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CCMS-89-11 


VIRGINIA TECH 


CENTER FOR 
COMPOSITE MATERIALS 
AND STRUCTURES 


VPI-E-89- 14 

r . /? AJ C t’ '/ 

//J'4 /- C/t . 

rZ O/ 


RTM User's Guide 


Steven J. Claus 
Alfred C. Loos 



3 m 


Virginia Polytechnic 
Institute 
and 

State University 

Blacksburg, Virginia 
24061 


May 1989 

(NASA-CR-186091) RTM USER*S GUIDE Interim 
Report (Virginia Polytechnic Inst, and 
State Univ.) 71 p CSCL 09B 


N90-13065 


Unci as 


G3/61 0293201 




College of Engineering 

Virginia Polytechnic Institute and State University 
Blacksburg, Virginia 24061 


May 1989 


CCMS-89-1 1 
VPI-E-89-14 


RTM User's Guide 


Steven J. Claus 3 
Alfred C. Loos 4 


Department of Engineering Science and Mechanics 
NASA Grant NAG-1-343 
Interim Report 76 

The NASA-Virginia Tech Composites Program 


Prepared for: Applied Materials Branch 

National Aeronautics and Space Administration 
Langley Research Center 
Hampton, Virginia 23665 


3 Graduate Student, Department of Engineering Science and Mechanics, 
Virginia Polytechnic Institute and State University 

* Associate Professor, Department of Engineering Science and Mechanics, 
Virginia Polytechnic Institute and State University 


ABSTRACT 


RTM is a Fortran 77 computer code which simulates the infiltration of textile re- 
inforcements and the kinetics of thermosetting polymer resin systems. The computer 
code is based on the process simulation model developed by the author [1]. The 
compaction of dry, woven textile composites is simulated to describe the increase in 
fiber volume fraction with increasing compaction pressure. Infiltration is assumed to 
follow D'Arcy's law for Newtonian viscous fluids. The chemical changes which occur 
in the resin during processing are simulated with a thermo-kinetics model. The 
computer code is discussed on the basis of the required input data, output files and 
some comments on how to interpret the results. An example problem is solved and 
a complete listing is included. 


ABSTRACT 



Acknowledgements 


This work was supported by the NASA-Virginia Tech Composites 


Program at Virginia Polytechnic Institute and State University through 


grant number NAG1-343. 


1.0 Table of Contents 

2.0 List of Illustrations II 

3.0 RTM 1 

3.1 Infiltration Model 2 

3.2 Cure Model 4 

4.0 COMPUTER PROGRAM INSTRUCTIONS 7 

4.1 Interactive Input 7 

4.2 Input Data Description 8 

5.0 EXAMPLE 11 

5.1 Input Data File 11 

5.2 Program Listing 12 

6.0 REFERENCES 23 

7.0 APPENDIX A 24 

Table of Contents 1 



7.1 Main Program 

7.2 Subroutine READIN 

7.3 Subroutine PERM . . 

7.4 Subroutine RESIN 

7.5 Subroutine FTEMP . 

7.6 Subroutine H35016 . 

7.7 Subroutine S1282 . . 

7.8 Subroutine GLOBL . 

7.9 Subroutine ASTIF . . 

7.10 Subroutine FINDB . 

7.11 Subroutine BOUNC 

7.12 Subroutine SOLVR 

7.13 Subroutine STRESS 

7.14 Subroutine RECON 

7.15 Subroutine MULT . 

7.16 Subroutine CURE . 

7.17 Subroutine TRIDAG 

7.18 Subroutine HCONV 


24 

30 

34 

35 

36 

37 

38 
40 
42 
44 

46 

47 

49 

50 

52 

53 

59 

60 


Table of Contents 


ii 


2.0 

Figure 

Figure 


List of Illustrations 


1. Logic diagram for the quasi-steady state infiltration process 3 

2. Computational flow chart for infiltration and cure models 6 


List of illustrations 


II 



3.0 RTM 


An infiltration/cure model was developed to simulate the production of composite 
laminates from advanced textile fabrics and thermosetting resin systems by the resin 
transfer molding process [1]. The model is composed of two sections: an infiltration 
model and a cure model. 


The infiltration model simulates the flow of a reactive resin system into a dry textile 
preform. The resin viscosity and degree of cure are calculated from a kinetics model 
assuming the resin temperature to be the same as the applied temperature. Position 
of the infiltration front, resin viscosity, degree of cure, and velocity are calculated as 
a function of time assuming the textile preform to behave as an elastic porous me- 
dium which is infiltrated with a Newtonian viscous fluid. Results from the infiltration 

model include, 

1. Material thickness 

2. Permeability 

3. Porosity 

4. Total resin mass 

5. Position of the infiltration front 

6. Resin degree of cure 

7. Resin viscosity 

8. Resin velocity. 


RTM 


1 


The cure model is initiated when the material is completely infiltrated and is used to 
predict the changes in the resin system as the cure cycle progresses. During this 
stage of the simulation the resin is assumed to be stationary. Heat transfer into the 
composite laminate is simulated with a transient heat transfer sub-model which in- 
cludes generation of heat by exothermic chemical reactions. Results of the cure 
model include; temperature, resin degree of cure, and resin viscosity as functions 
of position and time. 

Due to the nonlinear formulation of the governing equations, the solution of the infil- 
tration and cure models was accomplished by numerical techniques. The infiltration 
model is solved by a finite element technique and the cure model is solved by a finite 
difference technique. A Fortran 'll computer code was written to solve the models 
and a listing of the computer code is given in Appendix A. 


3.1 Infiltration Model 


Solution of the infiltration model was accomplished with an eight-node quadrilateral 
finite element technique. Infiltration was assumed to occur in one direction only. 
Motion of the resin was simulated by adding an element to the computational mesh 
at each time step of length, 


A z = v z At 

where Az represents the length of the new element, v sub z represents the velocity 
at the infiltration front, and At represents the time step. A logic diagram for the in- 
filtration solution is shown in Figure 1. 


RTM 


2 




Figure 1. Logic diagram for the quasi-steady state infiltration process. 


RTM 


3 







In this numerical scheme, the time increment is calculated according to the following 
expressions, 


Af(f (+1 ) = RPos(t i+1 ) + At(Q 


for Pos(f, +1 ) < PosA, 


Af(f j+1 ) = Btime 


for PosA < Pos{t i+ i) < PosB, and 

Af(fj +1 ) = Ctime 

for PosB < Pos(t M ) < PosC where R represents the rate of change of the time incre- 
ment, Pos represents the position of the infiltration front in percent, PosA, PosB rep- 
resent two distinct hold positions, and Btime, Ctime represent two constant time 
steps. 

The required input for the infiltration model includes the temperature history and 
pressures applied to the resin and fabric. 


3.2 Cure Model 


Solution of the cure model was accomplished by a finite difference technique. Using 
the known properties of the composite and tooling materials and the applied cure 
temperature, the system of transient heat equations was solved to obtain the tem- 
perature within the composite as a function of time. The degree of cure and viscosity 


RTM 


4 



of the resin are calculated with the known temperature distribution. Figure 2 is a flow 
chart for the computations necessary for the solution of the infiltration and cure 
models. 


The necessary input parameters for RTM are as follows: 


Problem Geometry: 

1. Length of the composite 

2. Width of the composite 

Solid Material Characteristics: 

1. Number of layers 

2. Areal weight 

3. Uncompacted thickness 

4. Fiber diameter 

5. Fiber density 

6. Compaction coefficients 

7. Kozeny-Carman coefficients 

Time Step Coefficients: 

1. Thickness Fraction for the First Time Increment 

2. Thickness Fraction for the Second Time Increment 

3. Rate Coefficient of the Time Scheme 

4. First Hold Time Step 

5. Second Hold Time Step 

Applied Pressures: 

1. Autoclave Pressure 

2. Vacuum Bag Pressure 

Heat Transfer Characteristics: 

1. Number of divisions in the tool plate 

2. Number of divisions in the composite 

3. Number of divisions in the breather plies 

4. Initial temperature 

5. Total heat of reaction of the resin 

6. Thermal conductivities of each material 

7. Convective heat transfer coefficients of the boundary materials 

8. Temperature history of the environment 


RTM 


5 


TEMPERATURE 

HISTORY 


COMPACTION 

PRESSURE 


FABRIC 

CHARACTERISTICS 



Figure 2. Computational flow chart for infiltration and cure models. 


