ML20215H973

Revised Buckle Users Manual:Creep Collapse of Thin-Walled Circular Cylindrical Shells Subj to Radial Pressure & Thermal Gradients

ML20215H973
Person / Time
Site:	Fort Saint Vrain
Issue date:	04/30/1987
From:	Almajan I, Charman C, Connors G GENERAL ATOMICS (FORMERLY GA TECHNOLOGIES, INC./GENER
To:
Shared Package
ML20215H965	List: ML20215H964 ML20215H973
References
909410, TAC-63576, NUDOCS 8705070171
Download: ML20215H973 (48)

Text

_ _ _ __

y.nasmav.can GA Technologies inc, ISSUE

SUMMARY

l LE BUCKLE USERS MANUAL 2 OV&S APPROVAL LEVEL O OESIGN DISCIPLINE SYSTEM 00C. TYPE PROJECT DOCUMENT NO.

M ISSUE NOJLTR.

01 MCP 1900 909410 NC QUALITY ASSURANCE LEVEL SAFETY CLASSIFICATION SEISMIC CATEGORY ELECTRICAL CLASStFICATION N/R N/R N/R N/R APPROVAL SSUE DATE PREPARED FUNDING APPLICABLE DES RI TION /

( fj PR03CT PROJECT CWBS NO.

0 )W9*W NC APR 2 91967 I .T . f- G.P. Initial Release Almaj an 7

Connors 2970503

.. . .s.

Chaman Kennedy CONTINUE ON GA FORM 14851 NEXT INOENTURED L'OCUMEf;TS Issua Summary 1 1 - iv 4 1 1-4 4 N3082 2 2-6 6

• 3 3-4 4 4-1 1 5-1 1 Appendix A Al-A18 18 Appendix B B1-B9 9 l

Total 48 l 8705070171 870430 l PDR ADOCK 05000267 P PDR N

RS NO GA PROPRIETARY INFORMATION SR-774 5 WORM >t DOC. If 40 lPAGF 1 0F 43

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909410/0 4

BUCKLE USER'S MANUAL i

4 CREEP COLLAPSE OF THIN-WALLED CIRCULAR CYLINDRICAL SHELLS SUBJECTED TO I

RADIAL PRESSURE AND THERMAL GRADIENTS 1

1 i

4 C. M. CHARMAN AND I. T. ALMAJAN 1

APRIL 1987 I

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909410/0 I

1 FORWARD t

The BUCKLE computer code described in this users manual is perma-nently filed in the archive library of the GA Technologies Computer Services Department (CSD) on the UNIVAC 1100 computer system under the following reference number:

BUCKLE-STSD 4092 l This UNIVAC version of the BUCKLE code was developed in-house at GA Technologies in the early seventies.

In 1986, the code was further developed by introducing double Precision and expanding the library of the CREEP equations to five materials.

The following command will access and execute the buckle code from the archive library (Controlled Program Library), on the UNIVAC 1100 computer systems i

"@ ADD,P GA* PROD. BUCKLE /4092" 1

l 4

11

- - . - - - - - - - - -- .- --- - - - - - , n -- . .+ - , - - . -

909410/0 CONTENTS FOREWARD . . . . . . . . . . . ... .............. 11 ABSTRACT

. . . . . . . . . . . .. ............... iv

1. CODE DESCRIPTION . . . . . .. ............... 1-1 1.1. Theoretical Base . . . ................ 1-1 1.2. Code Organization . . . . ............... 1-3

2. CODE INPUT . . . . . . . . .. ............... 2-1 2.1. Title Card (12A6) . . . . ............... 2-1 2.2. Tube Material and Loading Card _(7D10.4,I1D) . ..... 2-1 2.3. Tube Geometry Card (6D10.4, 2Il0) . .......... 2 2.4. Tube Temperature Distribution Card (8D10.4) . . . . . . 2-3 2.5. Time output Control Card (8D10.0) . . ......... 2-4 2.6. Temperature and/or Pressure Changes Time Card (8D10.0). 2-4 2.7. Pressure Change Card (8D10.0) ............. 2-5 2.8. Temperature Change Card (8D10.0) ........... 2-5

3. CODE OUTPUT - DATA . . . . . ................ 3-1

4. SAMPLE PROBLEM

. . . . . . . ................ 4-1 4.1. Model Description . . . . ............. .. 4-1 4.2. Input / Output . . . . . ................ 4-1

5. REFERENCES

. . . . . . . . . ................ 5-1 APPENDIX As

. . . . . . . . . . ............... . A-1 APPENDIX Bt

. . . . . . . . . . ............... . B-1 t

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909410/0 l

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I ABSTRACT This report provides a user's manual for BUCKLE, a finite

difference code for analysing creep buckling of thin-walled circular

cylindrical shells subjected to external pressure and circumferential

and radial thermal gradients.

i.

The equations developed for the time behavior of the cross section are based on the assumption that the shell material exhibits creep  ;

deformations expressible by the form ((t) = gng7, f

The usage of BUCKLE Code is illustrated by means of a sample problem. Additional solved problems can be found in the validation and j verification report Ref. 4.  !

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909410/0

1. CODE DESCRIPTION 1.1. THEORETICAL BASE A long cylinder, subjected to a constant external pressure "p",  !

which is less than the static-buckling pressure Per for a sufficient length of time, will eventually collapse, however small the constant pressure "p", if the temperature is high enough to cause the material to creep.

Analysis shows that the mechanism of this collapse is dependent I

on the presence of initial deviations from circularity in the shape of the cylinder cross section. Consequently, there exists, from the very

} start, a differential stressing in the fibers of the cylinder walls and, I

therefore, a differential creep rate which eventually causes collapse.

Although the final collapsed shape of the cylinder might resemble that of a cylinder which had " buckled" under a static load at ordinary temperatures, the creep collapse problem is not an eigenvalue problem.

That is, a bifurcation of the equilibrium positions does not suddenly occur at a certain critical time t = c cr. In other terms, a perfectly circular uniform cylinder at constant temperature and pressure, would i

not collapse due to the effects of creep alone. The terms " creep

] buckling" and " creep instability" often encountered in the literature must, therefore, be interpreted in this restricted sense.

l The computer program presented here is limited to the investigation of the creep collapse of a long thin tube with a known initial out-of-roundness, subjected to an external radial pressure "p" with variable i

radial and circumferential temperatures in the tube wall. In particu-i lar, a theoretical prediction is made to determine the " collapse time" 1-1

909410/0 or " critical time," cce, of such a cylinder under given conditions of temperature and pressure. For analytical purposes it is assumed that the cylinder is infinitely long. The theoretical derivation can be found in Ref. 1.

This analysis of the creep collapse of long tubes requires certain simplifying assumptions at the outset. Once these are made, the nnaly-sis can proceed in a manner very similar to that used in deriving the critical pressure of a long cylinder in the well-established case of elastic buckling.

These assumptions are as follows:

Small displacement thin-walled circular shell theory.

Von-Nases yield criterion.

i I

Prandti-Reuss assumption for inelastic strain increments.

Homogenous, isotropic and elastic propecies for shall material.

Critical time defined when any local point stress exceeds the

yield stress of the material.

The loading assumptions are:

Initial radial ovality.

Radial external pressure.

Axial force.

Thermal gradient through and around the tube wall.

1 l

1 1-2 i

- . . . . .- - .. . - . . . _ . = _ _ _ _

i 909410/0 1.2. CODE ORGANIZATION f

, The routines used in the code ares i

MAIN

• INPUT i DER 7PT (DERIV)

• WRITE 1 (WRITE 2)

FINDQF NVERSE t

ECREEP The functions for each routine are described as follows: [

t

1. MAIN The main routine of the code, all others are subroutines. .

2. INPUT Reads input data.

3. DER 7PT (DERIV) Integration routine.

4. WRITE 1 (WRITE 2) Output printout. '

5. FINDQP Rearrangement of elements in the matrix before f taking the inverse procedure. [

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i 1

1-3 i

. . . _ ~ . . . .- = - . . . . . .. _ _ _ . .

j . .

i 909410/0 ,

i

i

+

6. NVERSE

, Matrix inversion routine.

7. ECREEP User supplied creep equations.

1 .

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1 .

t, A listing of the code is shotm in Appendix A. i J

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=

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909410/0

2. CODE INPUT l

BUCKLE uses eight types of data cards to define a problem:

l

1. Title card.

2. Tube material and loading card.

3. Tube geometry card.

4. Tube temperature distribution card.

5. Time output control card.

6. Temperature and/or pressure changes time card.

7. Pressure change card.

8. Temperature change card.

All but the last three types (used to define varying temperature and pressure with respect to the time variable) are required for each problem. Detailed instructions for each input data card are given as follows.

2.1. TITLE CARD (12A6)

Column Quantity Format Notes 1.. 72 Any title to be printed with the output.

(TITLE) 12A6 2.2. TUBE MATERIAL AND LOADING CARD (7D10.4, I1D)

Column Quantity Fo rmat Notes 1.. 10 Modules of elasticity. (EM00) D10.4 11.. 20 Coef ficient of thermal expansion. (ALPIIA) D10.4 21.. 30 Poisson's ratio. (EMU) D10.4 31.. 40 Yield stress. (YS) D10.4 2-1

I 909410/0

, 41.. 50 Initial applied external pressure. (PRESS) D10.4

! 51.. 60 Applied axial force. (AP) D10.4 l 61.. 70 Load factor for pressure. (PSF) D10.4 (1) i 71.. 80 Type of loading. (NPTP) 110

= 0 constant temperature and pressure 4

f 0 varying temperature and pressure NOTES:

1. Based on Code Case N-47 of ASME Boiler and Pressure Vessel Code, the time-dependent load-controlled buckling load factors for various load levels are defined as follows: t Level A 1.5 Level 8 1.5 Level C 1.5 Level D 1.25 2.3. TUBE GEOMETRY CARD (6D10.4, 2110)

Column Quantity Format Notes  ;

1.. 10 Tube mean radius. (RAD) D10.4 11.. 20 Tube wall thickness. (H) D10.4 21.. 30 Initial ovality. (WA) D10.4 (1) 31.. 40 Maximum expected tube creep buckling time. i (STIME) D10.4 (2) '

41.. 50 Minimum time step allowable. (DTMIN) D10.4 (3) 51.. 60 Fraction of stress to relax in each time increment. (RELAX) D10.4 (4) 61.. 70 Tube material type. (MIYPE)

= 1. A800 Grade 1 high temperature i

l

= 2, T2 at high temperature l

l

= 3, A800H at high temperatura l

= 4, T22 at high temperature

= 5. SA-516 GR55 at high temperature 2-2

_, , _ _ , _ _ . _ _ . . . . _ _ . . _ . _ , _ _ _ _ _ _ _ . , . _ . _ _ _ _ . . _ _ . _ . , _ . ~ . _ . . -_ .- _ __ ___ _

909410/0 NOTES:

1. Initial tube radial ovality is defined as (Dmax - Dnin)/4' which is different from the non-dimensional value defined in the ASME Code as (Dmax - Dmin)/Dmean. To convert the ASME defined ovality to radial ovality, the following formula should be used.

Initial tube ovality = (ovality) ASME X 4

2. Without experience about the creep buckling time, a large value is suggested, say 1E20 h. This case occurs when the

, stress caused by the external pressure differential is very low.

3. For the minimum time step allowable, a value of 1.0 is recommended.

4. The value of fraction of stress to relax in each time increment will def ault to 0.1 if input is left blank.

2.4. TUBE TEMPERATURE DISTRIBUTION CARD (8D10.4)

Column Quantity Format Notes 1.. 10 Temperature coefficient in the radial direction. D10.4 (1)

(A6M) 11.. 20 Temperature gradient coef ficient in the radial direction. (A6MP) D10.4 (1) 21.. 30 Temperature coefficient in the circumferential direction. (A6) D10.4 (1) 31.. 40 Temperature gradient coefficient in the circumferentisi direction. (A6P) D10.4 (1) 2-3 I

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909410/0 l

NOTE:

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1. The temperature distribution in the tube can be empressed by '

the equations T(2,#)=A6M+[b+A4cos68+A4P(1-cos68)1+

(H) (2 N/  ;

where T is the temperature, H the tube thickness, # the circumferential coordinate and Z the radial coordinate measured from the adddle of the tube thickness. Figure 1 shows the typical shell element.

i 2.5. TIME OUTPUT CONTROI. CARDS (8D10.0)

Two cards are required as input (10 values) for the specific times.

CARD 1 Column Quantity hh 1.. 10 First specified output time. (PTIME(1)) D10.0 11.. 20 Second specified output time. (PTIME(2)) D10.0 71.. 80 Eighth specified output time. (PTIME(8)) D10.0 CARD 2 Column Quantity Format Noteg 1.. 10 Ninth specified output time (PTIME(9)) D10.0 i 11.. 20 Tenth specified output time (PTIME(10)) D10.0  ;

2.6.

TEMPERATURE AND/OR PRESSURE CHANCES TIME CARD (8010.0)

Skip this card if the temperature and the pressure remains constant  !

with time.

l 2-4

t b

909410/0 l 1

Five cards are required as input (36 values) for the specific l times.

