0 9 - 0 . 0 0 0 2 5 2 0 118 0 . 0 9 0 0 0 0 0 0 0 . 0 6 1 0 0 0 0 0 - 0 . 7 6 8 3 2 8 8 5 - 0 . 0 1 5 3 5 6 2 3 - 0 . 0 0 0 3 1 9 8 519 0 . 0 9 5 0 0 0 0 0 0 . 0 5 5 9 9 9 9 9 - 0 . 9 4 4 9 0 4 8 9 - 0 . 0 1 9 6 2 9 0 5 - 0 . 0 0 C4 06 9420 0 . 0 9 9 9 9 9 9 9 0 . 0 5 1 0 0 0 0 0 - 1 . 1 4 6 9 4 7 0 3 - 0 . 0 2 4 8 4 7 7 2 - 0 . 0 0 0 5 1 7 7 221 0 . 1 0 5 0 0 0 0 0 0 . 0 4 6 0 0 0 0 0 - 1 . 3 7 6 1 2 3 9 9 - 0 . 0 3 1 1 4 3 7 5 - 0 . 0 0 0 6 5 7 2 222 0 . 1 0 9 9 9 9 9 9 0 . 0 4 0 9 9 9 9 9 - 1 . 6 3 4 1 0 4 3 7 - 0 . 0 3 8 6 5 6 9 6 - 0 . 0 0 0 8 3 1 1 823 0 . 1 1 4 9 9 9 9 9 0 . 0 3 6 0 0 0 0 0 - 1 . 9 2 2 5 5 6 8 2 - 0 . 0 4 7 5 3 5 5 8 - 0 . 0 0 1 0 4 6 0 624 0 . 1 2 0 0 0 0 0 0 0 . 0 3 1 0 0 0 0 0 - 2 . 2 4 3 1 4 9 9 4 - 0 . 0 5 7 9 3 6 1 0 - 0 . 0 0 1 3 0 9 0 7

to

CF INAL = - 0 »602 I3E - 0 1 QTMIST = 0 . 3 1 2 16E 05______________CFI NI =__ - 0 . 1 3681 E - 0 2

CHOLD = - 0 . 6 0 2 I 3 E —0 1______________ QHOLD = 0 . 3 1 2 1 6 E 05_________________________________

SPECIMEN NO . OSP, C UTI_________________________________________ ;___________ _____ ___________________________________

CFINAL = 0 . QTMIST = 0 .

I D I S K I ) T H I C K I I ) S I ! )1 0 . 0 0 5 0 0 0 0 0 0 . 1 4 6 0 0 0 0 0 - 3 5 9 3 . 7 6 5 9 3 0 1 82 0 . 0 1 0 0 0 0 0 0 0 . 1 4 1 0 0 0 0 0 - 2 6 0 2 . 6 0 7 0 5 5 6 63 0 . 0 1 4 9 9 9 9 9 0 . 1 3 5 9 9 9 9 9 - 1 4 6 4 . 3 6 3 8 4 5 8 34 0 . 0 2 0 0 0 0 0 0 0 . 1 3 1 0 0 0 0 0 - 3 9 7 . 9 7 5 2 2 7 3 65 0 . 0 2 5 0 0 0 0 0 0 . 1 2 5 9 9 9 9 9 4 4 9 . 1 0 9 5 8 0 9 96 0 . 0 2 9 9 9 9 9 9 0 . 1 2 0 9 9 9 9 9 9 9 2 . 3 1 6 3 9 0 9 97 0 . 0 3 5 0 0 0 0 0 0 . 1 160 0 0 0 0 1 2 0 1 . 3 3 2 4 5 8 5 08 0 . 0 4 0 0 0 0 0 0 0 . 1 1 0 9 9 9 9 9 1 0 9 1 . 4 9 1 5 4 6 6 39 0 . 0 4 4 9 9 9 9 9 0 . 1 0 6 0 0 0 0 0 7 1 5 . 1 5 8 9 4 3 1 8

10 0 . 0 5 0 0 0 0 0 0 0 . 1 0 1 0 0 0 0 0 1 5 3 . 1 1 8 6 4 0 9 011 0 . 0 5 4 9 9 9 9 9 0 . 0 9 5 9 9 9 9 9 - 4 9 4 . 0 4 3 1 7 0 9 312 0 . 0 5 9 9 9 9 9 9 0 . 0 9 1 0 0 0 0 0 - 1 1 1 4 . 5 4 9 0 8 7 5 213 0 . 0 6 5 0 0 0 0 0 0 . 0 8 6 0 0 0 0 0 - 1 5 9 4 . 0 4 9 1 4 8 5 614 0 . 0 6 9 9 9 9 9 9 0 . 0 8 1 0 0 0 0 0 - 1 8 2 4 . 2 3 2 6 3 5 5 015 0 . 0 7 5 0 0 0 0 0 0 . 0 7 6 0 0 0 0 0 - 1 7 1 1 . 4 4 2 0 4 7 1 216 0 . 0 8 0 0 0 0 0 0 0 . 0 7 0 9 9 9 9 9 - 1 1 8 5 . 2 8 7 9 1 8 0 917 0 . 0 8 4 9 9 9 9 9 0 . 0 6 6 0 0 0 0 0 - 2 0 7 . 2 6 6 1 5 5 2 418 0 . 0 9 0 0 0 0 0 0 0 . 0 6 1 0 0 0 0 0 1 2 2 0 . 6 3 1 4 8 4 9 919 0 . 0 9 5 0 0 0 0 0 0 . 0 5 5 9 9 9 9 9 3 0 4 7 . 3 0 2 6 1 2 3 020 0 . 0 9 9 9 9 9 9 9 0 . 0 5 1 0 0 0 0 0 5 1 6 3 . 9 1 9 6 7 7 7 321 0 . 1 0 5 0 0 0 0 0 0 . 0 4 6 0 0 0 0 0 7 3 9 5 . 3 1 0 6 0 7 9 122 0 . 1 0 9 9 9 9 9 9 0 . 0 4 0 9 9 9 9 9 9 4 9 1 . 3 5 1 4 4 0 4 323 0 . 1 1 4 9 9 9 9 9 0 . 0 3 6 0 0 0 0 0 111 1 8 . 3 5 1 3 1 8 3 624 0 . 1 2 0 0 0 0 0 0 0 . 0 3 1 0 0 0 0 0 1 1 8 5 0 . 4 3 1 3 9 6 4 8

co

SPECIMEN NO. OSP, CUT2

NCUT =__2_______CC =_____ 0 . I 2 5 0 0 E - 0 5 _______ ___________ __________ __________

I T ( I ) XI I ) D ( I ) C ( I J

12345678 9

101_L12'1314

0 . 0 2 9 9 9 9 9 90 . 0 2 9 4 9 9 9 90 . 0 2 8 0 0 0 0 00 . 0 2 7 0 0 0 0 00 . 0 2 5 9 9 9 9 90 . 0 2 5 0 0 0 0 00 . 0 2 2 9 9 9 9 90 . 0 2 9 9 9 9 9 90 . 0 2 9 4 9 9 9 90 . 0 2 8 0 0 0 0 00 . 0 2 7 0 0 0 0 00 . 0 2 5 9 9 9 9 90 . 0 2 5 0 0 0 0 00 . 0 2 2 9 9 9 9 9