RTM 


6 














4.0 COMPUTER PROGRAM INSTRUCTIONS 


This chapter contains a line-by-line description of the input data required to run the 
computer program RTM, and some comments on how the output is formulated and 
can be interpreted. 


4.1 Interactive Input 


During execution of RTM, the names of four files must be specified. The first file 
contains the input data for the simulation and the content of this file is explained in 
detail in the next section. The last three files are output files which contain the 
complete listing, plotting data for the infiltration phase, and plotting data for the cure 
phase, respectively. An interactive prompt is given for each file name. 


COMPUTER PROGRAM INSTRUCTIONS 


7 



4.2 Input Data Description 


With the exception of input data Card 1, all input is format free. 


Value 

Description 

Card 1 (1 8A4) 

- 

ANAME 

Title of the problem 

Card 2 

NTIMES 

Number of time steps 

NTEMPS 

Number of temperature steps in infiltration 
and cure cycles 

IVSWH 

Viscosity switch 

= 1 Temperature dependant viscosity 
= 0 Constant viscosity 

IRESIN 

Resin switch 
= 1 Hercules 3501-6 
- 2 Shell RSL1 282/9470 32.4 PHR 

ICURE 

Curing switch 

= 0 Cure cycle is not simulated 
= 1 Cure cycle is simulated 

Card 3 

RLGTH 

Length of laminate 

WIDTH 

Width of laminate 

Card 4 thru Card 4 + NTEMPS 

TIMEIN 

Time of temperature change 

TAUTO 

Temperature in autoclave at TIMEIN 

NOTE: If IVSWH = 0 then substitute the cards above w 
the fluid viscosity 

COMPUTER PROGRAM INSTRUCTIONS 

8 



Card 4 + NTEMPS + 1 


NPLIES 

Number of plies of material 

ZETA 

Areal weight of fabric 

DIAFI 

Diameter of individual filaments 

RHOFI 

Density of solid material 

TUNCPT 

Thickness of uncompacted ply 

RKCC 

Kozeny-Carman constant 

PZERO 

Pressure at which d = 0 ( PZERO>0 ) 


Card 4 + NTEMPS + 2 

A(J) Coefficients of the compaction model 


Card 4 + NTEMPS + 3 

POSA 

POSB 

ATIME 

BTIME 

CTIME 


Card 4 + NTEMPS + 4 

PAUTO Pressure in the autoclave or applied by platens 

PBAG Pressure in the bleeder or dry material 

NOTE: all pressures in gage 


Card 4 + NTEMPS + 5 

NTOOL 

NPRESS 

IFREQ 

IRED 


Card 4 + NTEMPS + 6 


CPFL 

Specific heat of the resin 

CPFI 

Specific heat of the fiber 

KTFL 

Thermal conductivity of the resin 

KTFI 

Thermal conductivity of the fiber 


Number of divisions in tool plate 
Number of divisions in pressure plate 
Frequency of printout.. ..with respect to time 
Frequency of printout.. ..with respect to position 


Thickness fraction for first time increment hold 
Thickness fraction for second time increment hold 
Rate coefficient of the time scheme 
First hold time step 
Second hold time step 


COMPUTER PROGRAM INSTRUCTIONS 


9 


HR 


Heat of reaction of the resin 


Card 4 + NTEMPS + 7 

Time step for calculation during cure 
Heat transfer coefficient 


DELZ 

VEL 


Card 4 + NTEMPS + 8 


ZTOOL 

KTOOL 

RHOTOL 

CPTOOL 


Thickness of the tool plate 
Thermal conductivity of the tool plate 
Density of the tool plate 
Specific heat of the tool plate 


Card 4 + NTEMPS + 9 


ZPRES 

KPRES 

RHOPRE 

CPPRES 

NBLEED 


Thickness of the pressure plate 
Thermal conductivity of the pressure plate 
Density of the pressure plate 
Specific heat of the pressure plate 
Number of bleeder plies 


NOTE: All units should be in SI except the compaction coefficients. 


Two items which relate to the numerical solution should be discussed at this time. 
First, if the number of time steps and the time increment history are not sufficient to 
complete the simulation of the infiltration, the cure simulation will not be performed 
regardless of the value of ICURE. Second, when the infiltration simulation is com- 
pleted the numerical solution should be checked by plotting the position of the infil- 
tration front versus time. This curve should be smooth during the entire simulation. 


COMPUTER PROGRAM INSTRUCTIONS 


10 




5.0 EXAMPLE 


The simulation of the production of a laminate with 16 plies of IM7/8HS fabric infil- 
trated and cured with Shell 1282/9470 is shown in the next several sections. Tem- 
perature cycle for infiltration and cure consisted of heating the laminate from 20 C to 
80°C and holding for 1 hour. Additional holds at 120, 145, and 177°C were also used 
to completely cure the resin. A pressure of 70 kPa was applied to the dry material for 
infiltration and consolidation. 


5.1 Input Data File 


0 PSI CURE W/ SHELL RESIN 
70 10 1 2 1 
0.17145D0 0.1524D0 
0.0E + 0 20.0E + 0 
1200.0E + 0 80.0E + 0 
4800. 0E + 0 80.0E + 0 


EXAMPLE 


11 


5600. OE + 0 120.0E + 0 


9200.0E + 0 120.0E + 0 
9700.0E + 0 145.0E + 0 
13300.0E + 0 145. OE + 0 
13940.0E + 0 177. OE + 0 
17540.0E + 0 177.0E + 0 
19480.0E + 0 80. OE + 0 

16 0.4401 2896D0 4.9784D-6 1.7798D3 6.096D-4 2.8798D0 1.697894D3 
6.313D-3 -4.935D-3 1.009D-3 -4.866D-5 O.ODO 
0.15D0 0.3D0 0.5E0 0.7D0 2.0D0 
68.95E + 3 O.ODO 
8 4 20 4 

2.0934E3 7.1 176E2 0.207696E0 0.259770E2 0.288E6 
5.0E0 0.1 E5 

6.35E-3 0.20250E3 0.27074E4 0.87090E3 
3.175E-3 0.20250E3 0.27074E4 0.87090E3 0 


5.2 Program Listing 


0 PSI CURE W/ SHELL RESIN 


INPUT: 

PROBLEM PARAMETERS: 

NUMBER OF TIME STEPS 70 


EXAMPLE 


12 



NUMBER OF TEMPERATURE CHANGES 10 

VISCOSITY SWITCH ( 1 = TEMP DEPEND, 0 = CONSTANT ) . 1 

RESIN TYPE 2 


CURE SWITCH ( 0 = NO CURE, 1 = CURE ) 1 


MATERIAL CHARACTERISTICS: 


LAMINATE LENGTH 1.7145000E-01 

LAMINATE WIDTH 1.5240000E-01 


CHARACTERISTICS OF THE TEMPERATURE PROFILE: 


TIME OF TEMP CHANGE 
.OOOOOOOE + 00 
1.2000000E + 03 
4.8000000E + 03 
5.6000000E + 03 
9.2000000E + 03 
9.7000000E + 03 
1.3300000E + 04 
1.3940000E + 04 
1.7540000E + 04 
1.9480000E + 04 


AUTOCLAVE TEMP 
2.0000000E + 01 
8. OOOOOOOE + 01 
8.0000000E + 01 
1.2000000E + 02 
1.2000000E + 02 
1 .4500000E + 02 
1 .4500000E + 02 
1.7700000E + 02 
1.7700000E + 02 
8.0000000E + 01 


PRESSURES' 

~ AUTOCLAVE PRESSURE . . . 6.8950000E + 04 

BAG PRESSURE OOOOOOOE + 00 

COMPACTION PRESSURE. . . 6.8950000E + 04 


SOLID PROPERTIES: 

NUMBER OF PLIES 16 

AREAL WEIGHT 4.4012896E-01 

DIAMETER OF FIBER 4.9784000E-06 

DENSITY OF FIBER 1.7798000E + 03 

UNCOMPACTED THICKNESS. . 6.0960000E-04 
KOZENY-CARMEN CONSTANT . 2.8798000E + 00 
PRESSURE AT ZERO DEFL. . 1.6978940E + 03 


EXAMPLE 


13 


MATERIAL COEFFICIENTS. . 