CARD 1 to 5 Column Quaneiev Z1EEG. U2111 1.. 10 First specified time for changing the temperature and/or the pressure. (TPCT(1)) D10.0 11.. 20 Second specified time for changing the temperature and/or the pressure. (TPCT(2)) D10.0 i 71.. 80 Eighth specified time for changing the temperature and/or the pressure. (TPCT(8)) D10.0 i

2.7. PRESGURE CHAN0E CARD (8010.0) t Skip this card if the pressure remains constant with time.

Five cards are required as input (36 values) for changing the pressures.

Column Quantity Format Notes 1.. 10 Pressure at the first time. (PSI (1)) D10.0 11.. 20 Pressure at the second time. (PS!(2)) D10.0 71.. 80 Pressure at the eighth specific time. (PS!(8)) D10.0 t

2.8. TEMPERATURE CHANGE CARD (8010.0) i Skip this card if the temperature remains constant with time.

l rive cards are required as input (36 values) for changins the temperatures.

l 1

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909410/0 Column Cisantity Format Notes 1.. 10 Temperature at the first specified time.

(HEAT (1)) D10.0 11.. 20 Temperature at the second specified time.

(HEAT (2)) oto,o 71.. 80 Temperature at the eighth specified time.

(HEAT (8)) oto,o I

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3. CODE-0UTPUT DATA 1

The BUCKI,2 Code generates the following printed outputs f l 1. The input data card images are echoed back. This output is i

j printed in the same fonsat as the input card.

2  !

2. The pressure loading and temperature history for the defined (

j areep buckling problem. l l

3. Model description. Tube geometry (mean radius, well thtak-1 ness, initial ovality, see Fige. 1 and 2), tube matrial properties (modulus of elastietty, coefficient of thermal

)

I expansion, Foisson's ration, yield stress), tube temperature j distribution (coefficients for varying teiperature in the 1

J radial and circumferential directions) ant loading information l (maximum expected life, maximum time step pressure load  !

j factor, axial force).

j i

! l j 4. Tube elastic. creep response. Specific ti:e, last time incre-1 1

ment, current external pressure and tempen sture are listed.

f Also, the tangential and radial displaceaeits, axial and hoop stresses, and effective strains in the sui 1 and circumferen-tial (hoop) directions are printed at loca. ions indicated in

Fig. 3.

i

5. Creep buckling time (critical time). When he effective stress at any local point in the tube reaches or exceeds the l tube yield stress, the creep buckling time is defined and printed.

i l 31 i

1 iG410/0 t

I J

d f

t g

t v DISPL ACEMENTIN y '06MICTl34 w.CISPLACIMENT IN a DIMICTION i l

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nl4 ,e N 5 , N /

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/ PERPECTLY CIMCUL AR q TUBE

, DEPOPMED TURE (waSto 26)

Ft0VRE 2 .

3-3

.n..  ;..-.... . . . - . . . . . - . . . . . . . . , . . . .

909410/0 l

l k

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'N s fr/4 0 / \

~ H - \

/

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/____ _____\

109878 54321 r(+)

z(1) = 0.4869533H, a(2) = 0.3425317H (3) = 0.3397048H, :(4) = 0.2166977H r(5) = 0.074431717H,:(3) = -a(5)

(7) = -z(4), :(8) = - (3)

(9) = -r(2),:(10) = -z(1)

NOTES: IN ONE QUADRANT (a) THERE ARE TWENTY FIVE STATIONS ALONG THE CIRCUMFERENTIAL OlRECil0N (k)

(b) THERE ARE TEN STATIONS ALONG THE RADIAL DIRECTION (c) THERE ARE A TOTAL OF 250 N00AL PolNTSIN ONE QUADRANT OF THE TURE FIGURE 3 3-4 l

909410/0

4. SAMPLF PROBLEM 4.1. MODEL DESCRIPTION The following sample problem can be solved by SUCKLE. Consider a tube, with outer diameter 1.3 in, and thickness 0.1 in., made of Alloy 800H material. The tube having an assumed initial evality of 2%

is subjected to an external pressure differential of 1000 psi (6.895 MPa) and temperature 1562*F (850'C) under an ASME Level D loading condition. To be ready for BUCKLE input, the following calculations are needed:

Mean radius = (D, - t)/2 * (1*3

• 0.1)/2 = 0.6 in.

Ovality

= 2% x Do /4 = 2% X 1.3/4 = 0.0065 in.

The result from the BUCKLE computer run shows that the critical time for such a tube governed by the creep buckling failure mode is 2.6 h.

4.2. INPUT /0UTPUT 1 The input and output flies are shown in the Appendix 8.

)

l 4-1

909410/0 l

4

5. REFERENCES

1. Pan, Y. S., " Creep Buckling of Thin-Walled Circular cylindrical Shell Subject to Radial Pressure and Thermal Gradients,"

J. of Applied Mechanics, March 1971, pp. 206-216.

2. Hildebrand, F. B., Introduction to Numerical Analysis, McGraw-Hill Book Company, 1956.

3. Scarborough, J. B., Numerical Mathematical Analysis, John Hopkins Press, 1962.

4. Buckle, Validation and Verification Report, CA 909438, April 1987.

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5-1

909410/0 4

APPENDIX A ,

A-1

U1:(AUWAJANIT]C 801;1 2-APR-87 16:48:04 909410/0 1: CREEP CODE FOR CREEP-COLLAPSE OF FUEL ELEMENT CLADDINO MAI00100 2: C MAIC0200 3: C 00LSLE PRECISION 4: C 5: IWLICIT DOUBLE PRECISION (A-H,0-Z) 6: C 7: 00LELE PRECISION NYID,WID,MYIDD,NYI,WI MAIO13 8: C MAIO1400 9: C0hWON/ ,P(98) ,R(98) MAIOO300 10: ColWON/ EC((49,10)QP ,TAUYY(49,10) 98,98) ,TAUXX(49,10) MAIOO400 11: C0hWON CEPSYY(49,10) ,CEPSXX(49 ,DEPSYY(49,10) MAIOO500 12: C0hWON DEPSXX(49 ,T(49,10) ,10) ,SIOMA(49,10) MAIOO600 13: C0hWON WODD 49) ,10)PHW 9) ,V(49 MAIOO700 14: C0hWON W(49 ,VD(4 WDO( MAI00800 15: C0hWON/ DNYI ) 0MYI ,NYID i

16: ,MYI ) MAIOO900 C0hWON/ MYID ) ,

) ,NYI( MAIO1000 17: C0hWON/ MYI( ,THET( ,WD(4 MAIO1100 i 18: C 19: C0hWON IWUTS TITLE (12) ,DIVS MAIO1500 20: C0hWON IW UTS EM00 , ALPHA EMJ 21: MAI01600 C0hWON IWUTS PRESS ,H ,, RAD 22: MAIO1700 C0hWON IW UTS STIME ,DTMIN ,YS 23: MAIO1800 C0hWON IWUTS WA , PSI , HEAT MAIO1900 24: C0hWON IW UIS A6 ,A6P(36) ,A6M (36) MAIO2000 25: C0lWON IWUTS PTIME(12) , RELAX 26: MAIO2100 C0hWON IWUTS TPCT ,AP, IPR ,A6W MAIO2200 27: C0hWON IW UTS MTYPE (36) , PSF ,DA6MP MAIO2300 28: C MAIO2400 29: C0hWON/ SET 3/ A(2,14) ,ZOH(10) ,COEF(10) 30: MAIO2500 C0hWON/ SETS / COE(49) MAIO2600 31: C MAIO2700 32: C0hWON PARAMS DTH ,SLAWA , BETA 33: MAIO2800 C0hWON PARAMS OA6NA , ZETA , PHI j 34: MAIO2900 C0hWON PARAMS QA0H 35: MAIO3000 C0hWON PARAMS NDIVS ,NP 36: MAIO3100

] C0hWON PARAMS M , TIME ,DTIME MAIO3200 37: C0hWON PARAMS ICYCLE MAIO3300 38: C MAIO3400

39

.

C0hWON/ DER 7C 00 l 40: 01(7) D2(7) MAIO3500 C0hWON/ DER 7C D3 ,04(7)

, ,05(7)

, MAIO3600 41: C0hWON/ DER 7C D6 MAIO3700 i~

42: C MAIO3800 43: DIMENSION AJ(5) ,BJ(5) ,Y(49,10) ,YCL(49) MAIO3900 t

44: C MAIO4000 45: DATAAJ/.973906000,.865063000,.679409000,.43395000,.1488743000/ MAI 46: DATABJ/.06671000,.149451000,.219086000,.2692667000,.295524000/

I 47: C MAI MAIO4300 48: 00 5 J=1 K s 11-J,5 MAIO4400 49:

MAIO4500 50: ZOH = 0.5+AJ J) MAIO4600 51: ZOH =-ZOH(X MAIO4700

52

C0 = 0.5 8 MAIO4800 53:

54:

5 COEF J 10 CALL I

= COEF(K)(J) MAIO4900

! MAIO5000 55: SPLAMB=0.0 MAIO5100 56: DlANYa0.0 MAIO5200

!. 57: MAIO5300 j 58: nRITE DO 6{2000) 30 = ,36 DLWY,TPCT(1), PRESS,A6M MAIO5400 4

A-2

_ - - _ - - - -- _ . _ _= - _ - - - - . .

U1:[ALMAJANIT]C.801;1 2-APR-87 16:48:04 909410/0 59: IFy(I).CE.STIME.AND.TPCT(I+1.CE.STIME) C0 TO 31 MAIO5500 60:

61: 31 CONTIMJE,2001) TPCT(I),TPCT(I+1)), PSI (I), HEAT (I) 30 HR11t (6 ,

MAIO5600 MAIO5700 62: 2000 FORMAT (1H1,25X,30HCREEP COLLAPSE LOADING HISTORY // MAIO5800 63: 11H ,10X,19HTIME DLRATION (IRS),11X,1H.,5X,8HPRESSURE,6X,1H., MAIO5900 64: 14X,11HTBFERAllRE/ MAIO6000 65: 11H MAIO6100 66: 11H ,1X,

,8X,4HFROM,17X,2HTO,9X,1H.,7X,5H(PSI),7X,1H.,5X,9H(DEC.

(3X,1PD12.6,4X,1H )) F.)/

MAIO6200 67: 2001 FORMAT 1X,4(3X,1PD12.6,4X,1H.)) MAIO6300 68: 20 BETA = RAD). 2/12.0 MAIO6400 69: CAW 4A = 1.0-EMJ.EMJ). RAD /(EM00*H) MAIO6500 70: ZETA = *EM00/(1.0-EMU) MAIO6600 71: R0= RAD +0.5.H MAIO6700 72: RI= RAD-0.5 H MAIO6800 73: WI=2 MAIO6900 74: M)IVS=48 MAIO7000 75: W=49 MAIO7100 76: M=98 MAIO7200 77: WS-25 MAIO7300 78: DIVS = FLOAT (M)IVS) MAIO7400 79: DTH=3.1415926536/DIVS MAIO7500 80: CALL DER 7FT(DTH) MAIO7600 81: CNY = EMOD H/(1.-EMJ.EMJ) MAIO7700 82: CMY = CNY H MAIO7800 83: SLh0A = 0.5.A6P* ALPHA MAIO7900 84: EM. RAD = EM). RAD MAIO8000 85: C MAIO8100 86: IC0lNT=1 MAIO8200

87

ICYCLE=1 MAIO8300 88: TIME = 0.0 MAIO8400 89: POTIME = 0.0 MAIO8500 90: DTIME = 0.0 MAIO8600 91: PR=1 MAI08700 92: C MAIO8800 93: 410 00 411 K=1,W MAIO8900 94: 411 COE(K) = 3.0 MAIO9000 95: 00 412 K=1,W ,3 MAIO9100 96: 412 COE = 2.0 MAIO9200 97: COE = 1.0 MAIO9300 98: COE )= 1.0 MAIO9400 99: 00E=128.0 MAIO9500 100: 00 420 K=1,W MAIO9600 101: 420 COE(K) = COE(K)/00E MAIO9700 l'

102: C MAIO9800 103: HZETA = H ZETA MAIO9900 i

104: H2 ZETA =HZETA.H/12.0 MAIL 0000 105: C MAIL 0100 106: 00 450 K=1 W MAIL 0200 107: FKM1 = FLOAT (K)-1.0 MAIL 0300 108: THETA = FKM1.DTH MAIL 0400 109: THET = THETA *57.29578 MAIL 0500 110:

111:

C6TH(K)COS(6.0.