0 .0 . 0 0 0 4 9 9 9 90 . 0 0 2 0 0 0 0 00 . 0 0 3 0 0 0 0 00 . 0 0 3 9 9 9 9 90 . 0 0 5 0 0 0 0 00 . 0 0 7 0 0 0 0 00 .0 . 0 0 0 4 9 9 9 9 0 .0 0 2 0 0 0 0 0 0 . 0 0 3 0 0 0 0 0 0 . 0 0 3 9 9 9 9 9 0 . 0 0 5 0 0 0 0 0 0 . 0 0 7 0 0 0 0 0

0 . 0 3 1 0 0 0 0 0 0 . 0 2 5 0 0 0 0 0 0 . 0 1 1 4 9 9 9 9 0 . 0 0 7 9 9 9 9 9 0 . 0 0 5 0 0 0 0 0

- 0 . 0 0 5 0 0 0 0 0 - 0 . 0 0 3 0 0 0 0 0

0 . 0 2 9 9 9 9 9 9 0 . 0 2 5 9 9 9 9 9 0 . 0 1 1 9 9 9 9 9 0 . 0 0 7 9 9 9 9 9 0 . 0 0 6 0 0 0 0 0

- 0 .- 0.00200000

0 .- 0 . 0 1 1 9 5 2 5 2- 0 . 0 3 8 7 9 4 5 0- 0 . 0 4 5 6 7 4 2 0- 0 . 0 5 1 5 3 9 7 7- 0 . 0 7 1 3 8 8 8 9- 0 . 0 6 7 0 2 5 9 4- 0 . 0 0 4 7 7 7 7 7- 0 . 0 1 2 8 2 5 2 6- 0 . 0 4 0 9 3 3 2 7- 0 . 0 4 9 1 0 3 5 7- 0 . 0 5 3 2 3 8 0 0- 0 . 0 6 5 3 8 8 8 9- 0 . 0 6 9 7 5 1 8 4

DETERM = 3 . 2 9 1 9 4 1 8 5 E - 2 8

H {J ) G ( J , K )

K =_________________________________1_______________ 2 __________ 3 _____ 4 _

J = 1 - 0 . 5 8 2 4 E 0 0 0 . 1 4 0 0 E 02 0 . 4 3 0 0 E - 0 1 0 . 2 0 6 5 E - 0 3 0 . U 3 4 E - 0 5J = 2 - 0 . 2 5 1 7 E - 0 2 0 . 4 3 0 0 E - 0 1 0 . 2 0 6 5 E - 0 3 0 . 1 1 3 4 E - 0 5 ' 0 . 6 7 5 8 E - 0 8J = 3 _- 0 . 1 2 9 8 E - 0 4 0 . 2 0 6 5 E - 0 3 0 . 1 1 3 4 E - 0 5 0 . 6 7 5 8 E - 0 8 0 . 4 2 4 6 E - 1 0J = 4 - 0 . 7 3 9 2 E - 0 7 0 . 1 1 3 4 E - 0 5 0 . 6 7 5 8 E - 0 8 0 . 4 2 4 6 E - 1 0 0 . 2 7 6 3 E - 1 2


A C J ) GIV { J » K )

K = 1 2 3 4

J = 1 - 0 . 2 8 2 5 E - 0 2 0 . 3 6 9 4 E - 0 0 ' - 0 . 39 7 7 E 03 0 . 1 1 2 3 E 06 - 0 . 9 0 5 IE 0 7J = 2 - 0 . 2 0 5 4 E 02 - 0 . 3 9 7 7 E 03 0 . 9 5 8 0 E 06 - 0 . 3 3 8 5 E 09 0 . 3 0 2 2 E 11J = 3 0 . 1 8 8 9 E 04 0 . 1 1 2 3 E 06 - 0 . 3 3 8 5 E 09 0 . 1 2 7 8 E 12 - 0 . U 8 2 E 14J = 4 - 0 . 4 3 7 7 E 05 - 0 . 9 0 5 1 E 07 0 . 30 2 2 E 11 - 0 . 1 1 8 2 E 14 0 . 1 1 1 8 E 16

NPP - 16 • M = 3 Z = 0 . 1 6 4 2 0 E - 0 3 E = 0 . 29500E 08 ORIGT = 0 . 0 3 0 0

I. 0 IS T ( I ) THI CK( I ) □CURVE CURVE I I ) C URVE I I I )

I 0 . 0 0 0 4 9 9 9 9 0 . 0 2 9 4 9 9 9 9 - 1 8 . 6 8 6 0 3 7 5 4 - 0 . 0 1 2 6 2 9 0 5 - 0 . 0 0 0 0 0 3 9 02 0 . 0 0 0 9 9 9 9 9 0 . 0 2 9 0 0 0 0 0 - 1 6 . 8 9 5 6 1 0 9 1 - 0 . 0 2 1 5 2 1 7 3 - 0 . 0 0 0 0 1 2 4 73 0 . 0 0 1 5 0 0 0 0 0 . 0 2 9 5 0 0 0 0 - 1 5 . 1 7 0 8 3 9 9 1 - 0 . 0 2 9 5 3 5 6 1 - 0 . 0 0 0 0 2 5 2 74 0 . 0 0 2 0 0 0 0 0 0 . 0 2 8 0 0 0 0 0 - 1 3 . 5 1 1 7 2 4 3 3 - 0 . 0 3 6 7 0 3 5 1 - 0 . 0 0 0 0 4 1 8 65 0 . 0 0 2 5 0 0 0 0 0 . 0 2 7 5 0 0 0 0 - 1 1 . 9 1 8 2 6 5 4 6 - 0 . 0 4 3 0 5 8 2 8 - 0 . 0 0 0 0 6 1 8 46 0 . 0 0 3 0 0 0 0 0 0 . 0 2 7 0 0 0 0 0 - 1 0 . 3 9 0 4 6 1 8 0 - 0 . 0 4 8 6 3 2 7 2 - 0 . 0 0 0 0 8 4 8 07 0 . 0 0 3 5 0 0 0 0 0 . 0 2 6 4 9 9 9 9 - 8 . 9 2 8 3 1 4 0 9 - 0 . 0 5 3 4 5 9 6 8 - 0 . 0 0 0 1 1 0 3 58 0 . 0 0 3 9 9 9 9 9 0 . 0 2 5 9 9 9 9 9 - 7 . 5 3 1 8 2 2 0 3 - 0 . 0 5 7 5 7 1 9 8 - 0 . 0 0 0 1 3 8 1 39 0 . 0 0 4 4 9 9 9 9 0 . 0 2 5 5 0 0 0 0 - 6 . 2 0 0 9 8 5 9 1 - 0 . 0 6 1 0 0 2 4 4 - 0 . 0 0 0 1 6 7 8 1