6.3130000E-03 -4.9350000E-03 1.0090000E-03 -4.8660000E-05 
O.OOOOOOOE + OO 


TIME INCRIMENTS: 

TIME COEFF A 5.0000000E-01 

FIRST HOLD POSITION. . . 1.5000000E-01 

TIME COEFF B 7.0000000E-01 

SECOND HOLD POSITION . . 3.0000000E-01 
TIME COEFF C 2.0000000E + 00 


MATERIAL RESULTS: 

LAMINATE THICKNESS . . . 8.6092915E-03 

POROSITY 5.4041 980E-01 

TOTAL RESIN VOLUME . . . 1.2156852E-04 
PERMEABILITY 6.4311461E-12 


RESIN MASS 1.4077634E-01 


TEMP POSIT. OF DEGREE OF 
INFILTRATION CURE 


TIME 


.OOOOE + OO 

1.0000E-15 

6.4299E-07 

2.0689E-03 

6.2047E-03 

1.2408E-02 

2.0679E-02 

3.1018E-02 

4.3424E-02 

5.7898E-02 

7.4440E-02 

9.3050E-02 

1.1373E-01 

1.3647E-01 

1.6129E-01 

1.8817E-01 

2.1712E-01 

2.4814E-01 

2.8123E-01 


2.0000E + 01 
2.0000E + 01 
2.0000E + 01 
2.0000E + 01 
2.0000E + 01 

2.0001 E + 01 

2.0001 E + 01 
2.0002E + 01 
2.0002E + 01 
2.0003E + 01 
2.0004E + 01 
2.0005E + 01 
2.0006E + 01 
2.0007E + 01 
2.0008E + 01 
2.0009E + 01 

2.001 IE + 01 
2.0012E + 01 
2.0014E + 01 


.0000E + 00 
1.2860E-06 
4.1364E-03 
8.2716E-03 
1.2407E-02 
1.6542E-02 
2.0677E-02 
2.481 3E-02 
2.8948E-02 
3.3084E-02 
3.7220E-02 
4.1356E-02 
4.5493E-02 
4.9629E-02 
5.3766E-02 
5.7903E-02 
6.2041 E-02 
6.6179E-02 
7.0317E-02 


8.6387E-22 
1.2958E-21 
2.7773E-13 
8.9362E-10 
2.6805E-09 
5.3613E-09 
8.9365E-09 
1.3407E-08 
1.8772E-08 
2.5034E-08 
3.2193E-08 
4.0249E-08 
4.9203E-08 
5.9056E-08 
6.9808E-08 
8.1461E-08 
9.401 5E-08 
1.0747E-07 
1.2183E-07 


FLUID 

VISCOSITY 


7.2338E-01 
7.2338E-01 
7.2338E-01 
7.2337E-01 
7.2336E-01 
7.2335E-01 
7.2333E-01 
7.2331 E-01 
7.2328E-01 
7.2325E-01 
7.2321 E-01 
7.231 7E-01 
7.2312E-01 
7.2307E-01 
7.2301 E-01 
7.2295E-01 
7.2289E-01 
7.228 IE-01 
7.2274E-01 


VELOCITY 


1 . 1 07 1 E + 07 

5.5367E + 01 

1.7213E-02 

8.6080E-03 

5.7390E-03 

4.3045E-03 

3.4437E-03 

2.8698E-03 

2.4599E-03 

2.1525E-03 

1.9134E-03 

1.7222E-03 

1.5657E-03 

1.4353E-03 

1.3250E-03 

1.2304E-03 

1.1484E-03 

1.0767E-03 

1.0135E-03 


14 


EXAMPLE 



3.1639E-01 
3.5362E-01 
3.9292E-01 
4.3429E-01 
4.7772E-01 
5.2323E-01 
5.7081 E-01 
6.2046E-01 
6.721 8E-01 
7.2597E-01 
7.8184E-01 
8.3978E-01 
8.9979E-01 
9.6187E-01 
1.0260E + 00 
1.0923E + 00 
1.1606E + 00 
1.2309E + 00 
1.3034E + 00 
1.3779E + 00 
2.0779E + 00 
2.7779E + 00 
3.4779E + 00 
4.1779E + 00 
4.8779E + 00 
5.5779E + 00 
7.5779E + 00 
9.5779E + 00 
1.1578E + 01 
1.3578E + 01 
1.5578E + 01 
1.7578E + 01 
1.9578E + 01 
2.1578E + 01 
2.3578E + 01 
2.5578E + 01 
2.7578E + 01 
2.9578E + 01 
3.1578E + 01 
3.3578E + 01 
3.5578E 4- 01 
3.7578E + 01 
3.9578E + 01 
4.1578E + 01 
4.3578E + 01 
4.5578E + 01 
4.7578E + 01 
4.9578E + 01 
5.1578E + 01 
5.3578E + 01 
5.4195E + 01 


2.0016E + 01 
2.0018E + 01 
2.0020E + 01 
2.0022E + 01 
2.0024E + 01 
2.0026E + 01 
2.0029E + 01 
2.0031E + 01 
2.0034E + 01 
2.0036E + 01 
2.0039E + 01 
2.0042E + 01 
2.0045E + 01 
2.0048E + 01 
2.0051E + 01 
2.0055E + 01 
2.0058E + 01 
2.0062E + 01 
2.0065E + 01 
2.0069E + 01 
2.0104E + 01 
2.0139E + 01 
2.0174E + 01 
2.0209E + 01 
2.0244E + 01 
2.0279E + 01 
2.0379E + 01 
2.0479E + 01 
2.0579E + 01 
2.0679E + 01 
2.0779E + 01 
2.0879E + 01 
2.0979E + 01 
2.1079E + 01 
2.1179E + 01 
2.1279E + 01 
2.1379E + 01 
2.1479E + 01 
2.1579E + 01 
2.1679E + 01 
2.1779E + 01 
2.1879E + 01 
2.1979E + 01 
2.2079E + 01 
2.2179E + 01 
2.2279E + 01 
2.2379E + 01 
2.2479E + 01 
2.2579E + 01 
2.2679E + 01 
2.2710E + 01 


7.4456E-02 
7.8595E-02 
8.2735E-02 
8.6875E-02 
9.1016E-02 
9.5158E-02 
9.9300E-02 
1.0344E-01 
1.0759E-01 
1.1 173E-01 
1.1587E-01 
1.2002E-01 
1.2417E-01 
1.2831 E-01 
1.3246E-01 
1.3661 E-01 
1.4076E-01 
1.4491 E-01 
1.4906E-01 
1.5321 E-01 
1.91 16E-01 
2.2164E-01 
2.4799E-01 
2.7159E-01 
2.9319E-01 
3.1324E-01 
3.6697E-01 
4.1313E-01 
4.543BE-01 
4.9213E-01 
5.2720E-01 
5.6014E-01 
5.9133E-01 
6.2107E-01 
6.4956E-01 
6.7697E-01 
7.0343E-01 
7.2906E-01 
7.5394E-01 
7.7814E-01 
8.0175E-01 
8.2479E-01 
8.4734E-01 
8.6942E-01 
8.9107E-01 
9.1233E-01 
9.3322E-01 
9.5377E-01 
9.7400E-01 
9.9393E-01 
1.0000E + 00 


1.3709E-07 
1.5326E-07 
1.7033E-07 
1.8831E-07 
2.0720E-07 
2.2699E-07 
2.4770E-07 
2.6931 E-07 
2.9184E-07 
3.1528E-07 
3.3963E-07 
3.6490E-07 
3.9109E-07 
4.1819E-07 
4.4621 E-07 
4.751 5E-07 
5.0501 E-07 
5.3580E-07 
5.6750E-07 
6.001 4E-07 
9.0727E-07 
1.2158E-06 
1.5256E-06 
1.8367E-06 
2.1489E-06 
2.4622E-06 
3.3635E-06 
4.2733E-06 
5.1914E-06 
6.1 175E-06 
7.051 5E-06 
7.9931 E-06 
8.9423E-06 
9.8990E-06 
1.0863E-05 
1.1835E-05 
1.2814E-05 
1.3800E-05 
1.4793E-05 
1.5794E-05 
1.6802E-05 
1.7818E-05 
1.884 IE-05 
1.987 IE-05 
2.0908E-05 
2.1952E-05 
2.3004E-05 
2.4063E-05 
2.5130E-05 
2.6204E-05 
2.7281 E-05 