=

A6C = A6.C6TH THETA) MAIL 0600 MAIL 0700 112: A6PC = A6P.(1.0-C6TH) MAIL 0800 113: NYI = HZETA*(A6C+0.5.A6PC) MAIL 0900 i 114: DNY ) = 0.0 MAI11000 115: MYI( =H2 ZETA (A6PC+A6W) MAI11100 116: DMYI ) = 0.0 MAI11200 A-3

U1:[ALMAJANIT]C.801;1 2-APR-87 16:48:04 909410/0 117: WO(K)-WA.COS(2.0* THETA) 118: MAI11300 THETA = THETA +1.5707963268 119: 00 440 J=1,10 MAI11400 120: MAI11500 Y(K, = SIN (THETA)*(ZOH(J)*H+ RAD) MAI11600 121: T(K,J = A6C+A6PCe(0.5+ZOH(J))+A6WeZOH(J) 122: 440 C0 MAI11700 123: YCL MAI11800

= SIN (THETA)* RAD MAI11900 124: 450 CD 125: C MAI12000 126: MAI12100 YWP = CAWA RAD 127: MAI12200 YWQ = 1.0/(CAWA*H) MAI12300 128: YE = RAD *YWQ 129: C MAI12400 130: 00 470 J=1,10 MAI12500 131: 00 460 K=1,W MAI12600 132: CEPSYY ,J) = 0.0 MAI12700

, 133: CEPSXX ,J) = 0.0 MAI12800 l 134: F.C =0.0 MAI12900

' 135: 460 CD MAI13000 136: 470 CONTIMJE MAI13100 137: C MAI13200 138: MAI13300 CALL VRITEl(2) MAI13400 139:

140:

90 PHI = CAWA. PRESS *R0/ RAD MAI13500 QA0& PRESS *R0/H MAI13600 141:

QA02H:4.5.QA0H.R0/ RAD MAI13700 142: 100 00 110 J=1,7 143: JW = J+J MAI13800 144: JV = JW-1 MAI13900 145: A MAI14000 146:

= 02( ) MAI14100 A , = -01 )+ BETA *(Di(J)+03(J))

147: A MAI14200

= Di( MAI14300 148: A ,

149: 110 C = 00 )-BETA * (D2 (J) +04 (J)) -PHIe (00(J) +D2 (J)) MAI14400 150: C MAI14500 151: CALL FIN 04P(W,A) MAI14600 152: C - MAI14700 153: MAI14800 CALL 081V(2,WO,W000,W,1,1) 154: C MAI14900 155: C MAI15000 MAI15100 156: C ITSATION LOOP RETURN POINT .

157: II::o MAI15200 l 158: 550 00 555 K=1,W 159: MAI15300 160: NYI ) = NYI(K)+DNYI(K) MAI15400 161: C 555 MYI ) = MYI(K)+0MYI(KJ MAI15500 162: MAI15600 CALLOGIV1,NYI,NYID,W,1,1) MAI15700 163: CALL DERIV 1,MYI,MYID,W ,1,1) 164: CALL DERIV 2,MYI,MYIDO MAI15800 165: CALCULATE COLLAN MATRIX (P) ,W,1,1) MAI15900 166: 00 565 K=1 W MAI16000 167: -

MAI16100 168:

169:

PWO(K))= PHIeP(2.K-1 -CAWA*(NYID(K)-MYID(K)/ RAD)

(K)+W000(K))

MAI16200 MAI16300 AMt. TAM =EM.RADe SLAMDA) MAI16400 170: P(2*K) =

171: 565 CONTIMJE

• (NYI(K)+MYIDO(K)/ RAD) + PHWD(K) - AMJLAM MAI16500 172: C MAI16600 173: 568 CONTIMJE MAI16700 MAI16800 174: CALCLLATE DEFLECTION MATRIX, (R)=(QP)*(P) MAI16900 A-4

. . l U1:[ALMAJANIT]C.801;1 2-APR-87 16:48:04 909410/0 175: DO 570 I=1,M MAI17000 176: R(I) = 0.0 MAI17100 177: DO 570 J=1,M MAI17200 178: 570 R(I) = R(I) + (F(I,J)*P(J) MAI17300 179: C MAI17400 180: C MAI17500 181: DO 610 K=1,W MAI17600 182: V = R(2*K-1 MAI17700 183:

184: 610 W = R(2*K) ) MAI17800 MAI17900 185: C MAI18000 186: CALI. DERIV (1,V,VD W -1,-1) MAI18100 187: CALL DERIV (2,W,1100,PE,1,1) MAI18200 188: CALCLLATE atte.sdts MAI18300 189: SICAX=AP/ MAI18400 190:

191:

RMOI=4.0 DO 750 K=1,

.1415926536*(RO 2-RI. 2)) ))

.1415926536*(R0**4-RI e4 MAI18500 MAI18600 192: TYYY = YWQ. -W ) MAI18700 193:

194:

TYYW = (W(K)(VD(K)K))

DO 750 J=1,10

+WDD( MAI18800 195: MAI18900 ZT = ZETA *T MAI19000 196:

197:

TAY = TYYV-TBY=YE.

J)ZOH(J)

MAI19100 l 198: TAUYY(K(CEPSYY(K,J]+ EMU MAI19200 (CEPSXX(K,J)-SLAMDA-SPLADYCL(K)))

,J MAI19300 199: TAX = TAY)BAJ= TAY-TBY-ZT-QA0H MAI19400 200: TBX=YE. CEPSXX(K,J)-SLAnCA-SPLA6YCL(K)+EOCEPSYY(K,J))

201: MAI19500 SIG4= ,J) *RMOI 202: MAI19600 TAUXX J)= TAX-TBX-ZT-QA02H+SIGA-SICAX 203: 750 C MAI19700 204: MAI19800 TIME = TIME +DTIME MAI19900 205: IF (IFLAC .EQ.1) CALL WRITE 2 206: MAI20000 IFLAC=0 207: IF MAI20100

.CE.STIME) CD TO 995 MAI20200 208: IF .0001.LT.POTIME) CD TO 760 MAI20300 209: WRITE 2 210: MAI20400 769 CONTIMJE 211: MAI20500 MAI20600 212: WR(= WR+1IF PTIME(WR+1).LE.O.0) C0 TO 755 MAI20700 213: POTIME = PTIME(WR) 214: MAI20800 CD TD 760 ,

215: MAI20900 1 216: 755 P0 TIME = POTIME + PTIME(WR)-PTIME(WR-1) MAI21000 760 CONTIME MAI21100 217: C COWUTE TIE STEP TO PRODUCE A MAXIRM ALLOWABLE CREEP STRAINMAI21200 218: DTD&STIME-TIE 219: MAI21300 DO 775 J=1,10 MAI21400 220: 00 775 K=1'W 221: MAI21500 222: DS=REL(AX*SICMASIGAA ,J)/EMOD K,J)-SQRT AUYY(K,J)**2+TAUXX(K,J)**2-TAUYY(K,J)*T 223: MAI21700 TEW=T(K,J) +

224: MAI21800 IF (SIGMA (K,J) .LE.100.0) C0 TO 775 MAI21900 225: II=II+1 226: HOLD =0 TIME 227: MAI22000 DTIME= AMIN 1 (DTIME, ECREEP (TIME, DT, TEMP, SICMA (K, J) , EC (K, J) , DS,2,II MAI22100 228: A, 229: IF -HOLD .CE. 0.0) C0 TO 775 MAI22200 230: MAX J MAI22300 231: MAXX=K MAI22400 232: 775 CONTIMJE MAI22500 A-5

U1:[AudAJANIT]C.801;1 2-APR-87 16:48:04 909410/0 233: IFF.EQ.0) CD TO 969 234: IIRIIt (6,1002) ICOLNT,DTIE,MAXJ,MAXK, SIGMA (MAXK,MAXJ),EC(MAXK,MAXMAI22600 235: SJ) MAI22700 236: 969 CONTIME 237: 1002 FORMAT (1H ,Ilo,D20.6,2Ilo,2020.6) MAI22800 238: C MAI22900 239:

DO 780 J=1,10 MAI23000 i 240: DO 780 K=1,PP MAI23100  !

241: IF SIGMA , .LT.O.01) C0 TO 780 MAI23200 t 242: IF SIGMA .CT.YS) C0 TO 1000 MAI23300 243:

MAI23400 244: (TIME, DTIME,TBP, SIG4A (K, J) , EC (K, J) , DS ,1, II, MTYPE) MAI23

245

EC(K,J =EC(K,J)+EPSTAR MAI23600 246:

247:

EPOSIC)EPSTAR/ SIGMA (K

=

MAI23700 DEPSYY , = EPOSIC. -0.5eTAUXX(K,J)) MAI23800 248: DEPSXX , = EPOSIC. -0.5 TAUYY(K,J)) MAI23900 249: CEPSYY K, = CEPSYY ,J) (K,J) MAI24000 250: CEPSXX = CEPSXX ,J)+DEPSXX(K,J)

MAI24100 251: 780 MAI24200

252: C IEECRATE DEPS(K,J) OVER J TD FIPO DELTA NYI Me DELTA MYI AT EACH K MAI24300 1

253: DPUM=0.0 j 254: MAI24400 DLAAOA = 0.0 MAI24500 255: 800 DO 820 K=1,PP 256: MAI24600 CDEPS = 0.0 MAI24700 257: CZDEP = 0.0 258: MAI24800 DSRP-C.0 259: MAI24900 DSR = 0.0 MAI25000 260: 00 810 h i,10 MAI25100 261: DSR = DSR + COEF J)*DEPSXX 262: MAI25200 DSRP=DSRP+COEF *DEPSXX(K, 263:

MAI25300 DCDEPS = COEF (DEPSYY(K, *D (K,J))

264: MAI25400 CDEPS = CDEPS EPS 265: MAI25500 810 CZDEP = CZDEP+0CDEPS*ZOH MAI25600 266: DUMDA = DLAh0A + COE 267: MAI25700 DPLAAE=0 PLANE +COE(K)* MAI25800 268: DNYI = CNY.CDEPS 269: MAI25900 820 DMYI K = CMY CZDEP MAI26000 270: C 271: MAI26100 272: DPLAAS=DPLAAeh8 .

• RAD *H/ (R0 * *4-RIe *4) MAI26200 SLAA0A = SUWA+01.An0A MAI26300 273: SPLAle= Spun 6+0PLAAS MAI26400 274: IF .LE. 0.0 ) SPUM=0.0 275: 900 IF MAI26500

.LE.DTMIN) C0 TO 995 MAI26600 276: ICY ICYCLE+1 277: MAI26700 1 278: IF (TIEDTIME+.00001.CE.TPCT(IC0lNT)) C0 TO 950 MAI26800 CD _IU 550 279: MAI26900 280: 950 IF (ABS (PRESS-PSI (ICOLNT)).LE.lo) C0 TO 990 MAI27000 IFLAC=1 281: MAI27100 PRESS = PSI (ICOLNT MAI27200 282:

283:

A6n6= HEAT (IC0lNT))

DO 951 K=1,49 MAI27300 MAI27400 284: DO 952 J=1,10 MAI27500 285: T(K,J)=T 952 CONTIMJE(K,J)+ZOH(J)*DA6he MAI27600 286:

MAI27700 287: I MYJ)=MYI(K)+H2 ZETA *DA6AP MAI27800 288: 951 CONTIMJE MAI27900 289: IC0lNT=IC0lNT+1 MAI28000 290: CD TO 90 MAI28100 A-6

~....- , , , . . - - - - _ _ - , _ - _ , _ , - - - - _. -_ _ . - . . _ . - _ . , . . . _ - - . _. b.

U1:[ALMAJANIT]C.901;1 2-APR-87 16:48:04 909410/0 291: 990 A6nWEAT(IC4 MAI28200 292: IR.Ac=1 MAI28300 293: IC0lNf=IC0lNT+1 MAI28400 294: CD TO 550 MAI28500 295: 1000 CONTIME 296:

MAI2 M WRITEfS,1001 TIME,K,J MAI28700 297: 1001 FORMAT (* TliE)TlEE HAS C0llAPSED AFTER ',016.8,* H0lRS BASED 298: 1LD LIMIT K= ',I4,'J= ',I4) MAI28900 299:

300:

995 CALL WRITE 2 992 CALL EXIT mm MAI29100 301: EM) gm I

1

)

A-7 1

VI:(ALMAJANIT]C.904;1 2-APR-87 16:55:24 909410/0 1: Sl2 ROUTINE DER 7PT (DX) DER 00100 2: C DER 00200 1

3: C 00l2LE PRECISION 4: C 5: IW LICIT 00l2LE PRECISION l (A-H,0-Z) l 6: C 7: DIMENSION C1 ,C2 ,C3(7) DER 00300 l

8: DIMENSION C4 C5 DER 00400 9: C6(7)

DIMENSION C ,) ,Z( DER 00500  !