10 0 . 0 0 5 0 0 0 0 0 0 . 0 2 5 0 0 0 0 0 - 4 . 9 3 5 8 0 5 3 8 - 0 . 0 6 3 7 8 3 9 1 - 0 . 0 0 0 1 9 9 0 311 — 0 . 0 0 5 5 0 0 0 0 0 . 0 2 4 5 0 0 0 0 - 3 . 7 3 6 2 8 0 8 0 - 0 . 0 6 5 9 4 9 1 9 - 0 . 0 0 0 2 3 1 4 912 0 . 0 0 6 0 0 0 0 0 0 . 0 2 4 0 0 0 0 0 - 2 . 6 0 2 4 1 1 8 7 - 0 . 0 6 7 5 3 1 1 3 - 0 . 0 0 0 2 6 4 8 813 0 . 0 0 6 5 0 0 0 0 0 . 0 2 3 5 0 0 0 0 - 1 . 5 3 4 1 9 8 8 2 - 0 . 0 6 8 5 6 2 5 4 - 0 . 0 0 0 2 9 8 9 314 0 . 0 0 7 0 0 0 0 0 0 . 0 2 2 9 9 9 9 9 - 0 . 5 3 1 6 4 1 4 8 - 0 . 0 6 9 0 7 6 2 7 - 0 . 0 0 0 3 3 3 3 615 0 . 0 0 7 4 9 9 9 9 0 . 0 2 2 4 9 9 9 9 0 . 4 0 5 2 5 9 9 7 - 0 . 0 6 9 1 0 5 1 3 - 0 . 0 0 0 3 6 7 9 216 0 . 0 0 7 9 9 9 9 9 0 . 0 2 2 0 0 0 0 0 1 . 2 7 6 5 0 5 8 3 - 0 . 0 6 8 6 3 1 9 6 - 0 . 0 0 0 4 0 2 3 9

-aoi


CHOLD = - 0 . 6 0 2 I 3 E - 0 I QHOLD = 0 . 3 1 2 1 6 E 05

CFINAL = - 0 . 6 0 2 1 3 E - 0 I QTMIST = 0 . 3 1 2 1 6 E 05

I D I S K I ) T H I C K ! I ) S ( 1 11 0 . 0 0 0 4 9 9 9 9 0 . 0 2 9 4 9 9 9 9 - 1 0 2 9 9 2 . 0 7 9 1 0 1 5 62 0 . 0 0 0 9 9 9 9 9 0 . 0 2 9 0 0 0 0 0 - 8 7 1 5 0 . 1 0 1 5 6 2 5 03 0 . 0 0 1 5 0 0 0 0 0 . 0 2 8 5 0 0 0 0 - 7 2 8 3 1 . 4 3 4 5 7 0 3 14 0 . 0 0 2 0 0 0 0 0 0 . 0 2 8 0 0 0 0 0 - 5 9 9 4 7 . 2 7 3 4 3 7 5 05 0 . 0 0 2 5 0 0 0 0 0 . 0 2 7 5 0 0 0 0 - 4 8 4 1 1 . 2 3 3 3 9 8 4 46 0 . 0 0 3 0 0 0 0 0 0 . 0 2 7 0 0 0 0 0 - 3 8 1 3 9 . 3 5 5 4 6 8 7 57 0 . 0 0 3 5 0 0 0 0 0 . 0 2 6 4 9 9 9 9 - 2 9 0 5 0 . 0 9 8 1 4 4 5 38 0 . 0 0 3 9 9 9 9 9 0 . 0 2 5 9 9 9 9 9 - 2 1 0 6 4 . 3 4 0 0 8 7 8 99 0 . 0 0 4 4 9 9 9 9 0 . 0 2 5 5 0 0 0 0 - 1 4 1 0 5 . 3 8 2 8 1 2 5 0

10 0 . 0 0 5 0 0 0 0 0 0 . 0 2 5 0 0 0 0 0 - 8 0 9 8 . 9 4 8 2 4 2 1 911 0 . 0 0 5 5 0 0 0 0 0 . 0 2 4 5 0 0 0 0 - 2 9 7 3 . 1 8 0 6 6 4 0 612 0 . 0 0 6 0 0 0 0 0 0 . 0 2 4 0 0 0 0 0 1 3 4 1 . 3 5 7 4 2 1 8 813 0 . 0 0 6 5 0 0 0 0 0 . 0 2 3 5 0 0 0 0 4 9 1 1 . 6 7 8 9 5 5 0 814 0 . 0 0 7 0 0 0 0 0 0 . 0 2 2 9 9 9 9 9 7 8 0 2 . 3 7 7 6 8 5 5 515 0 . 0 0 7 4 9 9 9 9 0 . 0 2 2 4 9 9 9 9 1 0 0 7 5 . 6 2 7 1 9 7 2 716 0 . 0 0 7 9 9 9 9 9 0 . 0 2 2 0 0 0 0 0 1 1 7 9 1 . 1 8 0 4 1 9 9 2

-3a>

SPECIMEN NO. 8 SP, 11,100 CY, CUT 1

NCUT = 1 CC = 0 . 1 2 5 0 0 E - 0 5

I T ( I ) X ( I ) D C I ) c m

1 0 . 1 4 9 0 0 0 0 0 0 . - 0 . 0 0 1 5 0 0 0 0 - 0 .2 0 . 1 3 2 0 0 0 0 0 0 . 0 1 7 0 0 0 0 0 - 0 . 0 . 0 0 3 0 1 5 4 43 0 . 1 2 4 0 0 0 0 0 0 . 0 2 5 0 0 0 0 0 - 0 . 0 . 0 0 3 0 2 4 9 94 0 . 1 1 4 6 0 0 0 0 0 . 0 3 4 3 9 9 9 9 0 . 0 0 0 7 0 0 0 0 0 . 0 0 4 4 3 8 8 75 0 . 1 0 4 3 9 9 9 9 0 . 0 4 4 6 0 0 0 0 0 . 0 0 1 3 0 0 0 0 0 . 0 0 5 6 5 8 3 86 0 . 0 9 4 8 0 0 0 0 0 . 0 5 4 1 9 9 9 9 0 . 0 0 2 0 0 0 0 0 0 . 0 0 7 0 3 2 7 87 0 . 0 8 4 0 0 0 0 0

? ... 0 . 0 6 5 0 0 0 0 0 0 . 0 0 1 2 0 0 0 0 0 . 0 0 5 5 2 0 8 48 0 . 0 7 4 3 0 0 0 0 0 . 0 7 4 7 0 0 0 0 0 . 0 0 1 6 0 0 0 0 0 . 0 9 6 3 7 0 1 29 0 . 0 6 3 3 0 0 0 0 0 . 0 8 5 2 0 0 0 0 0 . 0 0 1 7 0 0 0 0 0 . 0 0 6 6 5 0 7 8