7.2266E-01 
7.2258E-01 
7.2249E-01 
7.2239E-01 
7.2230E-01 
7.2219E-01 
7.2208E-01 
7.2197E-01 
7.2186E-01 
7.2173E-01 
7.21 61 E-01 
7.2148E-01 
7.2134E-01 
7.2120E-01 
7.2106E-01 
7.2091 E-01 
7.2075E-01 
7.2059E-01 
7.2043E-01 
7.2026E-01 
7.1868E-01 
7. 1 71 1 E-01 
7.1554E-01 
7.1397E-01 
7.1241E-01 
7.1085E-01 
7.0642E-01 
7.0202E-01 
6.9765E-01 
6.9331 E-01 
6.8900E-01 
6.8472E-01 
6.8047E-01 
6.7625E-01 
6.7205E-01 
6.6789E-01 
6.6376E-01 
6.5965E-01 
6.5557E-01 
6.5152E-01 
6.4750E-01 
6.4350E-01 
6.3953E-01 
6.3559E-01 
6.3168E-01 
6.2779E-01 
6.2393E-01 
6.201 0E-01 
6.1629E-01 
6.1251 E-01 
6.1 134E-01 


9.5724E-04 
9.0693E-04 
8.6166E-04 
8.2070E-04 
7.8347E-04 
7.4948E-04 
7.1832E-04 
6.8966E-04 
6.6321 E-04 
6.3872E-04 
6.1598E-04 
5.9482E-04 
5.7506E-04 
5.5659E-04 
5.3927E-04 
5.2300E-04 
5.0769E-04 
4.9326E-04 
4.7963E-04 
4.6674E-04 
3.7490E-04 
3.2405E-04 
2.9026E-04 
2.6562E-04 
2.4659E-04 
2.3131E-04 
1.9868E-04 
1.7759E-04 
1.6248E-04 
1.5096E-04 
1.4180E-04 
1.3429E-04 
1.2800E-04 
1.2263E-04 
1.1799E-04 
1.1392E-04 
1.1 031 E-04 
1.0710E-04 
1.0421 E-04 
1.0159E-04 
9.921 6E-05 
9.7042E-05 
9.5046E-05 
9.3207E-05 
9.1506E-05 
8.9927E-05 
8.8458E-05 
8.7087E-05 
8.5805E-05 
8.4604E-05 
8.4604E-05 


EXAMPLE 


15 


* * * * 


INFILTRATION COMPLETE 


* * * * 


RESIN PROPERTIES 
CP = .20934E + 04 

KT = .20770E + 00 

HR = .28800E + 06 


FIBER PROPERTIES 
CP = .71176E + 03 

KT = .25977E + 02 


PLY PROPERTIES 
RHO = .14438E + 04 

CP = .13106E + 04 

KTZ = .50187E + 00 


TOOL PLATE PROPERTIES 
THICK = .63500E-02 

RHO = .27074E + 04 

CP = .87090E + 03 

KT = .20250E + 03 


PRESSURE PLATE PROPERTIES 
THICK = .31750E-02 

RHO = .27074E + 04 

CP = .87090E + 03 

KT = .20250E + 03 


PROGRAM CONSTANTS 
DELT - .50000E + 01 

VEL = .10000E + 05 


OPTIONS 
I FREQ = 200 
IRED = 4 


EXAMPLE 


16 



TIME = .105420E + 04 TAIR = 72.7 


1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.725708E + 02 

.294477E-02 

.446580E-01 

.00000 

13 

.215232E-02 

.712912E + 02 

.277224E-02 

.472844E-01 

.25000 

17 

.430465E-02 

.708731 E + 02 

.271813E-02 

.481807E-01 

.50000 

21 

.645697E-02 

.713171E 4- 02 

.277564E-02 

.472295E-01 

.75000 

25 

.860929E-02 

.726226E + 02 

.295199E-02 

.445553E-01 

1.00000 


TTOOL = .725950E + 02 TPLATE = .726319E + 02 


TIME = .205420E + 04 TAIR = 80.0 


1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.800020E + 02 

.177532E-01 

.33991 6E-01 

.00000 

13 

.215232E-02 

.800499E + 02 

.173122E-01 

.338686E-01 

.25000 

17 

.430465E-02 

.800658E + 02 

.17171 5E-01 

.338286E-01 

.50000 

21 

.645697E-02 

.800498E + 02 

.173210E-01 

.338698E-01 

.75000 

25 

.860929E-02 

.80001 7E + 02 

.177715E-01 

.339942E-01 

1.00000 


TTOOL = .80001 5E 4- 02 TPLATE = .800015E + 02 


TIME = .305420E + 04 TAIR = 80.0 


1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.800029E + 02 

.421976E-01 

.371496E-01 

.00000 

13 

.215232E-02 

.800746E 4- 02 

.415959E-01 

.369603E-01 

.25000 

17 

.430465E-02 

.800984E + 02 

.414040E-01 

.368987E-01 

.50000 

21 

.645697E-02 

.800745E 4- 02 

.416089E-01 

.369623E-01 

.75000 

25 

.860929E-02 

.800026E + 02 

.422244E-01 

.371538E-01 

1.00000 


TTOOL = .800022E + 02 TPLATE = .800022E + 02 


TIME = .405420E 4- 04 TAIR = 80.0 


1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E 4- 00 

.800039E 4- 02 

.762376E-01 

.420455E-01 

.00000 

13 

.215232E-02 

.801000E 4- 02 

.755332E-01 

.417820E-01 

.25000 

17 

.430465E-02 

.801318E 4- 02 

.753094E-01 

.416964E-01 

.50000 


17 


EXAMPLE 



21 .645697E-02 .800997E + 02 .755503E-01 .417850E-01 .75000 

25 .860929E-02 .800035E + 02 .762728E-01 .42051 7E-01 1.00000 

TTOOL = .800030E + 02 TPLATE = .800030E + 02 


TIME = .505420E + 04 TAIR = 92.7 


1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.925767E + 02 

.122645E + 00 

.324305E-01 

.00000 

13 

.215232E-02 

.914406E + 02 

.121430E + 00 

.334673E-01 

.25000 

17 

.430465E-02 

.910695E + 02 

.121049E + 00 

.338194E-01 

.50000 

21 

.645697E-02 

.914662E + 02 

.121462E + 00 

.334440E-01 

.75000 

25 

.860929E-02 

.926278E + 02 

.12271 IE + 00 

.323867E-01 

1.00000 


TTOOL = .925995E + 02 TPLATE = .926364E + 02 


TIME - .605420E + 04 TAIR - 120.0 


1 

Z(D 

Td) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.120025E + 03 

.297339E + 00 

.462572E-01 

.00000 

13 

.215232E-02 

. 1 20628E + 03 

.294262E + 00 

.450644E-01 

.25000 

17 

.430465E-02 

.120829E + 03 

.293288E + 00 

.446872E-01 

.50000 

21 

.645697E-02 

.120627E + 03 

.294390E + 00 

.451028E-01 

.75000 

25 

.860929E-02 

.120022E + 03 

.297582E + 00 

.46331 6E-01 

1.00000 


TTOOL = .120019E + 03 TPLATE = .120019E + 03 


TIME - .705420E + 04 TAIR = 120.0 


1 

Z(l) 