10: C DER 00600 11: C0hNON/ DER 7C/ 00(7) ,D(7,6) DER 00700 12: C DER 00000 1 1,' C5 , , lC D 15: C -

DERO 1100 16: DATA C1 -12.DO,108.D0,-540.00,0.00,540.00,-108.00,12.00/

17: DATA C2 4.00,-54.00,540.D0,-980.00,540.00,-54.DO,4.00/

18: DATA C3 15.00,-120.00,195.00,0.D0,-195.00,120.00,-15.00/

19: DATA C4 -5.00,60.00,-195.D0,280.00,-195.00,60.00,-5.D0/

20: DATA C5 -3.00,12.00,-15.00,0,00,15.00,-12.00,3.00/

21: DATA C6 1.00,-6.00,15.D0,-20.00,15.D0,-6.00,1.00/

22: C DER 01800 23: 10 00 11 J=1,7 DER 01900 24: 11 DO = 0.0 DER 02000 25: = 1.0 DER 02100 26: 0 = 720.*DX DER 02200 27: FI = 1.0 DER 02300 28: N=6 DER 02400 29: DO 30 I=1,N DER 02500 30: 00 20 J=1,7 DER 02600 31: 20 D(J,I) = C(J,I)/DENOM DER 02700 32: FI = FI+1.0 DER 02800 33: DENOM = DENOM*DX/FI DER 02900 34: 30 CONTINUE DER 03000 35: REREN DER 03100 36: C * * * * * * * * * * *

• DER 03200 37: ENTRY DERIV (ND,Y,YD,W,JA,JB) DER 03300 38: C DOUBLE PRECISION 39: C 40: IWLICIT DOUBLE PRECISION (A-H,0-Z) 41: C 42: DIMENSION Y(W),YD(W) DER 03400 43: IF (PO.GT.6) 70=6 DER 03500 44: 700 N = W .

DER 03600 45: DO 710 K=1,N DER 03700 46: 710Zp( = Y(K DER 03800 47: IF JA.LT.0))C0 TO 720 DER 03900 1 48: Z =Y DER 04000 l 49: Z =Y DER 04100 50: Z =Y DER 04200 1

51: C0 730 l DER 04300 '

52: 720 Z =Y DER 04400 53: Z =Y DER 04500 54: Z =Y DER 04600 55: 730 I JB. .0 C0 TO 740 DER 04700 56: Z + =Y -

DER 04800 57: Z + =Y -

DER 04900 58: Z+ =Y -

DER 05000 A-8 l

U1:[ALMAJANIT]C.904;1 2-APR-87 16:55:24 909410/0 59: C0 TO 750 DER 05100 60: 740 Z =Y -

DER 05200 61: Z N+5 =Y -

DER 05300 62: Z N+4 =Y -

DER 05400 63: 750 C0 TD (110,210,110,210,110,210),f0 DER 05500 64: 110 D0 120 K=1,N DER 05600 65: YD(K) = D(1,2)*(Z(K)-Z(K+6)) + D(2,2)*(Z(K+1)-Z(K+5)) DER 05700 66: 1 +D DER 05800 67: 120 CONTIWE (3,2)*(Z(K+2)-Z(K+4))

DER 05900 68: RERRN DER 06000 69: 210 00 220 K=1,N DER 06100

. 1 3,' *

+2) + )) + ,'

• 3) 72: 220 CONTIW E DER 06400 73: RERRN DER 06500 74: 80 . DER 06600 A-9 L

l D

U1:[ALMAJANIT]ECREEP.FOR;3 29-APR-87 08:48:12 909410/0 1: FWCTION ECREEP(CETI,DT,TEW, STRESS,SlRAIN,0S,IOP,II,MTYPE) 2: C 3: C DOLELE PRECISION 4: C 5: IWLICIT DOLELE PRECISION (A-H,0-Z) 6: C 7: C 8: C CREEP EQ. EC=A*(STRESSe =AN) (TIME..CAWA) 9: C WPIPE =1 A800G1 C HICH TE W 10: C WTYPE =2 T2 C HICH TE W 11: C MTYPE =3 A800H C HIGH TEW 12: C MTYPE =4 T22 C HICH TEW 13: C MTYPE =5 SA 516 CR 55 14: C MTYPE =6 HASTELLOY N, A hICKEL BASE ALLOY 15: C 16: C0 TD (100,200,300,400,500,600), MTYPE -

17: 100 U1=-1.304 1 18: U24.

19: U3=1.

20: U4=6.0404 1

21: U5=-23.44 22: C0 TO 101 23: 200 U1=-6.4503 24: U2=0.

l 25: U3=1.

! 26: U4=4.16404

, 27: U5=-19.9 i

28: C0 TO 101 1 29: 300 U1=-1.21626004 30: U2=1.07849003 31: U3=0.47166 ,

32: 04=5.141660004 i 33: U5=-19.0780 i 34: C0 TO 101 35: 400 U1=-1.22D04 36: U2=-1.169003

. 37: U3-2,125 38: U4=5.64004 39: U5=-25.49 40: C0 TO 101 41: 500 U1=-6.1468003 42: U2=0.

43: U3=1.

, 44: U4-2.79404 45: U5=-12.5245 46: 101 T=TEW i

47:

48: TR=T @ ).C=(T-32.*5./9.

' 49: CAWA=1./(U2/TRW3) 50: X=1./CAWA 51: AN=-01/TR.CAWA 52: A=10...(-

53: 102 IF (II.EQ(U4/TRW5)*CAWA)

.1) 10 FORMAT (5X,'C T A (ANWRITE 6,10) T,C,AN,A,CAWA 54: CAWA',/,5X,5016.8) 55: B=(STRESS /1000.)..AN i 56: TBAR=(STRAIN.100./(A 8))**X

{ 57: C0 TO (1,2 58: 1 CONTINUE ), IOP l A -10 1

s 01:[ALMAJANIT]ECREEP.FOR;3 29-APR-87 08:48:12 (09410/0' 59: C CREEP STRAIN INCREMENT 60:

ECREEP=A.B. ((TBAR+0T) * *CA24A-TBAR* *CM4A) /100.

61: RERRN 62: 2 CONTIW E 63: C TIME INCREMENT 64: ECREEP=

65: RERRN (DS.100./(A*8)+TBAR**CA24A)..X-TBAR 66: C 67: C CREEP EQ. EC=A*(STRESS..AN)*(TIME **CA24A) 68: C 69: 600 CONTIWE 70: C 71: A = 4.6510-25 72: AN = 5.04 73: CAW 4A = 1.0 74: IF IOP.EQ.1) ECREEP = A* STRESS **AN.DT 75: IF IOP.EQ.2) ECREEP = DS/(A* STRESS **AN) 76: R 77: EM)

A - 11

U1:[ALMAJANIT]C.803;2 2-APR-87 16:52:49 909410/0 1: SLEROUTINE FIEQP (W,A) FIN 00100 2: C FIN 00200 3: C 00lELE PRECISION

• 4: C 5: IWLICIT DOUBLE PRECISION (A-H,0-Z) 6: C 7: COWON/ / Q(98,98) FIN 00300 8: C FIN 00400 9: DIMENSION A(2,14) ,LDlM(98) ,MXM(98) FIN 00500 10: C FIN 00600 11: CLEAR Q MATRIX FIN 00700 12: M=W+F FIN 00800 13: C FIN 00900 14: 00 125 J=1,M FIN 01000 15: 00 125 I=1,M - FIN 01100 16: 125 Q(I,J) = 0.0 FIN 01200 17: C FIN 01300 18: D0 220 I=2,M,2 FIN 01400 19: 00 210 bl,14 FIN 01500 20: J = N+I-8 FIN 01600 21: IF J.LT.1) GO TO 210 FIN 01700 22: IF J.GT.M C0 TO 210 FIN 01800 23: Q(I 1,J) =)A(1,N FIN 01900 24: Q(I,J) = A(2,N) ) FINO2000 25: 210 CONTINJE FINO2100 26: 220 CONTIW E FINO2200 27: C FINO2300 28: DO 260 I=1,5,2 FINO2400 29: 00 260 J=3,7,2 FINO2500 30: IF FINO2600 31: JP =(I+J.GT.8) 7-I+J C0 TO 260 FINO2700 32: KP = 9-I-J FINO2800 33: JQ = 7+I-J FIN 02900 34: KQ = 5+I+J '

FINO3000 35: IM = M-I FINO3100 36: JM = M-J l FINO3200 37: Q I,J) = A(1 JP)- ( KP) FIN 03300 38: Q IM,JM) = A 1,JQ - 1,KQ FINO3400 39: Q I+1,J) = A 2,JP 2,KP -

FIN 03500 40: Q IM+1,JM) = A(2, -A(2, Q) FIN 03600 41: K = J+1 FINO3700 42: JP = JP+1 FINO3800 43: KP = KP+1 FINO3900 44: JQ = JQ+1 FIN 04000 45: KQ = KQ+1 FIN 04100 46: JM = Ji+1 FIN 04200 47: Q I, 1JP) FIN 04300 48: Q IM, = =A(A 1,J (+ KP) 1,KQ FIN 04400 49: Q I+1,K = A 2,JP 2,KP FIN 04500 50:

260 CONTINJE ) = A(2, A(2, Q)

Q IM+1 FIN 04600 51: FIN 04700 52: C FIN 04800 53: DET = 0. FIN 04900 54: CALL NVERSE(Q,Q,M,DET,0,LDW,MDlM,98) FIN 05000 55: RETURN FIN 05100 56: END FIN 05200 57:

A - 12

U1:[ALMAJANIT]C.805;2 2-APR-87 16:57:30 909410/0 1: SWROUTINE ITUT IWOO200 2: C IWOO300 3: C DOWLE PRECIBION 4: C 5: IWLICIT 00WLE PRECISION (A-H,0-Z) 6: C 7: CIM40N/IWUTS TITLE (12) ,DIVS IWOO400 8: C0 WON /ITUTS EM00 , ALPHA , EMU IWOO500 9: COWON/ITUTS PRESS ,H , RAD IWOO600 10: COWON/IWUTS STIME ,DTMIN ,YS IW OO700 11: COWON/IWUTS WA , PSI (36) HEAT IW OO800 12: COWON/ITUTS A6 ,A6P ,A6M (36)

, IWOO900 13: COWON/IWUTS PTIME(12) , RELAX IWO1000 i 14: C0 WON /IWUTS TPCT ,AP, IPR ,A6W IW O1100 MTYPE (36) t 15: COWON/ITUTS , PSF ,DA6MP IWO1200 16: C 17: 00 20 I=1,36 18: TPCT )=0.

19: PSI =0.

20: 20 =0.

21: C IW01300 22: READ (5,1) (I) ,I=1,12) IT01400 23: MITE (6,1) (I),I=1,12) IWO1500 24: C IW01600 25: READ (5,3) EM00, ALPHA,EMJ,YS, PRESS,AP, PSF,WTP 26: WRITE (6,3) EM00, ALPHA,ERJ,YS, PRESS,AP, PSF,WTP 27: C IWO1900 28: READ (5,4) RAD,H,WA,STIME,DTMIN, RELAX,MTYPE, IPR 29: WRITE (6,4) RAD,H,WA,STIME,DTMIN, RELAX,MTYPE, IPR 30: C IWO2200 31: READ ,2) A6M,A6W,A6,A6P IWo2300 32: IF .LE.O.0) RELAX =.1 IWO2400 33: WR (6,2) A6M,A6 W ,AS,A6P IWO2500 34: C INP02600 35: READ (5,2) (PTIME(I),I=1,10) IWO2800 36: WRITE (6,2)(PTIME(I),I=1,10) INP02900 37: C IWO3000 38: IF (NTPT.EQ.0) C0 T3 30 39: READ (5,2)(TPCT ,I=1,36) INP03100 40: READ (5, ) ) ,I=1,36) INP03200 41: READ (5,2 ) ,I=1,36) INP03300 i

1 42: 30 IF (PSF. . 0) PSF =1.0 INP03500 43: PRESS = PRESS. PSF INP03600 )

44: D0 10 I=1,36 IWO3700 l

45: PSI (I)= PSI INP03800 46:

47: C 10 IF (TPCT(I)(I)* PSF

.LE.O.0) TPCT(I)=1.D+10 IWO3900 INPO4100 48: C FORMAT STATEMENTS INPO4200 49: C INP04300 50: 1 FORMAT INPO4400 51: 2 FORMAT (12A6)