10 0 . 0 5 3 7 9 9 9 9 0 . 0 9 5 1 9 9 9 9 0 . 0 0 1 3 0 0 0 0 0 . 0 0 5 9 7 5 5 511 0 . 0 4 4 3 0 0 0 0 0 . 1 0 4 6 9 9 9 9 0 . 0 0 0 7 0 0 0 0 0 . 0 0 4 9 8 0 6 412 0 . 0 3 6 0 0 0 0 0 0 . 1 1 3 0 0 0 0 0 - 0 . 0 0 0 7 0 0 0 0 0 . 0 0 2 5 0 8 2 013 0 . 0 2 9 7 0 0 0 0 0 . 1 1 9 2 9 9 9 9 - 0 . 0 0 0 3 0 0 0 0 0 . 0 0 3 7 6 0 7 814 0 . 0 3 6 0 0 0 0 0 0 . 1 1 3 0 0 0 0 0 0 . 0 0 0 4 9 9 9 9 0 . 0 0 2 9 7 9 1 915 0 . 0 2 9 7 0 0 0 0 0 . 1 1 9 2 9 9 9 9 0 . 0 0 1 5 0 0 0 0 0 . 0 0 4 5 2 6 6 0

DETERM = 3 . 7 9 8 9 3 1 9 3 E - 2 4

H ( J ) G ( J »K }

K = 1 2 3 4 5

J = 1 0 . 6 6 4 9 E - 0 1 0 . 1500E 02 o T l 0 6 5 E 01 0 . 9 8 1 2 E - 0 1 0 . 9 9 1 1 E - 0 2 0 . 1 0 5 0 E - 0 2J L ^ _ 2 ____ 0 . 5 0 1 6 E - 02 0 . 1 0 6 5E 01____ 0 J . 9 8 1 2 E - 0 1 ___ J 0 . 9 9 1 1 E - 0 2 0 . 1 0 5 0 E - 0 2 0 . 1 1 4 3 E - 0 3J = 3 0 . 4 4 4 0 E- 0 3 0 . 9 8 1 2 E - 0 1 0 . 9 9 1 1 E - 0 2 0 . 1 0 5 0 E - 0 2 0 . 1 1 4 3 E - 0 3 0 . 1 2 6 6 E - 0 4J = 4 ____ 0 . 4 3 02 E - 0 4 0 . 9 9 1 I E - 0 2 0 . 1 0 5 0 E - 0 2 ____ 0 . 1 14 3 E - 0 3____0 . 1 2 6 6 E - 0 4___ 0 . 1 4 1 9 E - 0 5J = 5 0 . 4 4 0 L E - 0 5 0 . 1 0 5 0 E - 0 2 0 . 1 1 4 3 E - 0 3 0 . 1 2 6 6 E - 0 4 0 . 1 4 1 9 E - 0 5 0 . 1 6 0 6 E - 0 6

<1

SPECIMEN NO. 8 S P , 1 1 , 1 0 0 CY, CUT 1

A ( J ) G I V ( J , K )

K = 1 2 3 4 5

J = 1 0 . 1 5 2 7 E - 0 3 0 . 9 6 3 5 E 00 - 0 . 7 6 9 4 E 02 0 . 1 9 5 4 E 0 4 - 0 . 1 9 6 5 E 05 0 . 6 8 1 0 E 05J = 2 0 . 1 0 8 7 E - 0 0 - 0 . 7 6 9 4 E 02 0 . 1 2 9 2 E 05 - 0 . 4 4 3 0 E 06 0 . 5 2 6 5 E 07 - 0 . 2 0 3 1 E 0 3J = 3 0 . 1 9 1 9 E 01 0 . 1 9 5 4 E 04 - 0 . 4 4 3 0 E 0 6 0 . 1 6 8 3 E 08 - 0 . 2 1 1 7 E 09 0 . 8 4 6 4 E 09J = 4 - 0 . 4 3 5 5 E 02 - 0 . 1 9 6 5 E 05 0 . 5 2 6 5 E 0 7 - 0 . 2 1 1 7 E 09 0 . 2 7 5 IE 10 - 0 . U 2 5 E 11J = 5 0 . 1 8 2 7 E 03 0 . 6 8 1 0 E 05 - 0 . 2 0 3 1 E 0 8 0 . 8 4 6 4 E 09 - 0 . 1 1 2 5 E 11 0 . 4 6 7 7 E 11

NPP — 2 4 M = 4 Z = 0 . 7 3 7 6 9 E - 0 5 E = 0 . 29500E 0 8 ORIGT = 0 . 1 4 9 0

I D I S T ( I ) TH TCK( I ) DCURVE CURVE( I )' - . ■

CURVE 1 ( 1 )

1 0 . 0 0 5 0 0 0 0 0 0 . 1 4 3 9 9 9 9 9 0 . 1 2 4 6 9 5 0 7 0 . 0 0 0 7 3 8 7 4 0 . 0 0 0 0 0 2 1 92 0 . 0 1 0 0 0 0 0 0 0 . 1 3 8 9 9 9 9 9 0 . 1 3 4 7 3 0 2 3 0 . 0 0 1 3 3 9 6 3 0 . 30 0 . 0 0 7 5 03 0 . 0 1 4 9 9 9 9 9 0 . 1 3 4 0 0 0 0 0 0 . 1 3 9 3 2 9 3 9 0 . 0 0 2 0 7 6 9 8 0 . 0 0 0 0 1 6 1 54 0 . 0 2 0 0 0 0 0 0 0 . 1 2 8 9 9 9 9 9 0 . 1 3 9 0 4 0 7 4 0 . 0 0 2 7 7 4 8 3 0 . 0 0 0 0 2 8 2 35 0 . 0 2 5 0 0 0 0 0 0 . 1 2 4 0 0 0 0 0 0 . 1 3 4 4 1 2 5 0 0 . 0 0 3 4 6 0 1 6 0 . 0 0 0 0 4 3 8 86 0 . 0 2 9 9 9 9 9 9 0 . 1 1 9 0 0 0 0 0 0 . 1 2 5 9 9 2 8 6 0 . 0 0 4 1 1 2 6 4 0 . 0 0 0 0 6 2 8 27 0 . 0 3 5 0 0 0 0 0 0 . 1 1 3 9 9 9 9 9 0 . 1 1 4 3 3 0 0 4 0 . 0 0 4 7 1 4 6 3 0 . 0 0 0 0 8 4 9 28 0 . 0 4 0 0 0 0 0 0 0 . 1 0 9 0 0 0 0 0 0 . 0 9 9 9 7 2 2 3 0 . 0 0 5 2 5 1 4 4 0 . 0 0 0 1 0 9 8 79 0 . 0 4 4 9 9 9 9 9 0 . 1 0 3 9 9 9 9 9 0 . 0 8 3 4 6 7 6 5 0 . 0 0 5 7 1 0 8 3 0 . 0 0 0 1 3 7 3 1