T(D 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.120022E + 03 

.531046E + 00 

.21 1496E + 00 

.00000 

13 

.215232E-02 

.120571 E + 03 

.53051 IE + 00 

.211914E + 00 

.25000 

17 

.430465E-02 

.120755E + 03 

.530371 E + 00 

.2121 12E + 00 

.50000 

21 

.645697E-02 

.120570E + 03 

.530621 E + 00 

.212063E + 00 

.75000 

25 

.860929E-02 

.120020E + 03 

.531255E + 00 

.21 1779E + 00 

1.00000 


TTOOL = .120017E + 03 TPLATE = .120017E + 03 


TIME = .805420E + 04 TAIR = 120.0 


EXAMPLE 


18 



1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.120016E + 03 

.718074E + 00 

.714691E + 00 

.00000 

13 

.215232E-02 

.120408E + 03 

.718432E + 00 

.723659E + 00 

.25000 

17 

.430465E-02 

.120539E + 03 

.718580E + 00 

.726832E + 00 

.50000 

21 

.645697E-02 

.120407E + 03 

.718508E + 00 

.724002E + 00 

.75000 

25 

.860929E-02 

.120014E + 03 

.718219E + 00 

.715335E + 00 

1.00000 


TTOOL = .120012E + 03 TPLATE =? .120012E + 03 


TIME = .905420E + 04 TAIR « 120.0 


1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

. 12001 0E + 03 

.841983E + 00 

.160195E + 01 

.00000 

13 

.215232E-02 

.120251E + 03 

.842365E + 00 

.162010E + 01 

.25000 

17 

.430465E-02 

.120332E + 03 

.84251 IE + 00 

.162643E + 01 

.50000 

21 

.645697E-02 

. 1 20251 E + 03 

.84241 IE + 00 

.162056E + 01 

.75000 

25 

.860929E-02 

.120009E + 03 

.842072E + 00 

.160281E + 01 

1.00000 


TTOOL = .120008E + 03 TPLATE = .120008E + 03 


TIME = .100542E + 05 TAIR = 145.0 


1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.145010E + 03 

.951032E + 00 

.130465E + 02 

.00000 

13 

.215232E-02 

.145258E + 03 

. 95067 3E + 00 

.1321 69E + 02 

.25000 

17 

.430465E-02 

.145342E + 03 

.950590E + 00 

.132796E + 02 

.50000 

21 

.645697E-02 

.145257E + 03 

.95071 5E + 00 

.132213E + 02 

.75000 

25 

.860929E-02 

.145009E + 03 

.951120E + 00 

.130556E + 02 

1.00000 


TTOOL = .145008E + 03 TPLATE = .145008E + 03 


TIME = .1 10542E + 05 TAIR = 145.0 


1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.145002E + 03 

.992622E + 00 

.188824E + 02 

.00000 

13 

.215232E-02 

.145039E + 03 

.992705E + 00 

.189452E + 02 

.25000 

17 

.430465E-02 

.145051E + 03 

.992739E + 00 

.189673E + 02 

.50000 

21 

.645697E-02 

.145038E + 03 

.99271 IE + 00 

.189461E + 02 

.75000 

25 

.860929E-02 

.145001 E + 03 

.992635E + 00 

.188843E + 02 

1.00000 


TTOOL = .145001 E + 03 TPLATE = .145001 E + 03 


EXAMPLE 


19 


TIME = .120542E + 05 TAIR = 145.0 


1 

m 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.145000E + 03 

.99891 6E + 00 

.199692E 4- 02 

.00000 

13 

.215232E-02 

.145006E + 03 

.998932E + 00 

.199796E 4- 02 

.25000 

17 

.430465E-02 

.145007E + 03 

.998938E + 00 

.199832E + 02 

.50000 

21 

.645697E-02 

.145006E + 03 

.998933E + 00 

.199797E + 02 

.75000 

25 

.860929E-02 

.145000E + 03 

.99891 8E + 00 

.199695E + 02 

1.00000 


TTOOL = .145000E + 03 TPLATE - .145000E + 03 


TIME = .130542E + 05 TAIR = 145.0 


1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.145000E + 03 

.999841E + 00 

.201 341 E + 02 

.00000 

13 

.215232E-02 

.145001 E + 03 

.999844E + 00 

.201357E + 02 

.25000 

17 

.430465E-02 

. 145001 E + 03 

.999845E + 00 

.201362E + 02 

.50000 

21 

.645697E-02 

. 145001 E + 03 

.999844E + 00 

.201357E + 02 

.75000 

25 

.860929E-02 

.145000E + 03 

.999842E + 00 

.201342E + 02 

1.00000 


TTOOL = .145000E + 03 TPLATE = .145000E + 03 


TIME = .140542E + 05 TAIR = 177.0 


1 

2(1) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.176999E + 03 

.999993E + 00 

.2871 00E + 03 

.00000 

13 

.215232E-02 

.176962E + 03 

.999992E + 00 

.287377E + 03 

.25000 

17 

.430465E-02 

.176947E + 03 

.999992E + 00 

.287491 E + 03 

.50000 

21 

.645697E-02 

.176962E + 03 

.999992E + 00 

.287376E + 03 

.75000 

25 

.860929E-02 

.176999E + 03 

.999993E + 00 

.287098E + 03 

1.00000 


TTOOL = .176999E + 03 TPLATE - .176999E + 03 


TIME = .150542E + 05 TAIR = 177.0 


1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.177000E + 03 

.100000E + 01 

.2871 16E + 03 

.00000 

13 

.215232E-02 

.177000E + 03 

.100000E + 01 

.2871 16E + 03 

.25000 


EXAMPLE 


20 



17 

21 

25 

.430465E-02 

.645697E-02 

.860929E-02 

.177000E + 03 
.177000E + 03 
.177000E + 03 

.100000E + 01 
.100000E + 01 
.100000E + 01 

.2871 16E + 03 
.287116E + 03 
.2871 16E + 03 

.50000 

.75000 

1.00000 


TTOOL = .177000E + 03 TPLATE 

= .177000E + 03 





TIME = .160542E + 05 TAIR = 177.0 

- 


1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.177000E + 03 

.100000E + 01 

.2871 16E + 03 

.00000 

13 

.215232E-02 

.177000E + 03 

.100000E + 01 

.2871 16E + 03 

.25000 

17 

.430465E-02 

.177000E + 03 

.100000E + 01 

.287116E + 03 

.50000 

21 

.645697E-02 

.177000E + 03 

.100000E + 01 

.2871 16E + 03 

.75000 

25 

.860929E-02 

.177000E + 03 

.100000E + 01 

.2871 16E + 03 

1.0000' 


TTOOL = .177000E + 03 TPLATE = .177000E + 03 


TIME = .170542E + 05 TAIR = 177.0 


1 

Z(D 

T(l) 

9 

.000000E + 00 

.177000E + 03 

13 

.215232E-02 

.177000E + 03 

17 

.430465E-02 

.177000E + 03 

21 

.645697E-02 

.177000E + 03 

25 

.860929E-02 

.177000E + 03 


CALPHA(I) 

VISC(I) 

Z/ZI 

.100000E + 01 

.2871 16E + 03 

.00000 

.100000E + 01 

.2871 16E + 03 

.25000 

.100000E + 01 

.2871 16E + 03 

.50000 

.100000E + 01 

.2871 16E + 03 

.75000 

.100000E + 01 

.2871 16E + 03 

1.00000 


TTOOL = .177000E + 03 TPLATE = .177000E + 03 


TIME = .180542E + 05 TAIR = 151.3 


1 

Z(l) 

T(D 

9 

.000000E + 00 

.151430E + 03 

13 

.215232E-02 

.152727E + 03 

17 

.430465E-02 

.153151E + 03 

21 

.645697E-02 

. 1 52701 E + 03 

25 

.860929E-02 

.151378E + 03 


CALPHA(I) 

VISC(I) 

Z/ZI 

.100000E + 01 

.322806E + 02 

.00000 

.100000E + 01 

.35641 9E + 02 

.25000 

.100000E + 01 

.368251 E + 02 

.50000 

.100000E + 01 

.355709E + 02 

.75000 

.100000E + 01 

.321539E + 02 

1.00000 


TTOOL = .151406E 4- 03 TPLATE = .151369E + 03 


EXAMPLE 


21 


TIME - .190542E 4* 05 TAIR = 101.3 


1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.101430E + 03 

.100000E + 01 

.206639E + 01 

.00000 

13 

.215232E-02 

.102727E + 03 

.100000E + 01 

.216064E + 01 

.25000 

17 

.430465E-02 

.103151E + 03 

.100000E + 01 

.219304E + 01 

.50000 

21 

.645697E-02 

. 1 02701 E + 03 

.100000E + 01 

.215869E + 01 

.75000 

25 

.860929E-02 

.101378E + 03 

.100000E + 01 

.206277E + 01 

1.00000 


TTOOL = .101406E + 03 TPLATE 

= .101369E + 03 





TIME = .194842E + 05 TAIR = 80.0 



1 

Z(l) 