(8010.4) INPO4500 52: 3 FORMAT (7D10.4,Il0) 53: 4 FORMAT (6010.4,2Ilo) 54: RETURN INPO4600 55: END INPO4700 A - 13

U1:[ALMAJANIT.BKL] TEM.0VT;3 24-APR-87 13:44:28 909410/0 1: SLEROUTINE NVERSE (GRIG,A,N, DETER,M',L,M,KK) NVE00100 2: C NVE00200 3: C DOLELE PRECISION 4: C 5: IWLICIT DOUBLE PRECISION (A-H,0-Z) 6: C 7: DIMENSION ORIG (KK, KK) , A (KK, KK) , L (KK) ,M (KK) NVE00300 8: C NVE00400 9: C MATRIX INVERSION SUBROUTINE - DOUBLE PRECISION VERSION NVE00500 10: C ORIG = ORIGINAL MATRIX, A = ITS INVERSE. NVE00600 11: C DETER = DETERMINANT CIVEN INITIAL VALUE OF DETER NVE00700 12: C IN CALLING ROUTINE, SET DETER = DESIRED SCALE FACTOR NVE00800 13: C TO AVOID OVERFLOW PROBLEMS, SET DETER = 0.0 IF ITS VALUE IS NOT REQD NVE00900 14: C N = SIZE OF MATRIX BEING INVERTED. KK = SIZE OF DIMENSIONED ARRAYS NVE01000 15: C PRINT CONBOL'M'=1 PRINT, W=0 NO PRINT NVE01100 16: C NVE01200 17: 00 3002 I=1,N NVE01300 18: DO 3000 J=1,N NVE01400 19: 3000 A(I,J)=0 RIG (I,J) NVE01500 20: 3002 CONTINUE NVE01600 21: C SEARCH FOR LARCEST ELEMENT NVE01700 22: DO 80 K=1,N NVE01800 23: L =K NVE01900 24: M =K NVE02000 25: 8 GA=A(K,K) NVE02100 26: DO 20 I-K,N NVE02200 27: DO 20 J=K,N NVE02300 28: NVE02400 29: 10 BIGA=A(I,(J)IF (DABS BICA)-DABS (A(I,J))) 10,20,20 NVE02500 30: L(K =I NVE02600 31: M(K =J NVE02700 32: 20 C0 NVE02800 33: C INTERCHANGE R0WS NVE02900 34: JROW=L K NVE03000 35: IF(L(K - )35,35,25 NVE03100 i 36: 25 DO 30 = ,N NVE03200 37: HOLD =-A(K,I) NVE03300 38: A K,I) A JROW,I NVE03400 39: 30 A JROW,I)(= HOLD ) NVE03500 40: C I CHANGE COLlMNS NVE03600 41: 35 ICOL=M(K) NVE03700 42: IF NVE03800 43: 37 DO(M(K)-K)45,45,37 40 J=1,N NVE03900 44: HOLD =-A( K) NVE04000 45: A J,K)=A 'l,ICOL) NVE04100 46: 40 A J,ICOL = HOLD NVE04200 47: C D VIDE COLlMN BY MINUS PIVOT NVE04300 48: 45 DO 55 IC=1,N NVE04400 49: 46 IF(IC-K 50,55,50 NVE04500 50: 50 A(IC,K))A(IC,K)/(-A(K,K))

=

NVE04600 51: 55 CONTINUE NVE04700 52: C REDUCE MATRIX NVE04800 53: DO 65 I=1,N NVE04900 54: DO 65 J=1,N NVE05000 55: 56 IF I- 57,65,57 NVE05100 56: 57 IF J 60,65,60 NVE05200 57: 60 A( (I,K) *A(K, J) +A(I, J) NVE05300 58: 65 CONTI NVE05400 l

A - 14 l - _ - _ . _. . . -.

-- . - - - . . _ - . _ . . - = - _- --. -. - . - - . . -

U1:[ALMAJANIT.lEL] TEM.OllT;3 24-APR-87 13:44:28 909410/0 59: C DIVIDE R0W BY PIVOT NVE05500

, 60: DO 75 JR=1,N NVE05600 i

61: 68 IF(A-K 70,75,70 NVE05700 62: 70 A(K (X,JR)/A(K,K) NVE05800

, 63: 75 C NVE05900 4

64: C CONTIWED PRODUCT OF PIVOTS NVE06000 65: DETER = DETER *A(K,K) NVE06100 66: C REPLACE PIVOT BY RECIPROCAL NVE06200 i

67: A(K,K)=1.0/A(K,K) NVE06300 4

68: C CONTIWE COMPLETE OPERATION NVE06400 69: 80 CONTIWE NVE06500

. 70: C FINAL R0W Af0 COLLA #i INTERCHANGE NVE06600

71

Kd NVE06700 1 72: 100 K= 1) NVE05800

} 73: IF 50,150,103 NVE06900 74: 103 I NVE07000

! 75: IF 120,120,105 NVE07100 l 76: 105 DO(110 J=1,N NVE07200 i 77: HOLD =A J NVE07300

} 78: A , ,I) NVE07400 i 79: 110 A NVE07500 80: 120 NVE07600 l 81: IF( )100,100,125 NVE07700

{ 82: 125 DO 130 I=1,N NVE07800 83: HOLD =A NVE07900 84: A ,) ,I) NVE00000 85: 130 A ) NVE08100 86: 100 87: NVE08200 150 IFQP)156,156,152 NVE08300

88

152 WRITE (6,153) DETER NVE08400 89: <

90: 153 FORMAT D0 154 I=1,N (13H1 DETERMINANT =E16.8//15H0 INVERSE MATRIX) NVE08500  !

NVE08600 l 91: 154 WRITE (6,155) (A(I,J),J=1,N) NVE08700 j

! 92: 155 FORMAT (1H0(6E16.8)) NVE08800 l 93: 156 REIUtN NVE08900

{ 94: EPO NVE09000 l

l 1

4 s

l

\

r l

A - 15 l l 1

_ . , . , . , , , . ,-. . _ , - - _ - - , , . - .,-.--,en, - . - , - - - , , - - - - , . . . , . , . - , -

01:[ALMAJANIT]C.806;1 2-APR-87 16:59:26 909410'/0 1: SWROUTINE WRITEl(WID) WRI00100 2: C WRI00200 3: C 00WLE PRECISION '

4: C 5: IWLICIT 00WLE PRECISION (A-H,0-Z)

' 6: C 7: 00WLE PRECISION NYID,MYID,MYIDD,NYI,MYI WRIO1 8: C WRIO1400 9:

10:

COWON/ / QP(98,98) ,P(98) ,R(98) WRIOO300 COWON/ / EC(49,10) ,TAUYY(49,10) TAUXX(49,10) WRI00400 11: COWON/ CEPSYY(49,10) ,CEPSXX(49 ,DEPSYY(49,10

, WRI00500 l 12: DEPSXX(49,10) ,T(49,10) ,10) , SIGMA (49,10))

13:

COWON/

COWON/ ,PHWD(49 ,V(49 WRI00600 WRIOO700

)

WODD 49) 1 14: C M ON/ W(49 ,VD(49) ) ,WDD( WRIOO800 15: COWON DNYI ) ,DMYI(49 ,NYID 16: ) WRIOO900 COWON MYID ) ,MYIDD(4 ) ,NYI WRIO1000 17: COWON MYI( ,THET(49 ,WO( WRIO1100 18: C WRIO1200 19: CGNON/ITUTS TITLE (12) ,DIVS WRIO1500 20: COWON/IWUTS EM00 , ALPHA ,EW WRI0l600 21: COWON ITUTS PRESS ,H , RAD WRIO1700 22: COWJN IWUTS STIME ,DTMIN ,YS WRIO1800 23: COWON IWUTS WA , PSI (36) , HEAT (36) WRIO1900 24: CCWON IWUTS A6 ,A6P ,A6M WRIO2000 25: COWON/IWUTS , RELAX ,A6W WRIO2100 PT_IMEJ12) 26: COWON/ITUTS TPCT(36) ,AP, IPR %RIO2200 27: COWON/IWUTS WTYPE , PSF WRIO2300 28: C WRIO2400 29: COWON/ SETS / A(2,14) ,ZOH(10) ,COEF(10) WRIO2500 30: COWON/ SETS / COE(49) WRIO2600 31: C yRIO2700 32: COWON/PARAMS DTH , SLAM)A , BETA WRIO2800 33: COWON/PARAMS GAWA , ZETA , PHI WRIO2900 34: COWON/PARAMS QA0H WRIO3000 35: COWON/PARAMS M)IVS ,W WRIO3100 36: COWON/PARAMS M , TIME ,DTIME WRIO3200 37: COWON/PARAMS ICYCLE WRIO3300 38: C WRIO3400 39: DIMENSION KP(5) WRIO3500 40: C WRIO3600 41: WRITE TITLE WRIO3700 42: WRITE (6,511 (6,101 RAD,H ,EM00, ALPHA, EW,YS,WA, WRIO3800 43: 1 ,DTMIN, A6W, A6, A6P,MTYPE, PSF, AP, STIME WRIO3900 44: 101 FORMAT (* nEAN RADIUS =',D12.6/, WRIO4000 45: 1

• WALL THICKNESS =',012.6/, WRIO4100 46: 1

• MODlLUS OF ELASTICITY =',D12.6/, WR104200 47: 1 D12.6/, WRIO4300 48: 1 ** POISSONS COEFFICIENT RATIO OF EXPANSION= ='I,D12.6/, WRIO4400 49: 1

• YIELD STRESS =',012.6/, WRIO4500 50: 1

• INITIAL OVALITY =',012.6/, WRIO4600 51: 1 ' MAXIEN TIME =',D12.6/, WRIO4700 52: 1 ' MINIEN TINE STEP =',D12.6/, WRIO4800 53: 1

• CONSTANT RADIAL DIFF. =',D12.6/, WRIO4900 54: 1

• COEFFICIENT A6 =',D12.6/, WRIO5000 55: 1 ' COEFFICIENT A6P =',D12.6/, WRIO5100 56: 1

• MATERIAL TYPE =',I10/, WRIOS200

57: 1

• PRESSURE S. F. =',012.6/, WRIO5300 58: 1

• APPLIED AXIAL FORCE =',D12.6/, WRIO5500

, A - 16 1

01:[AUMJANIT]C.806;1 2-APR-87 16:59:26 t

909410/0 59: 1

• REQUIRED LIFE =',D12.6/) WRIO5600 60: C WIO5700 61: W I = W ID WRIO5800 62: WI2 = W I+W I WIO5900 63: RETutN WRIO6000 64: C e * * * * * * * * * * * * * * * * * * *

• WRIO6100 65: ENTRY MITE 2 WRIO6200 66: C WRI00200 67: C DOLELE PRECISION 68: C 69: IWLICIT 00lELE PRECISION (A-H,0-Z) 70: C 71: C WIO1400 72: KY = 1 WIO6300 73: KYZ = 4.WI WRIO6400 74: 500 00 590 KX=1,21,5 WRIO6500 75: KZ = KY+KYZ WRIO6600 76: JY = KY+KY WRIO6700 77: JZ = KZ+KZ WRIO6800 78: JYM = JY-1 79: WIO6900 JZM = JZ-1 EIO7000 80: KXP4 = KX+4 81: EIO7100 KP(1) = KX EIO7200

!- 82: 00 510 N=2,5 WRIO7300 83: 510 KP(N) = MP(N-1)+1 WRIO7400 84: MITE 85: 511 FORMAT (6,511) TITLE (1H1,12A6)

WRIO7500 WRIO7600 86: WRITE 87: 512 FORMA {6,512) TIME,DTIME, PRESS,A6M,ICYCLE WRIO7700 (14X,, TIME *,D15.8 2X,

• DTIME',015.8,2X, WRIO7800 1

88:

89:

1 'PRESSLRE' I WRIO7900 90: 521MITE FORMAT (6,521),015.8,2X,'

(KP(N)

(1HO,13X,1}E,5I15

,76:1,5) EWERATlRE',D15.8,'ICYCLE WRIO8000 WRIO8100 i 91: WRITE (6,523) f(K),KdY),KZ,WI WRIO8200 1 92: 523 FORMAT (1HO,13X,1HV,5X,1PSD15.4 l WRIO8300 93: WRITE (6,525) (W(K),K=KY,KZ,WI WRIO8400 94: 525 FORMAT (14X,1HW,5X,1P5015.4) WRIO8500 l 95: 600 FORMAT (20X,1P5015.4 WRIO8600 96: WRITE 6,600 (NYI K=KY,KZ,WI

' WRIO8700 97: WRITE 6,600 (MYI K ,K=KY,KZ,W  ;

WRIO8800

98: WRITE 6,600 I(K) ,K=KY,KZ, I WRIO8900 l 99: WRITE 6,600 DMYI(K),K=KY,KZ,WI) ) WRIO9000 100: WRITE ,600 ,K=KY,KZ,WI) WRIO9100 101: MITE 6,600 ,K=KY,KZ,WI WRIO9200 102: MITE 6,600 (K =KY,KZ,WI) ) WRIO9300 103: WRITE 6,600 ) ,K=KY,KZ,WI) WRIO9400 104: WRITE 6,600 ,KdY,KZ,WI) WRIO9500 105: WRITE 6,600 P(J), ,JZM,WI2 l

WRIO9600 i 106: WRITE 6,600 P(J),J=JY,JZ,NPI2) ) WRIO9700 107: MITE ,527 WRIO9800 108: 527 FORMAT 1H ) WRIO9900 109: DO 528 1,10 WRIl0000.

110: (TAUYY(K,J) K=KY,KZ WRIl0100 111: 528FORMAT 529 WRITE (10X,5HTA (6,529) J,0YY,I3,2X,1E5D15.4),WI) WRIl0200 112: WRITE (6,527) WRIl0300 1 113: DO 530 J=1,10 WRIl0400 1

114: 530 WRITE WRIl0500 l 115: 531 FORMAT (6,531) J,(TAUXX(K,J),K=KY,KZ 116: 535 FORMAT (10X,5HTAUXX,I3,2X,1PSD15.4),WI)

(16X,2H10,2X,1P5015.4)

WRIl0600 WRIl0700 i

A - 17 a- . . ,, -. .n-. - - - .