10 0 . 0 5 0 0 0 0 0 0 0 . 0 9 8 9 9 9 9 9 0 . 0 6 5 3 6 4 4 9 0 . 0 0 6 0 8 3 4 6 0 . 0 0 0 1 6 6 8 311 0 . 0 5 4 9 9 9 9 9 0 . 0 9 4 0 0 0 0 0 0 . 0 4 6 2 1 0 9 7 0 . 0 0 6 3 6 2 7 2 0 . 0 0 0 1 9 7 9 812 0 . 0 5 9 9 9 9 9 9 0 . 0 8 8 9 9 9 9 9 0 . 0 2 6 5 5 5 2 9 0 . 0 0 6 5 4 4 7 3 0 . 0 0 0 2 3 0 2 913 0 . 0 6 5 0 0 0 0 0 0 . 0 8 4 0 0 0 0 0 0 . 0 0 6 9 4 5 6 5 0 . 0 0 6 6 2 8 3 5 0 . 0 0 0 2 6 3 2 714 0 . 0 6 9 9 9 9 9 9 0 . 0 7 9 0 0 0 0 0 - 0 . 0 1 2 0 6 9 7 2 0 . 0 0 6 6 1 5 1 8 0 . 0 0 0 2 9 6 4 115 0 . 0 7 5 0 0 0 0 0 0 . 0 7 3 9 9 9 9 9 - 0 . 0 2 9 9 4 2 6 4 0 . 0 0 6 5 0 9 5 6 0 . 0 0 0 3 2 9 2 616 0 . 0 8 0 0 0 0 0 0 0 . 0 6 9 0 0 0 0 0 - 0 . 0 4 6 1 2 4 9 2 0 . 0 0 6 3 1 8 5 7 0 . 0 0 0 3 6 1 3 717 0 . 0 8 4 9 9 9 9 9 0 . 0 6 4 0 0 0 0 0 - 0 . 0 6 0 0 6 8 3 2 0 . 0 0 6 0 5 2 0 4 0 . 0 0 0 3 9 2 3 318 0 . 0 9 0 0 0 0 0 0 0 . 0 5 8 9 9 9 9 9 - 0 . 0 7 1 2 2 4 6 4 0 . 0 0 5 7 2 2 5 3 0 . 0 0 0 4 2 1 7 819 0 . 0 9 5 0 0 0 0 0 0 . 0 5 4 0 0 0 0 0 - 0 . 0 7 9 0 4 5 6 8 0 . 0 0 5 3 4 5 3 5 0 . 0 0 0 4 4 9 4 720 0 . 0 9 9 9 9 9 9 9 0 . 0 4 8 9 9 9 9 9 - 0 . 0 8 2 9 8 3 2 6 0 . 0 0 4 9 3 8 5 5 0 . 0 0 0 4 7 5 1 921 0 . 1 0 5 0 0 0 0 0 0 . 0 4 4 0 0 0 0 0 - 0 . 0 8 2 4 8 9 1 5 0 . 0 0 4 5 2 2 9 0 0 . 0 0 0 4 9 8 8 422 0 . 1 0 9 9 9 9 9 9 0 . 0 3 9 0 0 0 0 0 - 0 . 0 7 7 0 1 5 1 2 0 . 0 0 4 1 2 1 9 6 0 . 0 0 0 5 2 0 4 423 0 . 1 1 4 9 9 9 9 9 0 . 0 3 3 9 9 9 9 9 - 0 . 0 6 6 0 1 3 0 2 0 . 0 0 3 7 6 1 9 7 0 . 0 0 0 5 4 0 1 324 0 . 1 2 0 0 0 0 0 0 0 . 0 2 9 0 0 0 0 0 - 0 . 0 4 8 9 3 4 6 1 0 . 0 0 3 4 7 1 9 6 0 . 0 0 0 5 5 8 1 8

•300

CF INAL = 0 . 3 5 0 7 2 E - 0 2_______________________________ QTMIST = - 0 . 6 4 8 9 0 E 0 4 CFINI = 0 . 5 5 5 7 4 E - 0 3

CHOLD = 0 . 3 5 0 7 2 E - 0 2 _QHOLD = - 0 . 6 4890E 0 4 _____________________________ j

C FIN A L = 0 . _______ ___________________ QTMIST = 0 . ____________________________________________ _____

SPECIMEN NO. 8 S P, l l t l 00 CY , CUT 1_______________________ _____________ ____________________________________

I D I S K I ) T H I C K ! I ) s m1 0 . 0 0 5 0 0 0 0 0 0 . 1 4 3 9 9 9 9 9 1 0 6 4 2 . 3 6 6 8 2 1 2 92 0 . 0 1 0 0 0 0 0 0 0 . 1 3 8 9 9 9 9 9 9 0 7 3 . 4 4 4 5 8 0 0 83 0 . 0 1 4 9 9 9 9 9 0 . 1 3 4 0 0 0 0 0 6 9 8 5 . 7 8 3 6 9 1 4 14 0 . 0 2 0 0 0 0 0 0 0 . 1 2 8 9 9 9 9 9 4 6 1 4 . 4 2 2 5 4 6 3 95 0 . 0 2 5 0 0 0 0 0 0 . 1 2 4 0 0 0 0 0 2 1 5 4 . 7 0 4 8 9 5 0 26 0 . 0 2 9 9 9 9 9 9 0 . 1 1 9 0 0 0 0 0 - 2 3 4 . 8 8 9 2 4 7 8 97 0 . 0 3 5 0 0 0 0 0 0 . 1 1 3 9 9 9 9 9 - 2 4 2 9 . 9 1 4 2 4 5 6 18 0 . 0 4 0 0 0 0 0 0 0 . 1 0 9 0 0 0 0 0 - 4 3 3 7 . 1 2 9 0 2 8 3 29 0 . 0 4 4 9 9 9 9 9 0 . 1 0 3 9 9 9 9 9 - 5 8 9 1 . 6 6 4 6 7 2 8 5