T(l) 

CALPHA(I) 

VISC(I) 

Z/ZI 

9 

.000000E + 00 

.800784E + 02 

.100000E + 01 

.121939E + 01 

.00000 

13 

.215232E-02 

.812509E + 02 

.100000E + 01 

.124257E + 01 

.25000 

17 

.430465E-02 

.816585E + 02 

.100000E + 01 

.125108E + 01 

.50000 

21 

.645697E-02 

.812287E + 02 

.100000E + 01 

.12421 IE + 01 

.75000 

25 

.860929E-02 

.800508E + 02 

.100000E + 01 

.121887E + 01 

1.00000 


TTOOL = .800632E 

+ 02 TPLATE 

= .800447E + 02 




EXAMPLE 


22 



6.0 REFERENCES 


1. Claus, S.J., "A Cure Process Model for Resin Transfer Molding of Advanced 
Composites", M.S. Thesis, Department of Engineering Science and Mechanics, 
Virginia Polytechnic Institute and State University, April, 1989. 


REFERENCES 


23 


ooooooooooooooooooooooooo 


7.0 APPENDIX A 


7,1 Main Program 


INFILTRATION MODEL AND CURE MODELS FOR 1-D RESIN TRANSFER MOLDING 
ASSUMPTIONS: 

1. THREE STAGE RAMP-HOLD INFILTRATION TEMPERATURE PROFILE 

2. HOMOGENOUS POROUS MEDIUM 

3. CONSTANT COMPACTION PRESSURE 

4. NEWTONIAN FLUID 

CONTACT- STEVE CLAUS DEPT OF ESM VPI&SU. BLACKSBURG VA 24061 


INPUT DATA FORMAT 
LINE 1 : ANAME 

ANAME - TITLE OF THE PROBLEM 

LINE 2 : NTIMES, NTEMPS, IVSWH, IRESIN, ICURE 
NTIMES = NUMBER OF TIME STEPS FOR EACH PROBLEM 
NTEMPS = NUMBER OF TEMPERATURE STEPS IN INFILTRATION AND CURE 
CYCLES 

IVSWH = VISCOSITY SWITCH 

= 1 TEMPERATURE DEPENDANT VISCOSITY 
= 0 CONSTANT VISCOSITY 
IRESIN = RESIN SWITCH 


APPENDIX A 


24 



C = 1 HERCULES 3501-6 

C =2 SHELL RSL1 282/9470 32.4 PHR 

C ICURE = CUREING SWITCH 

C =0 CURE CYCLE IS NOT SIMULATED 

C = 1 CURE CYCLE IS SIMULATED 

C 

C LINE 3 : RLGTH, WIDTH 
C RLGTH = LENGTH OF LAMINATE 
C WIDTH = WIDTH OF LAMINATE 

C 

C LINE 4 : TIMEIN, TAUTO (NTEMPS NUMBER OF LINES) 

C TIMEIN = TIME OF TEMPERATURE CHANGE 
C TAUTO = TEMPERATURE IN AUTOCLAVE AT TIMEIN 
C 

C NOTE: IF IVSWH = 0 THEN ADD A LINE HERE WITH VISCFL 
C 

C LINE 5: NPLIES, ZETA, DIAFI, RHOFI, TUNCPT, RKCC, PZERO 
C NPLIES = NUMBER OF PLIES OF MATERIAL 
C ZETA - AREAL WEIGHT OF FABRIC 
C DIAFI = DIAMETER OF INDIVIDUAL FILLAMENTS 
C RHOFI = DENSITY OF SOLID MATERIAL 
C TUNCPT = THICKNESS OF UNCOMPACTED PLY 
C RKCC = KOZENY-CARMEN CONSTANT 

C PZERO = PRESSURE AT WHICH D = 0 ( PZERO>0) 

C 

C LINE 6: A(J) 

C A(J) = COEFFICIENTS OF THE COMPACTION MODEL 
C 

C LINE 7 : POSA, POSB, ATIME, BTIME, CTIME 
C DTIME(MATL) = DTIME(I) + ATIME*POS 

C IF (POS.GE.POSA) DTIME(MATL) = BTIME 

C IF (POS.GE.POSB) DTIME(MATL) = CTIME 

C 

C POSA = THK FRACTION FOR FIRST TIME INCRIMENT HOLD 

C POSB = THK FRACTION FOR SECOND TIME INCRIMENT HOLD 

C ATIME = RATE COEFFICIENT OF THE TIME SCHEME 

C BTIME = FIRST HOLD TIME STEP 

C CTIME = SECOND HOLD TIME STEP 

C 

C LINE 8 : PAUTO, PBAG 

C PAUTO = PRESSURE IN THE AUTOCLAVE OR APPLIED BY PLATENS 

C PBAG = PRESSURE IN THE BLEEDER 

C 

C NOTE: ALL PRESSURES IN GAGE 
C 

C LINE 9 : NTOOL, NPRESS, I FREQ, IRED 
C NTOOL = NUMBER OF DIVISIONS IN TOOL PLATE 

C NPRESS = NUMBER OF DIVISIONS IN PRESSURE PLATE 

C IFREQ = FREQUENCY OF PRINTOUT....WR2 TIME 

C IRED = FREQUENCY OF PRINTOUT.. ..WR2 POSITION 

C 


APPENDIX A 


25 



LINE 9 : CPFL, CPFI, KTFL, KTFI, HR 
CPFL = SPECIFIC HEAT OF THE RESIN 
CPFI = SPECIFIC HEAT OF THE FIBER 
KTFL = THERMAL CONDUCTIVITY OF THE RESIN 
KTFI = THERMAL CONDUCTIVITY OF THE FIBER 
HR = HEAT OF REACTION OF THE RESIN 

LINE 10: DELT, VEL 

DELZ = TIME STEP FOR CALCULATION DURING CURE 
VEL = HEAT TRANSFER COEFFICIENT 

LINE 11: ZTOOL, KTOOL, RHOTOL, CPTOOL 
ZTOOL = THICKNESS OF THE TOOL PLATE 
KTOOL = THERMAL CONDUCTIVITY OF THE TOOL PLATE 
RHOTOL = DENSITY OF THE TOOL PLATE 
CPTOOL = SPECIFIC HEAT OF THE TOOL PLATE 

LINE 12: ZPRES, KPRES, RHOPRE, CPPRES, NBLEED 
ZPRES = THICKNESS OF THE PRESSURE PLATE 
KPRES = THERMAL CONDUCTIVITY OF THE PRESSURE PLATE 
RHOPRE = DENSITY OF THE PRESSURE PLATE 
CPPRES = SPECIFIC HEAT OF THE PRESSURE PLATE 
NBLEED = NUMBER OF BLEEDER PLIES 

NOTE: UNITS SHOULD BE IN SI EXCEPT THE COMPACTION COEFFICIENTS. 