, . - , , - . - - - . . , . - . - - . , ,. ,,.,_.---.,.7 - , - - . , _ _ , , - -. - - - - . - --_ . , , ,

U1:[ALMAJANIT]C.806;1 2-APR-87 16:59:26 /

909410'o 117: MITE WIl0800 118: 537 FORMAT (6,537) (CEPSW(K,1),K=KY,KZ,WI)

(1HO,9X,8HEPSW 1,2X,1P5D15.4) WIl0900 119: MITE WI11000 120: MITE (6,535) (CEPSYY ,10 ,K=KY,KZ,W I 121: 539 FORMAT (1HO,9X, (6,539) (CEPSXX K,1)),K=KY,KZ,WI))

1,2X,1P5015.4)

W I11100 WI11200 122: MITE (6,535 WI11300 -

123: KY = KZMI ) (CEPSXX(K,10),K=KY,KZ,WI) mI11400 124: 590 CONTIMJE 125:

WI11500.

RERRN WI11600 126: EM)

WI117oo e

A - 18

1 e e t

909410/0 APPENDIX B i

q i

l d

I e

i 1

i i

l l

l i

J l

l B-1

.,_m _ 2 - - -%-

U1:[AUMJANIT]EXBPLE.IN;2 24-APR-87 10:32:26 909410/0 1: SAAFLE PROBLE MM

• 1.3 IN. , TH= 0.1 IN , ALLOY 800H 2: .1960+008 .1014-004 .4040 '12 + - 1 + 4 .0000 .1250+001 0 3: l 3 0 4: N .1000+000

.1562+004 .0000 .6500-002

.0000 ' ' m +003 .6000-006 .1000+000

.6000+001 .8000+001 .1000+002 .1200+002 .1300+002 .1400+002 6f . ,

4 8-2

.- __ - . _ . _ __ - ___m _ . _ _ _ _ _ _ _ ,_ __ _ _ _ _ _ _ _

+

J 909410/0 SAMPLE PR00LEW

.190e+80s .1814-es4 THe e.1 IN ALLOY eseH IHXTutt.0.0.=1.3IN.lese+es4.

.4eee+ese .Itte+es5 . sees e

.SeSe+ese

.1542+e84 . sees.1e00+00s .45e8

. sees 002 .1000+003 .Se00-see . lese +ees .1250+ect 3 e  !

. sees 1

. .1500+e02 .18ee+882.2000+e81 .4000+es1 .sese+est .Sege+ect .130s,0e2 .123e+002 +13ee+002 .14ee+ee2 '

1 <

t CREEP COLLAPSE LOAOING HISTORY l e PRESSURE e TIME OURATION (HRS)TO 1

FROW TEMPERATURE

) s.000000 e

. (PSI) = (DEC. F.)

1.000000+e1e e 1.25e000+S83 e 1.582ess+003 e 1 SAMPLE PR00LEW WEAN RA01US IHX Tuet. 0.D.= 1.3 IN. THe e.1 IN , ALLOY eseH WALL THICNNESS e .essese+ese

a .100000 00s WODULUS OF ELASTICITY a .19000s.004 COEFFICIENT OF EXPANSION e .381488-044 POISSON'S RATIQ e .434e00,000 i

YIELD STRESS = .121088+005 INITIAL. OVALITY a .85s000-0e2 WAXIWUW TIME a .tecesseegs WIN!WUW T!WE STEP e .Seesse-eee CONSTANT RAOIAL DIFF. a .00000s COEFFICIENT As a .sessee COEFFICIENT ASP e .300e00 WATERIAL TYPE a 1 3 PRESSURE 5. F. s .12500e+881 +

i APPLIED AXIAL FORCE = .90000s

REQUIRED LIFE a .100000,083 s

! 1 SAMPLE PR00LEW

} IHX Tuet. 0.0.a TIME .seeeeece 1.3 IN. , THe e.1 IN , ALLOY eseH ,

O M DTIWE .50000000 I e V 1 2 PRESSURE 3 .125eesse+es4 4 TEMPERATURE .15eteese*er41 CYCLE1 e.9999 4.4533-005 0.0032-005 5

I W 3.4175-e04 3.3411-984 1.2187-004 1.4901-804 c.880s 2.9597-804 2.4184-e04 1.7800-884 e.0000 e. sees 0.0008

e. sees e. Gees e ecce s. eses

e. sees e. sees e.3000 e. sees e.cose e.0000 e.0000 e. sees e.90ee 0.0000 e.Sece i 3.4413-se4 3.3244-004 2.94e2-0e4 9.0000

e. sees e.sese 2.4333-ee4 1.7200-804 l e.eese e.0006 0.0000

-1.3870-093 -1.32e4-es3 -1.1e39-e03

-2.0068-092 -9.ses2-e84 -0.e351-004

?

-2.5114-est -2.2517 002 -1.8385-802 -1.3898-882

-e.7642-see -0.5337 098 -5.8508-0e8

e. sees e.0006 -4.7838-808 -3.3821-ece '

i 4.0000 0.000s

-6.7642-908 -e.5337-see -5.85s0-ee8 8.rees

-4.7839-ees -3.3821-006 TAUYY 1 -1.1281+004 -1.1173+fe4 TAUYY 2 -1.091e+0e4 1.0858 804 -1.e350+es4 -9.7020+e83 TAUYY 3 -1.e823+s94 -1.e544 884 -1.0100 004

-1.8294. -1.e224+ -1.0007+s94 -0.1213+883 i TAuYY . 9. 4 79, +.484 3 -9. m e..e84 03

-9.081e+es: -9 211 TAUYY 5 -0.5209 883 -9.2902.es3 -9.8029+003 -e.se2.7+003

.S 3 TAUYY e -e.5151+003 -0.4748 003 -e.4108+ee3

-7.5358 e03 -T.5550+eS3 -7.8147+e93 -0.327e*es3 TAUYY 7 -4.5858 003 -e.83T4+ees =F.7084+e03 -T.8384+ee3 TAUYY e -5.7643+ess -e.7913 003 -T.8380+e83 -7.3558 003 TAUYY 9 -5.84e6 983 -0.0423+003 -e.4571+e83

-4.147s.003 -5.24e5,463 -5.5480 003 -e.945e+083 TAUYY te 4.Tp4e+ees -4.8979.ees -e.0193+003 -8.83ee+se3

-5.2310+#e3 -5.702e+ee3 -0.4545+ee3 TAUXX 1 -5.8758+883 -5.8325 003 TAUXX 2 -5.5e61+es2 -5.3825+883 -5.8385+883

-5.5293 003 -5.4968 003 -5.3701+e83 TAUXX 3 -5.2791+4e3 -5.2492+863

-5.1988 e03 -4.9852+es3 TAUXX 4 -5.1615+003 -5.8219 803 -4.ede1+e03

-4.3404+ees -4.9297+4e3 -4.875e+ee3 4 TAUXX 5 -4.5642+043 -4.5587 003 -4.7881 003 -4.874T*e03 TAUXX e -4.163e+ee3

-4.5424 893 -4.5184+003 -4.4e20 003 TAuxX 7 -4.1711+ees -4.1949+ee3 -4.2327+0e3

! -3.7789+ee3 -3.Seel+ee3 -3.e622 003 -4.2829 003 TAUXX e -3.4481+eet 3.40e6 993 -3.9411+s93 =4.coes.ee3 TAUXX 9 -3,1gTg+eg3 -3.576eeee3 -3.72T2+883 -3.9248 003 j -3,23gg,eg3 -3,36g1+es3 -3.gge3+eg3 l TAUXX 10 -3.8513+063 -3.79g5+ee3

-3.0973+403 -3.2321+083 -3.444e+e03 -3.T202+es3 l

I

}

i i

8-3 t

i I

u_ -

-' ~~ ~ ' ' ~ ~ ' '

__ _ m _ -_.____.m ___ - _ _ _ _ _ _._m . . _ _ _ _ _ _ _ _ _ _ _ . . _ _ - ._ _ _ _ _ _ _ _ .. _ ___

4 e 909410/0 1 +

P 1

i I

l

~ [

+

e EPSYY 1 S.0000 0.0000 0.0000 0.0000 e.0000 l SS 8.8000 9.80e9 e.0000 0.0000

, e EPSXX 1 S.9000 e.0000 0.0000 j 0.0000 0.0000 0.0000 to 4.0000 9.0000 9.8000 8.8888 1

1 SAkPLE PR00LEM INX TUGE. 0.0.s 1.3 IN. S. Sees I THe 4.1 IN , ALLOY seSH T1WE .99900009 OTIME .s8000000 l

9 N e 7 PRESSURE .12500000+004 TEMPERA 7URE .15820seS+es41 CYCLE 1 0 V e . 9 19 1

1.8020 804 1.7280-804 1.8828-884 1.4901-884 i

W 3.0452-905 2.8972 913 1.2187-804

=8.0452 885 -1,7000-8e4 -2.4108 884

' 0.0000 0.0000 e.0000 8.8085 O.8000 S.8000 e.8000 i S.8089 0.0000 0.0000 8.8000 0.8000 0.8000 e.0000 i 8.0000 S.0000 0.808e j 8.0000 0.0000 0.0000 8.9004-885 2.3000-813 -0.0000-805 *1.7208-804 0.0000 e.0000 =2.4333 004 0.0000 e.8088 0.0000 3.5381 484 1.0523 812 3.5301-404 8.0351 884

=e.7293 883 =2.5794-811 9.8842 804 8.7293 003 1.3000-882 1.8385-892

=1.7587=006 4.7107 815 1.7587 000 3.3021 000 S.0000 0.9000 4.7830 808 0.8006 0. Sees e.0000

, =1.T5ef 004 -4.T1ST.815 1.75e7 488 3.3821=eSe 4.7e30 000 TAUYY 1 5.941S+e03 -0.1250+883 -7.3002+803 TAUYY 2 -0.0470+003 -4.5472+404 -5.8934+493

=0.1250+883 =7.4822+093 =4.7297*003 4.1583+883 i

TAUYY 3 =5.4875+483 4.125e+093 7.5825+083 TAUYY 4 =0.4764+003 .T.0303+493 =0.5082+003

-i 8.1250+003 7.7744+003 =7.4470+003 7.1871+s83 TAUYY 5 .e.2295+083 =0.1258+003 =0.8205+003

-7.923e+403 TAUYY a -7,9725+ee3 4.125e+883 -7.0394+883 TAUYY 7 -0.2775+e83 =0.4198+003 -F. 5418+003

=7.7204+003 =8.125e+483 =e.5234+093 i TAUYY e ~7.5145+4e3 .e.0950+093 =0.214e+483 4 4.1250 883 =0.7385 003 =9.3044+483 =e.7929+883 TAUYY 9 -7.3542 883 =0.1250+883 .e.9950+093 TAUYY 10 -7.2003+883 =9.814e+883 1.8231+894

=0.1250+803 =e.900T+003 =e.7955+483 -1.4437+004 TAUXX 1 4.7318 0e3 -4.4810+483 -4.0711+483 l TAUXX 2 =4.8931+003 4.4810+003 -3.7830 003 3.4998+883 4

TAUXX 3 4.1999+003 3.83egee03 3.8833+S83 i -4.6203+463 4.4 ele +S83 4.1730+003 3.9020+003 TAUXX 4 =4.542T+S83 4.4810+883 3.7002+403 TAUXX 5 4.2594+483 4.1274+003 4.014e+883

-4.4433+893 4.4010+883 4.3500+893 4.3195+003 TAUXX e =4.3394+083 +4.491e+803 =4.2857+403 TAUXX 7 4.4020+083 4.5201+083 4.5494*ee3

-4.2400+e83 =4.4810+403 4.5421+003 4.7121*e03 TAUXX 0 -4.1544+003 4.4619 003 4.0410*003 TAUXX 9 -4.0477+083 4.0775+403 5.s749+ee3 4

i

~4.0097+003 4.4810+8e3 4.7124*e03 5.0e20+003

' TAUXX 10 -4.9517+883 -4.4810+883 5.2510+0e3 s EPSYY 1 0.0000 4.7584+003 5.9759+003 =8.3555+003 8.eSte 4. sees 8.0000 0.0000 le 8.0000 0.000e e. sees 0.0000 e EPSXX 1 0.0000 0.0000 0.0000 9.0000 0.eSee 8.000s 10 S. sees e.eece e coes 1

1 SAWPLE PR00LEM IHX TUSE. 0.0.m 1.3 IN. 0.000e e. sees i THe e.1 IN , ALLOY SeSH TIME .00000008 DTIME ,.r3000004 e M 11 12 PRES $URE .12500e80+e94 TEMPERATURE .15420000+ee41 CYCLE 1 1 e V 13 14 15 0.0032-005 4.4533-805 2.3701 013 4.4533 000

{ W =2.9507 804 -3.Je11.e84 -0.0832-885

=3.4175-804 -3.3811 004 2.9597 004 0.000s S. Sees S. sees S. sees i

s.SeSe S. sees e.eOSS e.eece 9.e00s 0.0008 S. Sees e. Sees S. sees S eees 0.000s S.8088 8.0000 e.8000 0.000e

-2.9002-004 -3.3248-804 e.8000 0.000s

-3.4413-404 =3.3248 404 =2.9802 004 1

8.0000 0.0000 e. sees e.0000 1.1939 003 1.3204 003 1.347e-803 1.3294-003 2.251F.002 2.5114.ee2 1.1939 883 5.8508-800 2.8000 002 2.5114-002 2.2517-892