10 0 . 0 5 0 0 0 0 0 0 0 . 0 9 8 9 9 9 9 9 - 7 0 5 4 . 1 9 7 9 9 8 0 511 0 . 0 5 4 9 9 9 9 9 0 . 0 9 4 0 0 0 0 0 - 7 8 0 8 . 1 1 8 0 4 1 9 912 0 . 0 5 9 9 9 9 9 9 0 . 0 8 8 9 9 9 9 9 - 8 1 5 6 . 6 9 8 3 0 3 2 213 0 . 0 6 5 0 0 0 0 0 0 . 0 8 4 0 0 0 0 0 - 8 1 2 0 . 2 6 5 3 6 9 1 414 0 . 0 6 9 9 9 9 9 9 0 . 0 7 9 0 0 0 0 0 - 7 7 3 3 . 3 6 9 8 7 3 0 515 0 . 0 7 5 0 0 0 0 0 0 . 0 7 3 9 9 9 9 9 - 7 0 4 1 . 9 5 3 7 3 5 3 516 0 . 0 8 0 0 0 0 0 0 0 . 0 6 9 0 0 0 0 0 - 6 1 0 0 . 5 2 4 4 1 4 0 617 0 . 0 8 4 9 9 9 9 9 0 . 0 6 4 0 0 0 0 0 - 4 9 6 9 . 3 2 0 5 5 6 6 418 0 . 0 9 0 0 0 0 0 0 0 . 0 5 8 9 9 9 9 9 - 3 7 1 1 . 4 8 4 6 8 0 1 819 0 . 0 9 5 0 0 0 0 0 0 . 0 5 4 0 0 0 0 0 - 2 3 9 0 . 2 3 1 5 0 6 3 520 0 . 0 9 9 9 9 9 9 9 0 . 0 4 8 9 9 9 9 9 - 1 0 6 6 . 0 1 9 7 4 4 3 721 0 . 1 0 5 0 0 0 0 0 0 . 0 4 4 0 0 0 0 0 2 0 6 . 2 8 1 1 3 5 5 622 0 . 1 0 9 9 9 9 9 9 0 . 0 3 9 0 0 0 0 0 1 3 8 0 . 2 1 9 1 3 1 4 723 0 . 1 1 4 9 9 9 9 9 0 . 0 3 3 9 9 9 9 9 2 4 2 0 . 5 8 8 2 5 6 8 424 0 . 1 2 0 0 0 0 0 0 0 . 0 2 9 0 0 0 0 0 3 3 0 6 . 2 6 0 4 9 8 0 5

CD


NCUT = 2 CC = 0 . 1 2 5 0 0 E - 0 5

I TI I ) X { I ) D ( I ) C ( I )

1 0 . 0 2 9 7 0 0 0 0 0 . - 0 . 0 0 1 5 0 0 0 0 - 0 .2 0 . 0 2 9 4 9 9 9 9 0 . 0 0 0 2 0 0 0 0 0 . 0 0 2 2 0 0 0 0 0 . 0 0 7 4 1 9 2 73 0 . 0 2 8 8 0 0 0 0 0 . 0 0 0 8 9 9 9 9 - 0 . 0 0 1 7 0 0 0 0 - 0 . 0 0 0 3 1 0 0 44 0 . 0 2 7 5 0 0 0 0 0 . 0 0 2 2 0 0 0 0 - 0 . 0 0 4 3 0 0 0 0 - 0 . 0 0 5 3 6 4 1 95 0 . 0 2 6 8 0 0 0 0 0 . 0 0 2 9 0 0 0 0 - 0 . 0 0 4 8 0 0 0 0 - 0 . 0 0 6 2 7 6 7 26 0 . 0 2 5 8 0 0 0 0 0 . 0 0 3 9 0 0 0 0 - 0 . 0 0 7 2 0 0 0 0 - 0 . 0 1 0 9 3 9 2 07 0 . 0 2 5 0 9 9 9 9 0 . 0 0 4 6 0 0 0 0 - 0 . 0 0 7 8 0 0 0 0 - 0 . 0 1 2 0 3 2 9 98 0 . 0 2 9 7 0 0 0 0 0 . 0 . 0 0 0 3 0 0 0 0 0 . 0 0 0 7 6 5 8 29 0 . 0 2 9 4 9 9 9 9 0 . 0 0 0 2 0 0 0 0 0 . 0 0 1 5 0 0 0 0 0 . 0 0 3 1 4 6 5 4

10 0 . 0 2 8 8 0 0 0 0 0 . 0 0 0 8 9 9 9 9 - 0 . 0 0 0 3 0 0 0 0 - 0 . 0 0 0 5 2 4 1 311 0 . 0 2 7 5 0 0 0 0 0 . 0 0 2 2 0 0 0 0 - 0 . 0 0 2 6 9 9 9 9 - 0 . 0 0 5 4 6 9 9 312 0 . 0 2 6 8 0 0 0 0 0 . 0 0 2 9 0 0 0 0 - 0 . 0 0 3 1 9 9 9 9 - 0 . 0 0 6 5 5 7 4 513 0 . 0 2 5 8 0 0 0 0 0 . 0 0 3 9 0 0 0 0 - 0 . 0 0 6 4 0 0 0 0 - 0 . 0 1 3 0 9 4 9 814 0 . 0 2 5 0 9 9 9 9 0 . 0 0 4 6 0 0 0 0 - 0 . 0 0 5 7 9 9 9 9 - 0 . 0 1 2 0 0 1 1 8

DETERM = 2 . 1 5 4 6 1 0 4 0 E - 30

H ( J ) G ( J t K )

K = 1 2 3 4

J = 1 - 0 . 6 1 2 4 E - 0 1 0 . 1 4 0 0 E 02 0 . 2 9 4 0 E - 0 1 0 . 1 0 0 9 E - 0 3 0 . 3 8 4 9 E - 0 6J = 2 - 0 . 2 6 4 0 E - 0 3 0 . 2 9 4 0 E - 0 1 0 . 1 0 0 9 E - 0 3 0 . 3 8 4 9 E - 0 6 0 . 1 5 4 8 E - 0 8J = 3 - 0 . 1 0 3 5 E - 0 5 0 . 1 0 0 9 E - 0 3 0 . 3 8 4 9 E - 0 6 0 . 1 5 4 8 E - 0 8 0 . 6 4 3 8 E - 1 1J = 4 - 0 . 4 1 9 4 E - 0 8 0 . 3 8 4 9 E - 0 6 0 . 1 5 4 8 E - 0 8 0 . 6 4 3 8 E - 1 1 0 . 2 7 4 0 E - 1 3

00o

A C J)________ G1V( J»K ) 1____K = 1 _________ 2___________3__________ 4____J = I 0 . 2 4 7 6 E - 0 2 0 . 3 2 6 9 E - 0 0 - 0 . 5 9 1 5 E 0 3 0 . 2 5 8 8 E 0 6 - 0 . 3 1 9 9 E 08

S PECIMEN NO. 8 S P , 11,100 CY, CUT 2 ________________ ______________________________________

J = 2 - 0 . 8 0 6 3 E 00 - 0 . 5 9 1 5 E 03 0 . 2 4 4 0 E 07 - 0 . 1 2 9 4 E 10 0 . 1 7 4 5 E 12J = 3 - 0 . 1658E 04 0 . 2 5 8 8 E 06 - 0 . 1294E 10 0 . 7 3 0 9 E 12 - 0 . 1 0 2 3 E 15J = 4 0 . 2 4 7 2 E 0 6 - 0 . 3 1 9 9 E 08 0 . 1745E 12 - 0 . 1 0 2 3 E 15 0 . 1 4 6 6 E 17

NPP = 18 M = 3 Z = 0 . 4 7 1 1 6 E - 0 4 E = 0 . 2 9 5 0 0 E 08 ORIGT = 0 . 0 3 0 0

I D I S K I ) T H I C K ! I ) • DCURVE CURVE! I ) CURVE I I I )