ALL INPUT IS IN FREE FORMAT 


MAIN PROGRAM ** 


IMPLICIT REAL*8 (A-H.O-Z) 

COMMON NODMAT(200,9),RPERM(10,2,2),VISCFL,RHOFL, 

1 KSTRG(600),STI F(8,8),VELSTO(200,2) 

COMMON/ONE/ X(600),Y(600),CENTX(200),CENTY(200) 

COMMON/TWO/ NEQ,IBWTH,STIFF(600,50),RHSV(600) 

COMMOWFIVE/ NOEL,NNODES,NMATR,NTIMES 
COMMON/MATLS/ A(5),COMPP,RLGTH, WIDTH, RVOL.RMASS, 

1 TUNCPT,ZETA,DIAFI,RHOFI, 

2 RKCC,PORO,THK,TEMP, 

3 FRATE, ALPHA, FVISC, GAS, PZERO, IVSWH,IRESIN,NPLIES,ICURE 
COMMON/TIMES/ TIME,DTIME(2),ATIME,BTIME,CTIME,POSA,POSB,ITIME 
DIMENSION ANAME(18),SRHSV(600),ARHSV(600) 

CHARACTER* 12 FNDAT.FNLIST.FNIPLT.FNCPLT 

WRITE(\'(A/)') ' ENTER THE INPUT DATA FN.FT' 

READ(\'(A/)') FNDAT 

WRITE(Y(A/)') ' ENTER THE LISTING FN.FT' 

READ(Y(A/)') FNLIST 

WRITE(\'(A/)') ' ENTER THE INFILTRATION PLOTTING FN.FT' 


APPENDIX A 


26 



OOO O O O rj, ooo o o ooo 


READ(Y(A/)') FNIPLT 

WRITE(Y(A/)') ' ENTER THE CURE PLOTTING FN.FT' 

READ(Y(A/)') FNCPLT 

OPEN(5,FILE = FNDAT, STATUS = 'OLD') 

OPEN(6,FILE = FNLIST, STATUS = 'NEW') 

OPEN(7,FILE = FNIPLT, STATUS = 'NEW') 

OPEN(8,FILE = FNCPLT.STATUS = 'NEW') 

C 

MAXBW = 50 

** PROBLEM IDENTIFICATION AND DESCRIPTION ** 

READ(5,1) (ANAME(I).I = 1.18) 

WRITE (6,7) (ANAME(I).I = 1,18) 


NTS = 1 
ITIME = 1 
TEMP = 0.0D0 
ALPHA = 0.0D0 
TIME = 0.0D0 
MAXDOF = 600 

CALL READIN (ITRUN) 

IF (IVSWH.EQ.1) THEN 
TEMP = FTEMP(TIME, ITIME) 

CALL RESIN(2) 

ALPHA = ALPHA + FRATE‘DTIME(2) 

RM ASS = RHOFL'RVOL 
WRITE(6,8) RMASS 
END IF 

** BEGIN TIME STEPPING LOOP ** 

WRITE(6,2) 

5 IF ((X(N NODES). GT.THK + X(7)).OR.(NTS.GT.NTIMES)) GO TO 52 

** CALCULATE THE RESIN TEMPERATURE, VISCOSITY, AND DEGREE OF CURE ** 

IF (IVSWH.EQ.1) THEN 
TEMP = FTEMP(TIME, ITIME) 

CALL RESIN(2) 

ALPHA = ALPHA + FRATE*DTIME(2) 

END IF 

** COMPUTE MAX. NODAL DIFF AND BANDWIDTH ** 

MAXDIF = 0 
DO 60 1 = 1, NOEL 
DO 60 J = 1,8 
DO 60 K= 1,8 

LL = IABS(NODMAT(l,J)-NODMAT(l,K)) 


APPENDIX A 


27 


o o o 


IF (LL.GT.MAXDIF) MAXDIF = LL 
60 CONTINUE 
C 

IBWTH = MAXDIF + 1 
NEQ-NNODES 

IF (IBWTH.GT.MAXBW) GO TO 65 
C 

CALL GLOBL (ITRUN) 

C 

IF (ITRUN. GT.O) GOTO 50 
C 

70 CALL SOLVR 
C 

95 CALL STRESS 

POS = (X(NNODES)-X(8))/THK 

WRITE(6,3) TIME, TEMP, POS, ALPHA, VISCFL,VELSTO(NOEL,1) 
WRITE(7,3) TIME, TEMP, POS, ALPHA, VISCFL,VELSTO(NOEL,1) 
CALL RECON 
C 

NTS = NTS + 1 
GO TO 55 

65 WRITE(6,4) IBWTH, MAXBW 
C 

GO TO 55 

52 IF (X(NNODES).GT.THK + X(7)) THEN 
TIME = TIME-DTIME(NODMAT(NOEL,9)) 

1 + (THK + X(7)-X(NNODES-7))/VELSTO(NOEL-1,1) 

C 

IF (IVSWH.EQ.1) THEN 
TEMP = FTEMP(TIME.ITIME) 

CALL RESIN(2) 

ALPHA = ALPHA + FRATE*DTIME(2) 

END IF 
C 

POS = 1.0D0 

WRITE(6,3) TIME, TEMP, POS, ALPHA, VISCFL,VELSTO(NOEL-1,1) 
WRITE(7,3) TIME, TEMP, POS, ALPHA, VISCFL,VELSTO(NOEL-1,1) 
WRITE (6,5) 

IF ((IVSWH.EQ.I).AND.(ICURE.EQ.I)) CALL CURE 
END IF 

IF (NTS.GT.NTIMES) WRITE (6,6) 

50 CONTINUE 
STOP 

** FORMATS FOR MAIN PROGRAM ** 


1 FORMAT (18A4) 

2 FORMAT(///' TIME', 7X, 'TEMP', 4X, 'POSIT. OF', 4X, 'DEGREE OF',5X, 

1 'FLUID720X, 'INFILTRATION', 5X, 'CURE', 4X, 'VISCOSITY', 

2 2X, 'VELOCITY'///) 

3 FORMAT(7(1PE11.4)) 


APPENDIX A 


28 



4 FORMAT (//'**** BANDWIDTH =',14,' EXCEEDS MAX. ALLOWABLE =', 
114//) 

5 FORMAT(///' **** INFILTRATION COMPLETE ///) 

6 FORM AT(///' **** OUT OF TIME ****'///) 

7 FORMAT (1X.18A4//) 

8 FORMAT(8X, 'RESIN MASS '.1PE15.7) 

END 


APPENDIX A 


29 



ooo ooo no o o ooo 


7.2 Subroutine READIN 


** READS IN DATA AND GENERATES PRELIMINARY MESH ** 

SUBROUTINE READIN(ITRUN) 

IMPLICIT REAL‘8 (A-H.O-Z) 

COMMON NODMAT(200,9),RPERM(10,2,2),VISCFL,RHOFL, 

1 KSTRG(600),STIF(8,8),VELSTO(200,2) 

COMMON/ONE/ X(600),Y(600),CENTX(200),CENTY(200) 

COMMON/FOUR/ PRESS(600) 

COMMON/FIVE/ NOEL,NNODES,NMATR,NTIMES 
COMMON/MATLS/ A(5), COM PP, RLGTH, WIDTH, RVOL.RM ASS, 

1 TUNCPT.ZETA.DIAFI.RHOFI, 

2 RKCC,PORO,THK,TEMP, 

3 FR ATE, ALPHA, FVISC, GAS, PZERO, IVSWH,IRESIN,NPLIES,ICURE 
COMMON/TIMES/ TIME,DTIME(2),ATIME,BTIME,CTIME,POSA,POSB,ITIME 
COMMON/TEMPS/ TIMEIN(300),TAUTO(300),NTEMPS 

ITRUN = 0 
ISTOP = 0 
NNODES = 8 
NOEL= 1 
NMATR = 1 
DTIME(I) = 1.0D-15 
DTIME(2) = 1.0D-15 
FRAC = 1.0D0 

READ (5,*) NTIMES,NTEMPS,IVSWH,IRESIN,ICURE 

WRITE (6,1) NTIMES,NTEMPS,IVSWH,IRESIN,ICURE 

** READS AND PRINTS DATA SPECIFIC TO THE PROBLEM ** 

READ (5,*) RLGTH, WIDTH 
WRITE (6,2) RLGTH, WIDTH 

** READS AND PRINTS MATERIAL SPECIFIC DATA ** 

IF (IVSWH.EQ.O) THEN 
READ(5,‘) VISCFL 
WRITE(6,3) VISCFL 
ELSE 

READ(5,*) (TIMEIN(l),TAUTO(l),l = 1.NTEMPS) 

WRITE(6,4) (TIMEIN(l),TAUTO(l),l = 1.NTEMPS) 

GAS = 8.314D-3 
END IF 
C 

RPERM(1,1,1) = 1.0D0 


APPENDIX A 


30 



o o o o o o 


RPERM(1,2,2) = 1.0D + 0 
RPERM(1,1,2) = O.ODO 
R PER M( 1,2,1) = O.DO 
C 

READ (5,*) NPUES,ZETA,DIAFI,RHOFI,TUNCPT,RKCC, PZERO 
1 ,(A(J),J = 1,5) 