0.5337 000 e.7842-800 e.5337. Gee 5.8508-808

8. sees S.seSe e. Sees S.eSoo 5.8500-800 e.5337 888 S.eOSe 8.7842-004 e.5331 884 5.0588-400 TAUYY 1 5.3921+863 5.9780+003 .4.9493+083 i TAUYY 2 5.7985+983 5.0700+e83 5.3921+#83 5.4275+883 5.3323 083 5.4275+883 5.7985+#e3 j TAUYY 3 -4.2428*ee3 4.9266 963 5.9510+s83 TAUYY 4 4.9510+883 4.0250+e83 0.2428+093

.e. ele 4+ee3

.e.7783+ces .e.0184 003 .s.9510+083

\

i B-4 1

4 4

1

909410'/0 TAUYY 8 7.7752+e83 7.7349+883 7.7211+ess -7.7349 003 7.7752+493 TAUYY e .e.ess3+ee3 .G.0941+es3 .e.7142+893 .e.0941+083 -0.6353+083 TAUYY 7 9,4507+ess .e.612e+e03 9.0060+0e3 8.812e+003 =0.4507+0e3 TAUYY a =1. ele 8+ee4 =1.e4e3+ee4 1,e4e4+ee4 1.e4e3+ee4 1.etse+ee4 TAUYY 9 .g,efe4+ee4 .g,ge01,se4 1.1103+es4 1,1ee1+es4 1,spe4+eed TAuYY le =1. tete +ese 1.1352 804 -1.1464+884 1.1352+884 =1.1ste+ee4 TAUXX 1 =3.2989+es3 3.1499+ee3 =3.12el+003 =3.1998+Sc3 =3.2909+003 TAUXX 2 -3.4240+003 3.3113+483 *3.2720+0e3 -3.3113+883 -3.424S+ee3 ThuxX 3 3.e4eG+e03 3.8529+083 *3.823e+803 -3.5529+403 =3.0490+883 TAUXX 4 -3.9271+e03 -3.0724+003 -3.es37+ee3 3.0724+0e3 3.e271+003 TAUXX 5 -4.2697+003 4.2434+e83 -4.2379+003 4.2434+003 =4.2597+0e3 TAUXX e 4.6e 72 *ee3 .4.031e+ssa 4.0391+003 .4.631e+803 4.0872+083 TAUXX 7 4.9399+ees .g.sete+0e3 =8.8232+093 5.e02e+e03 .4.9399+e03 TAUXX e 6.2203+s83 8.3215+ess 5.354e+883 5.3216+s83 5.22e3+s03 TAUXX 9 5,443e 003 .g.ge31+es3 5.0041+0e3 8.5031+003 5.443e+e03 TAUXX to .s.syse+ess .g.7ese+ees .s.75e0 003 .g.7e4e.003 8.67es.003 e EPSYY 1 e.sese e. sees e. sees e. sees 5.0000 1e 0.esos e. sees e, sees e. sees e. sees e EPSXX 1 s sese e. sees e. sees e. sees e. sees le e. sees e. sees e. sees S.sese e. sees 1 SAWPLE PRoeLEW IHX TUet. 0.0.m 1.3 IN. THe 0.1 IN , ALLOY SeeH TIME .sesseees 0 TIME ,.00000000 PRESSURE +12880ese+es4 TEMPERATURE .15028888+ee41CYCt.E 1 e M to 17 le 19 2e e V =1.21ef.es4 1.49et.ges =1.0010 004 1.7200 084 *1.0828 .

W 2.4144 004 1.789e.404 -0.e442 005 -2.6112 113 0.e482

c. Gees e. sees 0.000s e. sees e. sees e.e000 e. sees e. sees e. sees e.eGee

e. sees e, sees e. esse e. esse e. sees

e. Gees e. Sees e, sees e. esse e,seeg 2.4333.e04 =1.7200 004 =0.9004 006 2.373e 813 0.9008 006

e. sees e. sees e.eSee e.00ef e. sees 9.6002 0e4 0.e3f1 004 3.5381 8e4 3.384. 812 3.5381 884 1.0385 002 1.3e00 002 e.7293 003 7.737*.011 0.7293 003 4.703e.ees 3.3921 800 1.7507 000 2.81~2 414 =1.7507 000

e. Sees 8.000e e.seet e.se e e. Sees 4.7038 884 3.3821 000 1.7587 000 2.8*J2 014 1.7607 000 TAUYY 1 5.e93e+003 .G.5472+s93 7.3002+S83 .e.t.88+883 .e.9410+883 TAUYY 2 .e.1583+003 .e.7207+083 =7.4822+003 -e 250+883 =e.e470+8e3 TAUYY 3 .G.5802+e03 7.e303+e83 -7.8026+e83 0 .258+083 8.6875+883 TAUYY 4 -7.te71+se3 =7.44Fe+ee3 7.7744+003 8.1258+083 =0.475e+083 TAUYY $ =7.8394*ee3 7.9230+eG3 .e.02e6+093 -0.1254*e03 =e.2295+483 TAUYY e .e.541e+883 =e.4194+ee3 =0.2776+S83 =0.1288+003 -7.972E+8e3 TAUYY 7 0.214e+se3 -8.8968+0e3 =0.823e+003 0.125e+003 =7.7264+983 TAUYY e 9.7929+S83 9.3844+0e3 .e.735E+883 .e.1*50*893 =7.814E+S83 TAUYY 9 1.e231+884 =9.e14e+093 .e.095e+883 =0.1258+003 =7.3642+803 TAUYY 10 -1.e407+004 -0.7965+003 -0.9097+e33 0.1258+003 =7.2003+s83 i TAUXX 1 -3.4998+s83 =3.703S+003 4.e711+8e3 =4.4 ele +ee3 4.731eese3 I

TAUXX 2 -3.es33+ee3 3.03e9+ee3 4.199e+003 4.4ste+ee3 4.0931*ses TAUXX 3 -3.7082+003 =3.9420*ee3 4.173e*e03 -4.431S*803 -4.02s3+803 TAUXX 4 4.014eese3 -4.1274 003 =4.2594+003 4.4ete+0e3 4.5427+003 TAUXX $ 4.2857+003 =4.3195+003 4.3600+e83 - 4.4818+083 -4.4433+s83 TAUXX e =4.5094+s83 4.52e1*003 4.4020+003 -4.4Gle+003 4.3394+ee3 TAUXX 7 -4.e41e+003 =4.7121 083 4.5421+e03 4.4010+s83 4.2400+e83 TAUXX e .g.0749+es3 .4.8775+es3 4.e477+883 4.481e 003 4.1644*0e3 TAUXX 9 5.251e*e03 .E.002e 003 -4.7124*se3 4.4010+s83 -4.0097+8e3 TAUXX le 5.355E+e03 -8.0759+883 4.7584+883 4.4810+003 -4.8617+e03 e EP5YY 1 e.0000 e.seee 8.0000 0.0000 8.e006 le e.Sese e. Sees e.eGee 8.0000 0.000s 9 EPSXX 1 s. sees e.eees e.0000 e. sees e. sees le e. Sees e. Sees e.80ee e.0000 e.sese 1 SAWPLE PROBLEW IHX 70et. 0.D.s 1.3 IN. 7He e.1 IN , ALLOY seeH 71WE .eeeeeees DT!WE ,.00000099 PRES $URE .12599000+004 TEWPERATURE .18620ece+0041 CYCLE 1 e M 21 22 23 24 25 e V 1.4941 8e4 =1.2167 004 .e.0e32 806 .4.4533 006 0.0000 B =. 5

I l

. 4 l

+ 909410/0 W 1.7ett -884 2.4184-ee4 2.959T-904 3.3811-904 3.4175-804 0.e#ee e. Sees e 9000 0. sees e,0000 0.0000 e.Sete e. sees e.0888 0.0000 0.0000 e.0000 e. sees S.sese e.0000 0.0000 8.0000 0. sees 8.0000 8.0000 1.7204-004 2.4333 804 2.9042-804 3.3248-804 3.4413-884 e.000e e. Sees e. Sees S. Sees e. sees

=4.0351 884 =9.8842-884 -1.1839-803 -1.3204-803 =1.3478-803

-1.3000-892 =1.03e5 882 =2.2517-802 =2.5114-Set =2.8000-802

-3.3021 000 -4.7038-804 -5.05ee-80s =e.5337-See =0.7842-008 0.0000 0.0000 e. sees 0.0000 S. sees

-3.3021 006 4.7030-800 =5.0588-60s -4.5337-806 -4.7842 000 TAUYY 1 -9.7820 003 -1.935e+ee4 -1.0060+s84 -1.1173+es4 =1.1201+es4 TAUYY 2 =s.5213+e83 =1.elee+ee4 =1.0544+884 -1.es23+ee4 -1.091S+e94 TAUYY 3 =0.2117 003 =0.0010+003 -1.000T+884 -1.8224+004 =1.0298+8e4 TAUYY 4 =0.0024+083 =9.0829+e03 -0.2902*e83 =0.433e+083 -9.4797+e83 TAUYY 5 -0.327e*SG3 =e.4100 0e3 -e.474s+ee3 =e.5151+ess -0.5209 003 TAUYY e =7.e384+0e3 =7.7894+883 =7.e147+883 -T.5559+ee3 -F.535e+083 TAUYY 7 =7.3558+8e3 =7.8300+e83 -4.7913+003 -4.8374 803 4.5850+e83 TAUYY 0 4.9458+e03 4.4571+983 -e.0023+003 5.e444+es3 =E.7e43+eG3 TAUYY 9 =0.0300*003 4.0193+003 -5.5480+883 -5.2485+ees =5.1470+e03 TAUYY le -4.4545+083 5.702s+esa -8.231e+s83 -4.0979 003 =4.704e+ess TAUXX 1 -E.8305+8e3 -5.302E+893 -5.5881+003 -5.032E+ee3 5.4750+e03 '

TAUXX 2 4.9452+003 5.1980+083 =6.3751+883 5.490s 003 -5.5293 003 TAUXX 3 4.0401+ee3 -5.8219+003 -5.1815+883 5.2492 883 5.2791+003 T'UXX 4 =4.e747+003 =4.70e1+883 =4.0750+083 4.9147+003 TAUXX 5 4.4826 883 -4.9404+S83

=4.5184+ees -4.5424+e83 4.5587+003 =4.5442+883 TAUXX e =4.2920*ee3 =4.2327+883 =4.1948+e83 -4.1711+883 =4.1e38 883 TAUXX 7 =4.0909+e83 =3.9411+883 =3.0822+8e3 =3.0001+e03 -3.7789+ee3 TAUXX 0 -3.9248*083 -3.7272+083 -3.5750+S83 3.4000*893 -3.4481+883 TAU 1X 9 =3.7998+e83 -3.5583+#e3 -3.3591+003 -3.2309+003 TALXX 18 =3.7262+e03 -3.1979+883

-3.4484*SS3 -3.2321*003 -3.e973+e03 -3.9613+403 e EP3YY 1 e. sees e. sees e. sees 0.0000 e.eees e. sees le e.0000 0.0000 0.0000 e.Sese e EPSXX 1 c.8888 s.0 Gee S. Sees e. sees 8.0000 le e.0099 0.0000 e. sees e. sees e. sees THE TU8E HAS CCLLAPSED AFTER .25995943+e81 HOURS 8ASED ON TIELO LIMIT Na 25Je le 1 SAWPLE PROSLEW IHX TU8E. 0.0.e 1.3 IN. THe e.1 IN , ALLOY SeeH TIME .25995943+#el 071WE

.42589538-892 PRESSURE .12500000+e04 TEMPERATURE .15420000+0841 CYCLE 205 8 K 1 2 3 4 5 e V G.000s 1.9840-ee3 3.8994 003 5.2772-003 e.5482-ess W 1.7128 802 1.8500-882 1.5019-882 1.2580-802 9.4243-003

=0.5939+883 -9.1205 003 =7.9093 893 =0.334e+4e3 -4.7454+ee3 2.3413+082 2.2810+es2 1.0350+882 1.3017 002

-3.8252 8e1 9.5555+e81 3.5230+e41 =2.7973 001 =1.9000+0e1 =1.2790+ect 1.0920+ees 1.e978+008 7.0426-881 4.9259-881 2.8824-001 1.4692 002 1.4271-e82 1.3814-082 1.e965-902 0.2288-es3 0.0000 =2.0802+002 =3.3009+002 -3.3909 892 =3.1971+002

=e.3651 002 as.e438-SS2 5.1782-002 =4.e424-es2 =2.8T43-e92

=2.8000-802 =2.5114-882 -2.2517 002 =1.e305 982 -1.3000-002 4.7042-894 -e.5337-see -5.9588-004 -4.703e-006 -3.3821 006 s.Sese 1.e466-883 3.0134-883 3.3413-ee3 3.0384-es3

-3.1698 883 =2.9155-003 =2.248T-883 =1.5213-883 =1.1293 903 TAUYY 1 =1.3550+884 =1.3371 004 -1.2842+884 =1.1983+004 -1.183F+004 TAUYY 2 =1.3301 004 =1.3294+004 =1.2302+004 =1.194c+004 1.091e+004 TAUYY 3 =1.380F+884 =1.2094 004 =1.2305+004 =1.1575 004 TAUYY 4 =1.2504+004 -1.0875 984