1 0 . 0 0 0 4 9 9 9 9 0 . 0 2 9 4 9 9 9 9 - 2 . 2 7 8 7 8 2 6 4 0 . 0 0 1 6 8 9 4 3 0 . 0 0 0 0 0 1 0 72 0 . 0 0 0 9 9 9 9 9 0 . 0 2 9 0 0 0 0 0 - 3 . 3 8 0 4 3 5 6 2 0 . 0 0 0 2 5 9 1 8 0 . 0 0 0 0 0 1 5 83 0 . 0 0 1 5 0 0 0 0 0 . 0 2 8 5 0 0 0 0 - 4 . 1 1 1 2 3 3 1 2 - 0 . 0 0 1 6 2 9 1 9 0 . 0 0 0 0 0 1 2 54 0 . 0 0 2 0 0 0 0 0 0 . 0 2 8 0 0 0 0 0 - 4 . 4 7 1 1 7 5 0 7 - 0 . 0 0 3 7 9 0 2 4 - 0 . 0 0 0 0 0 0 0 95 0 . 0 0 2 5 0 0 0 0 0 . 0 2 7 5 0 0 0 0 - 4 . 4 6 0 2 6 1 4 0 - 0 . 0 0 6 0 3 8 5 5 - 0 . 0 0 0 0 0 2 5 56 0 . 0 0 3 0 0 0 0 0 0 . 0 2 7 0 0 0 0 0 - 4 . 0 7 8 4 9 2 4 0 - 0 . 0 0 8 1 8 8 6 9 - 0 . 0 0 0 0 0 6 1 17 0 . 0 0 3 5 0 0 0 0 0 . 0 2 6 4 9 9 9 9 - 3 . 3 2 5 8 6 7 7 7 - 0 . 0 1 0 0 5 5 2 4 - 0 . 0 0 0 0 1 0 6 88 0 . 0 0 3 9 9 9 9 9 0 . 0 2 5 9 9 9 9 9 - 2 . 2 0 2 3 8 7 8 1 - 0 . 0 1 1 4 5 2 7 5 - 0 . 0 0 0 0 1 6 0 99 0 . 0 0 4 4 9 9 9 9 0 . 0 2 5 5 0 0 0 0 - 0 . 7 0 3 0 5 2 1 6 - 0 . 0 1 2 1 9 5 8 1 - 0 . 0 0 0 0 2 2 0 3

10 0 . 0 0 5 0 0 0 0 0 0 . 0 2 5 0 0 0 0 0 1 . 1 5 7 1 3 9 3 0 - 0 . 0 1 2 0 9 8 9 9 - 0 . 0 0 0 0 2 8 1 41 L 0 . 0 0 5 5 0 0 0 0 0 . 0 2 4 5 0 0 0 0 3 . 3 9 3 1 8 5 6 2 - 0 . 0 1 0 9 7 6 8 7 - 0 . 0 0 0 0 3 3 9 612 0 . 0 0 6 0 0 0 0 0 0 . 0 2 4 0 0 0 0 0 6 . 0 0 0 0 8 7 9 8 - 0 . 0 0 8 6 4 4 0 0 - 0 . 0 0 0 0 3 8 9 213 0 . 0 0 6 5 0 0 0 0 0 . 0 2 3 5 0 0 0 0 8 . 9 7 7 8 4 5 4 3 - 0 . 0 0 4 9 1 4 9 7 - 0 . 0 0 0 0 4 2 3 714 0 . 0 0 7 0 0 0 0 0 0 . 0 2 2 9 9 9 9 9 1 2 . 3 2 6 4 5 8 9 3 0 . 0 0 0 3 9 5 6 5 - 0 . 0 0 0 0 4 3 5 715 0 . 0 0 7 4 9 9 9 9 0 . 0 2 2 4 9 9 9 9 1 6 . 0 4 5 9 2 7 5 2 0 . 0 0 7 4 7 3 3 0 - 0 . 0 0 0 0 4 1 6 816 0 . 0 0 7 9 9 9 9 9 0 . 0 2 2 0 0 0 0 0 2 0 . 1 3 6 2 5 1 4 5 0 . 0 1 6 5 0 3 3 9 - 0 . 0 0 0 0 3 5 7 717 0 . 0 0 8 4 9 9 9 9 0 . 0 2 1 5 0 0 0 0 2 4 . 5 9 7 4 3 0 7 1 0 . 0 2 7 6 7 1 3 5 - 0 . 0 0 0 0 2 4 8 218 0 . 0 0 9 0 0 0 0 0 0 . 0 2 1 0 0 0 0 0 2 9 . 4 2 9 4 6 6 2 5 0 . 0 4 1 1 6 2 6 2 - 0 . 0 0 0 0 0 7 7 1

00h-1


CHOLD = 0 . 3 5 0 7 2 E - 0 2 QHOLD = - 0 . 6 4 8 9 0 E 04

CFINAL = 0 . 3 5 0 7 2 E - 0 2 QTMIST = - 0 . 6 4 8 9 0 E 04

I DI S T( I ) THICK( I ) S ( I >1 0.00049999 0.02949999 - 4075.336608892 0.00099999 0.02900000 - 7435.282287603 0.00150000 0.02850000 - 8824.907836914 0.00200000 0.02800000 - 8521.552973525 0 . 0 0 2 5 0 0 0 0 0 . 0 2 7 5 0 0 0 0 - 6 7 8 8 . 8 8 2 8 7 3 5 46 0 . 0 0 3 0 0 0 0 0 0 . 0 2 7 0 0 0 0 0 - 3 8 7 6 . 8 3 8 1 2 2 5 67 0 . 0 0 3 5 0 0 0 0 0 . 0 2 6 4 9 9 9 9 - 2 1 . 8 8 1 8 9 6 9 78 0 . 0 0 3 9 9 9 9 9 0 . 0 2 5 9 9 9 9 9 4 5 5 3 . 4 9 5 7 8 3 5 79 0 . 0 0 4 4 9 9 9 9 0 . 0 2 5 5 0 0 0 0 9 6 4 0 . 2 3 2 3 4 8 6 3

10 0 . 0 0 5 0 0 0 0 0 0 . 0 2 5 0 0 0 0 0 1 5 0 4 3 . 1 8 9 4 5 3 1 311 0 . 0 0 5 5 0 0 0 0 0 . 0 2 4 5 0 0 0 0 2 0 5 8 0 . 6 0 1 8 0 6 6 412 0 . 0 0 6 0 0 0 0 0 0 . 0 2 4 0 0 0 0 0 2 6 0 8 4 . 5 8 4 2 2 8 5 213 0 . 0 0 6 5 0 0 0 0 0 . 0 2 3 5 0 0 0 0 3 1 4 0 0 . 8 7 1 3 3 7 8 914 0 . 0 0 7 0 0 0 0 0 0 . 0 2 2 9 9 9 9 9 3 6 3 8 8 . 8 7 9 3 9 4 5 315 0 . 0 0 7 4 9 9 9 9 0 . 0 2 2 4 9 9 9 9 4 0 9 2 1 . 6 9 3 3 5 9 3 816 0 . 0 0 7 9 9 9 9 9 0 . 0 2 2 0 0 0 0 0 4 4 8 8 6 . 0 7 8 6 1 3 2 817 0 . 0 0 8 4 9 9 9 9 0 . 0 2 1 5 0 0 0 0 4 8 1 8 2 . 4 7 0 2 1 4 8 418 0 . 0 0 9 0 0 0 0 0 0 . 0 2 1 0 0 0 0 0 5 0 7 2 4 . 9 8 8 7 6 9 5 3

00to

APPENDIX F

83

EFFECTS OF POSSIBLE DISSECTION GRINDING INDUCED STRESSES

If the grinding proceeds too fast local heating can occur inducing su rface

ten sile s tre s s e s .