=1.241T+004 =1.1920+884 =1.1171+004 =1.8319+004 TAUYY 5 -1.1975+684 =1.171e+ee4 =1.128e+004 =1.9509.se4 TAUYY a =1.8084+#e4 =9.e112+s63

-1.0658 884 -1.8250 004 =9.745E+ees =9.0935+ee3 l

TAUYY 7 =0.7844+e83 -0.8408*e83 =0.4403+983 =S.3892+e83 TAUYY 0 1.5582 883 -T.9804+ee3 I

5. 208 7 + 482 -2.2831+983 4.7573 083 5.6503 003 TAUYY 9 1.e255 884 1.9996+004 9.4662+993 8.9847 043 TAUY1 le 1.8844 884 0.4310+e82 1.8896+ee4 1.8100+ee4 9. sele +ees e.3 eel +#es 8-6 ,

i

+

909410'0/

j TAUXX 1 -4.7853+983 -8.8972+993 -6.4374+983 -4.8237+083 .E.5765+983 TAUXX 2 6.7922+983 -8.8152+0e3 -4.3594+983 -8.9558 883 =5.5171 993 TAUXX 3 -8.5475 003 -6.4627+983 -6.214E+983 -5.8279+893 -E.4679+993 TAUXX 4 -e.310E+983 .g.2293+0e3 5.9934+983 .E.8382 003 -5.245e+0e3 TAUXX 5 -5.960s+003 -5.8992+983 -E.6745 993 -5.3652+983 -E.0194+983 TAUXX e -5,459e+0e3 -8.3920+983 -5.2137+983 -4.99e1+0e3 -4.72e1+993 TAUXX 7 -4.gget,og3 4.34g1+983 -4,473e+993 4.4538 983 -4.3200+e83 TAUXX 0 -1.1475+0e3 1.5347+993 -2.5439 993 -3.4580+983 -3.7220+003 TAUXX 9 4.5933+983 4.3778+983 3.4496+983 1.9857+983 -1.6954+983 TAUXX to E.2140 003 5.1999+993 4.8473+983 3.4817+983 7.e784+#82 e EPSYY 1 -1.0178-902 -9.0123 003 -0.1466-943 -0.2972-963 -4.4978-903 le 1.4783-903 1.3166-903 0.0027-904 3.8751-984 -1.3173-905 e EPSXX 1 -4.6103-905 -4.6991-905 -4.9343-905 -5.2779-995 -5.8192-995 10 -1.5587-904 -1.5316-964 -1.4859-984 -1.0182-904 -1.9480-905 1 $AWPLE PROBLEW IHX TUBE. 0.0.s 1.3 IN. , 7We 0.1 IN , ALLOY 899H TIWE .2599E943+981 DTIME .+tss9534-Se2 PRESSURE +125000e8+004 TEkPERATURE .154200ee+es4ICYCLE 266 0 K e y e 9 le e V 7.49E9-903 7.8962-003 7.0061-903 7.e2O3-903 5.9302-903 W 5.7804-903 1.670s-Sc3 -2.8826-903 -5.0152-983 -9.9936 903

-3.4730+993 =2.9585+983 -3.6283+993 5.2294+983 -7.3079+983 5.3927+981 1.0584+00s -6.5476+961 -1.0368 992 -1.5571+982

-7.4934*ees -4.8288+000 7.3123+ece =1.3619+861 -2.2777+981 1.5443-901 1.0288-902 -1.4283-901 -2.9139-901 -5.3294-901 4.9148-963 1.1291-903 2.9994-003 -7.1443-903 -1.9966-902

- 3. 5000 + 982 -4.4199+062 -3.9559+982 -3.7867+982 -4.1999+992 .

-1.8678-902 2.1513 903 1.3094-002 2.6479-802 4.9059-902

-4.7293-983 =2.5794-811 0.7293-903 1.3998-062 1.0305-092

=1.7587-884 -6.7187-015 1.7587-906 3.3021-906 4.7830-900 2.1002-903 8.5138-905 -2.2422-963 -3.5883-903 -4.8943-903

, =1.2411-902 -0.4101-904 -5.5884-904 -1.4768-903 -1.9514-963 TAUYY 1 -1.De27+0e4 -e.3671+es3 -3.5517+883 E.5922+983 8.8783+983 TAUYY 2 -9.9144+983 -3.348e+8e3 6.e513+003 -4.8037+992 5.9040+983 l TAUYY 3 -9.7872+ee3 -0.2931+883 -8.561e+983 -6.3443+9e3 -E.9434+983

TAUYY 4 -9.3950+S83 .e.2295+S83 =7.8244+es3 -8.2369+983 -8.7087+983 i TAUYY E -8.9547+s83 -0.1523+e93 -0.3789+993 -9.2374+993 -1.9031+004 j TAUYY a -0.3464+ee3 -e.eTee+es3 -e.9154+983 -9.9126+S83 -1.9829 964

TAUYY 7 -7.4727 9e3 -7.9889+8e3 -0.3192+993 -1.0398+984 -1.1391*e64

? TAUYY O -0.1245+003 7.9168+983 -9.6093+893 -1.0742+994 -1.1785+984

TAUYY 9 -4.1133 983 -7.0693+883 -0.8833+#83 -1.897e+004 -1.284E+984 TAUYY 18 -2.24e2+ee3 -7.82ES+0e3 -9.pese+0e3 -1.1893+984 =1.2185+004 TAUXX 1 5.1163+ses -4.4411+9e3 -3.8220+983 3.1974+982 3.3298+e83 TAUXX 2 -E.8666 883 -4.4309.e83 -3.4716 003 -2.134t+983 4.4552+ee2 TAUXX 3 -4.970e+ee3 .4.4132 003 -3.0561+#93 -3.9185+983 -3.7081.se3 TAUXX 4 -4.843s+ee3 4.3e92+e83 4.1917+993 -4.4872+S83 -4.6834+863 TAUXX 5 -4.6637+ee3 -4.3686*es3 -4.4414+093 -4.7777+003 -5.1149+e83 TAUXX 6 -4.4352+ee3 -4.3258+e83 -4.6474+983 -8.964e+es3 -E.4774+993 TAUXX 7 -4.1464 003 -4.2993+983 -4.8120 003 -5.2826+963 -E.7417+eS3 TAUXX e 3.7512*ee3 4.2722+883 -4.9352+883 -5.4487+483 -5.9290+083 TAUXX 9 -3.1464 963 -4.2612+983 -5.8196+983 -E.547e*893 -6.0549+983 TAUXX 10 -2.5293+s83 -4.2386+983 -E.9681 003 -E.6868+883 -6.122T+883 S EPSYY 1 2.852T-903 1.2658-963 -2.4358-864 -2.2168-095 3.7957-Se4 13 -2.4520-084 -1.2118-883 -2.9478-903 -4.8978-8e3 7.1451-963 0 EPSXX 1 -E.eTe9-eeE -5.9012-ee5 -3.2838-se6 -1.4314-Se5 =1.8864-884 18 -3.8332-995 -E.8178-896 -E.8995-005 -6.5020-905 -5.1888-905 1 SAWPLE PROSLEW IHX TU9E, 0 D.= 1.3 IN. THe e.1 IN , ALLOY 8eeH TIME .2599E943+eet DTIME ,.42589536-082 PRES $URE .12Escoce+0e4 TEMPERATURE .1562960e+8e41 CYCLE 265 0 N 11 12 13 14 15 0 V 4.1814-983 2.1955-883 -2.1316-012 -2.1855-983 -4.1814-963 W =1.1685-062 =1.3363-882 -1.3944-882 -1.3363-882 -1.160E-882 9.4291+e83 -1.1101+884 -1.1748+004 =1.11e1+984 9.4291+983

-2.1226 862 -2.6810+ee2 2.7872+982 -2.6816+8e2 -2.122S+es2

-3.3450+e61 4.3484+881 -4.7601 801 -4.3484+881 -3.3450+081

-0.0083-e01 -1.1995 966 -1.304E+ese -1.1896+008 -8.8983-081

-1.4093-082 -1.6199-862 -1.8947-e82 -1.6199-882 =1.4e93-ee2 4.2987+882 -2.73e3+es2 -1.4215-883 2.7383*e82 4.2900+e82 1

B-7 1

.- , -~ _ - _

. . . _ . . - . . - ,- . _- .- , _ .. ~_. . _ _ _ _ - -

+

+

9}9410/0 t

5.3819-962 8.4409-9e2 e.8414-902 8.4409-902 5.3819 982 2.2517-892 2.5114-802 2.0000-902 2.5114-002 2.2517-882

' 5.8598-906 8.5337-Pe8 c.7842-006 8.3337-See 5.8586-906

-3.7185-993 -2.3175-803 -4.8188-0e9 2.3178-083 3.7185-De3

-2.1985-903 -2.9839-903 -2.8280-903 -2.9839-903 -2.1985-903 TAUYY 1 1.82st+0s4 1.0e33+e04 1.1811+004 TAUYY 2 1.0833+984 1.0281+e04 9.34s4 9e3 1.e170+0e4 1.e381+004 1.917e+0e4 9.3404+983 TAUYY 3 -4.1895+983 -1.8102 403 -4.0127+982 TAUYY 4 -0.015S+983 -1.8162+083 -4.1995+883

-9.2643+083 -0.3937+p83 -0.2844+083 -0.015S+883 TAUYY 5 -1.9835+984 -1.1898+984 -1.1288+984 TAUYY 8 -1.1593+984 -1.1998+004 -1.9835+894

-1.2127+004 -1.2313+884 -1.2127+984 -1.1593+884 j' TAUYY 7 -1.2248+984 -1.2021+994 -1.3810+004 TAUYY $ -1.2897+984 -1.2921+es4 -1.2248+984

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TAUYY 18 -1.3150+884 -1.3889+004 -1.2992+984

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TAUXX 4 -4.8892+0e3 -2.2053+993 -3.1538+s83

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TAUXX 8 -5.834e+003 -5.8787+983 -5.5978+983 5.3082+0e3

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TAUYY 1 8.8783+963 5.5922+983 -3.5517+883 f

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TAUYY 4 -8.7067+883 -8.2369+es3 i

TAUYY 5 -1.fe31+ee4 -7.6244 883 -0.2295+993 -9.395e+883

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TAUXX 3 -3.4718+993 -4.4309+0e3 -5.8666+993

-3.7881+883 -3.9105+083 -3.0861+003

TAUXX 4 -4.6834 883 -4.4132+993 -4.9768+ee3 TAUXX 5

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-4.9*52+e83 -4.2722+883 -3.7513+883 P

8-8 9

r

I j

4 I

909410/0 l l

4 1

3 t

4 TAUXX 9 -0.0549+es3 TAUXX 10 -5.5478 083 -5.e199+ee3 4.2512+983 e -e.1227+ee3 -5.8950+es3 -5.ees t +ess -3.1484+0e3 EP$YY 1 3.7957-9e4 -4.2387+s83 -2.5293 883 le -2.2148-005 -2.4358-004 -1.2658-9e3 e -7.1217-003 -4.8837-883 -2.9483-803 -2.8527-883 EPSXX 1 -1.pe84-es4

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M Y

21 OTIME 22 -,.42589538-882 23 PRESSURE 24

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-2.8743-882 -4.8424-862 -5.1782-te2 e. Sees

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TAUYY 2 -1.1993+894 -1.2842+8e4 -1.3371+s94

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-2,2831 003 5.2813+ee2 1.5542+s83 TAVYY le 4.9647+s83 9.4653+S83 1.9894+004 4.3est+ee3 9.seSe+ess 1.ette+es4 1.8255+e84 i 1.9696 004 1.0844+es4 TAUXX 1 -5.5765+483 TAUXX 2 -0.8237+es3 -6.4374+#e3

-5.5171 003 -5.955e+ee3 -6.8972 003 -4.7853+e83 i TAUXX 3 -5.4879+083 -e.3594+893 -6.6152+883 -6.7822+0e3 TAUXX 4 -5.5279 003 -6.2145 003 -6.4627+ee3

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TAUXX 8 -5.3652+e93 -5.8745+483

-4.7201+983 -4.99e1+003 -5.8902 8e3 -5.9668 883 TAUXX 7 -4.3200+e03 -5.2137 003 -5.3928+963 -5.459e+ee3 TAUXX a -4.453e+ee3 4.4F3e+s93 -4.5491 083 3.7228 883 -3.4580+ee3 -2.5439 003 -4.5901 883

' TAUXX 9 -1.se64+es3 -1.5347 003 -1.1475+es3 TAUXX le 1.se57+ees 3.44e5+ess e 7.87e4+882 3.4817+es3 4.3778+se3 4.5933 003 EPSYY 1 -4.4978-se3 4.6473+es3 E.1999+e83 5.2148+883 le -6.2972-863 -0.1468-es3 -9.8123-903 e -1.4803-095 3.8314-Se4 8.7952-994 -1.8178-892 EPSXX 1 -5.8102-895 1.3046-903 1.4845-003 18 -5.2779-885 -4.9343-095 -4.6991-805

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-1.5283-094 -1.5557-884 4

k 1

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4 8-9

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