A ssum ptions:

1. Initially annealed specim en

2. Grinding has induced a lay er of ten sile residual s tre s s

on the su rface of constant m agnitude Og and of depth D .

The in ternal moment is th e re fo re

M = - 4 cr D t w here t = th ickness of bar g 2 g

Making use of Equation (1) and (4) of Chapter IV

C - c = - g D t (12) = _ 6 ^ g D g o 2 E t 3 E t 2

(F - l)

c 'g

6<*gD _d_ / 1 \ 2 _ - 12<igD E dx \ t Q - x ) E t 3

(F-2)

S0 S * 1. .--6 J s E f x + C x = ± e ° t i . i \ + c x

E • 'o ( t0 - x ) 2 0 E At(F-3)

Combining the above th ree equations with Equation (20) of Chapter IV

84

E C“ 1212 CgD 1 2 t2 as D 3" [ 2 E t 3 + E t 2

°~gD

(V2) (F-4)

A constant res id u a l s tre s s induced a t the su rface during the grinding p ro cedu re

w ill not only destroy the orig inal su rface s t r e s s and induce non-constant negative

curvature-, but w ill cause a constant positive shift in the calcu lated s t r e s s pa tte rn .

It is in te resting to note tha t if a second cut is m ade on the opposite su rface of

the f i r s t cut th is effect w ill tend to cancel itse lf.

REFERENCES

85

LIST OF REFERENCES

86

A. BOOKS

1. Almen, John O. and Paul H. B lack, R esidual S tresses and Fatigue in M etals. New York: M cGraw-Hill Book Company, L ie ., 1963, pp. 82-90

2. B a rre tt, C harles S. S tructure of M etals. New York: M cGraw-Hill Book Company, Lie. 1952

3. Heindlhofer, K Evaluation of R esidual S tress . New York: M cGraw- Hill Book Company, 1948

4. Organic, E lliot I. A F o rtra n P r im e r. Reading M assachusetts: Addison- W esley Publishing Company, Inc. , 1963, pp. 169-171

5. Osgood, W illiam R. R esidual S tre sses in M etals and M etal Construction. New York: Reinhold Publishing Corporation, 1954

6. Popov, E. P. M echanics of M aterials. Englewood Cliffs, New Je rse y : P ren tice -H all, Lie. , 1952, pp. 270-271

7. R assw eile r, G erald M. and W illiam L. Grube, L iternal S tre sses and Fatigue in M etals. A m sterdam : E lsev ie r Publishing Company, 1959, pp. 311-331

8. Sines, George and J . L. W aism an. Metal Fatigue. New York: M cGraw-Hill Book Company, Lie. , 1953

B. PUBLICATIONS OF THE GOVERNMENT

9. R ollins, F red . U ltrasonic Methods fo r NonDestructive M easurem ent of Residual S tress . Wadd Technical R eport 61-42, p a r t 1, p. 1

C. PERIODICALS

10. Almen, J. O. "Fatigue F a ilu res a re T ensile F a ilu re s ," P roduct Engineering, M arch 1951, pp. 101-124

87

11. Almen, J . O. "Fatigue Loss and Gain by E lectrop lating ," Product Engineering, June 1951

12. , "Fatigue W eakness of S urfaces," Product Engineering,November 1950, pp. 117-140

13. "Peened Surfaces Im prove Endurance of Machine P a r ts ,"Metal P ro g re ss , F eb ruary 1943, pp. 209-216

14. , "Shot B lasting to In c rease Fatigue R esis tan ce ," SAE Journal(T ransactions), July 1943, Vol. 51, No. 7, pp. 247-268

15. , "T orsional Fatigue F a ilu re s ," Product Engineering, Septem ber1951, pp. 167-182

16. C hristensen , A. L. "M easurem ent of S tress by X -ray ," SAE, TR-182 1960

17. Littm an, W. E, "Reaping Benefits from Residual S tre sses in S teel," Machine Design, F eb ruary 27, 1964, pp. 166-172

18. Obrzut, J. J. "Fighting F ric tio n s, D rag on M otion," Iron Age, May 21, 1964, p. 134

19. "Evaluation of Methods of M easurem ent of R esidual S tre s s e s ," SAE,

TR-147

20. Machine Design, July 19, 1962, p. 30

21. Machine Design, August 16, 1962, p. 10

D. UNPUBLISHED MATERIALS

22. G u rre ra , Carm in. "Residual S tress G rinding," (Reproduced in Appendix A .)

23. Johnson, Leonard G. "Residual S tre sses in S traight R ectangular B ars, C ircu la r D iscs, and Split C ircu la r R ings," S-982

24. P erc iva l, C. M ark. "The Design of a Six Specimen T ensile Fatigue M achine," Unpublished M asters T hesis, the Brigham Young U niversity, Provo, Utah, 1961

A B S T R A C T

The purpose of th is investigation was two fold. (1) Develop the m echanical

techniques and com puter-o rien ted com putational p ro ced u res for the d e te rm i

nation of te s t sam ple in itia l re sidual s t r e s s conditions. (2) By using the

developed method, analyze the change in res id u a l s tre s s d istribution of sho t-

peened and nonshot-peened stee l ten sile specim ens subjected to various

num bers of ten sile s tre s s cycles.

Fatigue te s t specim ens w ere fab rica ted from surp lus a irc ra f t m aste r rod

bolts, som e of which w ere shot-peened. The thus p rep a red specim ens w ere#

subjected to fo rm one to 11,100 ten sile load cycles. The ten sile load m agni

tude was above the endurance lim it and below the yield point of the stee l

m ateria l.

The analysis of the re s id u a l s t r e s s conditions was accom plished using the

d issection m ethod and an orig inal F o rtra n com puter com putational routine.

The detail com puter routine logic, m athem atical derivation, and use d e sc rip

tion a re contained in th is work.

W ithin the conditions of th is study it was found tha t ten sile loading below the

yield point induced in the shot-peened and nonshot-peened specim ens local

88

ten sile yielding at the su rface . This local su rface yielding eventually,

effectively neu tra lized the residual s tre s s e s tha t existed in the shot-peened

specim ens.

By equipping the specim en with a su rface p ro tec tive res id u a l com pressive

s tre s s before the fatigue loading, the form ation of su rface residual tensile

s tre s s e s was significantly delayed.

A PP R O V E RDate

89

residual stress distribution changes during dynamic

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