READ (5,*) POSA,POSB,ATIME,BTIME,CTIME 
C 

READ(5,‘) PAUTO.PBAG 
COMPP = PAUTO-PBAG 
WRITE(6,8) PAUTO.PBAG, COMPP 

** CALCULATES THE PERMEABILITY TENSOR ** 

CALL PERM 

WRITE (6,5) NPLIES,ZETA,DIAFI,RHOFI,TUNCPT, 

1 RKCC, PZERO, (A(J),J = 1,5) 

WRITE (6,6) ATIME,POSA,BTIME,POSB,CTIME 
WRITE (6,7) THK,PORO,RVOL,RPERM(2,1,1) 

** GENERATE INITIAL MESH *’ 

XMAX = O.DO 
X(1) = O.ODO 
Y(1) = O.ODO 
X(2) = O.ODO 
Y(2) = 1.0D0 
X(3) = O.ODO 
Y(3) = 2.0D0 
X(4) = 1.0D0 
Y(4) = O.ODO 
X(5) = 1.0D0 
Y(5) = 2.0D0 
X(6) = 2.0D0 
Y(6) = O.ODO 
X(7) = 2.0D0 
Y(7) = 1.0D0 
X(8) = 2.0D0 
Y(8) = ?.0D0 
C 

DO 15 M = 1,8 
KSTRG(M) = 0 
X(M) = X(M)/2.0D0*THK 
15 Y(M) = Y(M)/2.0D0*THK 
C 

NODMAT(1,1) = 1 
NODMAT(1,2) = 4 
NODMAT(1,3) = 6 
NODMAT(1,4) = 7 
NODMAT(1,5) = 8 
NODMAT(1,6) = 5 


APPENDIX A 


31 


^toi\3— ^ oo '-J cn cn w w 


NODMAT(1,7) = 3 
NODMAT(1,8) = 2 
NODMAT(1,9) = 1 
C 

NPRESS = 6 
C 

PRESS(I) = PAUTO 
PRESS(2) = PAUTO 
PRESS(3) = PAUTO 
PRESS(6) = PBAG 
PRESS(7) = PBAG 
PRESS(8) = PBAG 
C 

KSTRG(I) = 1 
KSTRG(2) = 1 
KSTRG(3) = 1 
KSTRG(6) = 1 
KSTRG(7) = 1 
KSTRG(8) = 1 
C 

RETURN 

C ** FORMATS FOR SUBROUTINE READIN ** 

1 FORMAT (//' INPUT:'//' PROBLEM PARAMETERS:'//5X ( 

1' NUMBER OF TIME STEPS M5/5X, 

2' NUMBER OF TEMPERATURE CHANGES M5/5X, 

3' VISCOSITY SWITCH ( 1 = TEMP DEPEND, 0 = CONSTANT ) .',I5/5X, 

4' RESIN TYPE '.I5/5X, 

5' CURE SWITCH ( 0 - NO CURE, 1 = CURE ) M5) 

2 FORMAT (////' MATERIAL CHARACTERISTICS:'//// 

1 8X, 'LAMINATE LENGTH '.1PE15.7/ 

2 8X, 'LAMINATE WIDTH ',1 PE15.7/) 

3 FORMAT (8X, 'FLUID VISCOSITY '.1PE15.7) 

4 FORMAT (////' CHARACTERISTICS OF THE TEMPERATURE PROFILE:'// 

1 8X/TIME OF TEMP CHANGE', 

2 8X, 'AUTOCLAVE TEMP'/2(10X,1PE15.7)) 

5 FORMAT (' SOLID PROPERTIES:'// 

1 8X, 'NUMBER OF PLIES ',15/ 

8X, 'AREAL WEIGHT MPE15.7/ 

8X, 'DIAMETER OF FIBER '.1PE15.7/ 

8X, 'DENSITY OF FIBER '.1PE15.7/ 

8X, 'UNCOMPACTED THICKNESS. .'.1PE15.7/ 

8X/KOZENY-C ARMEN CONSTANT .'.1PE15.7/ 

8X, 'PRESSURE AT ZERO DEFL. .'.1PE15.7// 

8X, 'MATERIAL COEFFICIENTS. ,7/10X,5(1PE15.7)///) 

FORMAT (' TIME INCRIMENTS:'/ 

8X/TIME COEFF A '.1PE15.7/ 

8X, 'FIRST HOLD POSITION. . .'.1PE15.7/ 

8X/TIME COEFF B '.1PE15.7/ 

8X, 'SECOND HOLD POSITION . .'.1PE15.7/ 


APPENDIX A 


32 



cm co 


7 


8 


5 8X/TIME COEFF C ',1 PE 15.7///) 

FORMAT( ' MATERIAL RESULTS:'/ 

1 8X, 'LAMINATE THICKNESS . . .'.1PE15.7/ 

8X, 'POROSITY 1 PEI 5.7/ 

8X, 'TOTAL RESIN VOLUME . . .'.1PE15.7/ 

8X, 'PERMEABILITY '.1PE15.7/)) 

FORMAT(////' PRESSURES:'/ 

1 8X, 'AUTOCLAVE PRESSURE . . .'.1PE15.7/ 

2 8X/BAG PRESSURE '.1PE15.7/ 

3 8X, 'COMPACTION PRESSURE. . .MPE15.7//) 
END 


APPENDIX A 


33 


ooo o ooo oooo 


7.3 Subroutine PERM 


** CALCULATES THE MATERIAL PERMEABILITY TENSOR 


SUBROUTINE PERM 
IMPLICIT REAL*8 (A-H,0-Z) 

COMMON NODMAT^OO.^RPERMOO^^KVISCFL.RHOFL, 

1 KSTRG(600),STIF(8,8),VELSTO(200,2) 

COMMON/FIVE/ NOEL,NNODES,NMATR,NTIMES 
COMMON/MATLS/ A(5),COMPP,RLGTH,WIDTH > RVOL.RMASS, 

1 TUNCPT,ZETA,DIAFI,RHOFI, 

2 RKCC.PORO.THKJEMP, 

3 FRATE, ALPHA, FVISC.GAS.PZEROJVSWH.IRESIN.NPLIES.ICURE 

** CALCULATES THE DEFORMED THICKNESS ** 

AREA = 6.0D0*6.75D0 

RLNZ = DLOG(PZERO/6895,ODO* AREA) 

DZ = A(1) + RLNZ*(A(2) + RLNZ*(A(3) + RLNZ*(A(4) + RLNZ‘A(5)))) 

RLNP = DLOG(COMPP/6895,ODO* AREA) 

DEFL = A(1) + RLNP*(A(2) + RLNP*(A(3) + RLNP*(A(4) + 

1 RLNP*A(5))))-DZ 

THK = N PLIES* (TUNC PT-2.54D-2*DEFL) 

** CALCULATES POROSITY AND PERMEABILITY ** 


1 = 2 

PORO = 1.DO-NPLIES*ZETA/THK/RHOFI 

RPERM(I,1,1) = DIAFI*‘2/RKCC*PORO“3/(1.DO-PORO)**2 

RPERM(I,2,2) = DIAFI**2/RKCC*PORO**3/(1.DO-PORO)**2 

RPERM(I,1,2) = 0.0D0 

RPERM(I,2,1) = 0.D0 

R VOL = THK*RLGTH* WIDTH* PORO 

RETURN 

END 


APPENDIX A 


34 



o o o o o o o 


7.4 Subroutine RESIN 


” CALCULATES THE TEMPERATURE, DEGREE OF CURE, VISCOSITY 


SUBROUTINE RESIN(I) 

IMPLICIT REAL*8 (A-H.O-Z) 

COMMON NODMAT(200,9),RPERM(10,2,2),VISCFL,RHOFL, 

1 KSTRG(600),STIF(8,8),VELSTO(200,2) 

COMMON/M ATLS/ A(5), COM PP,R LGTH, WIDTH, RVOL.RM ASS, 

1 TUNCPT,ZETA,DIAFI,RHOFI, 

2 RKCC,PORO,THK,TEMP, 

3 FRATE, ALPHA, FVISC, GAS, PZERO, IVSWH.IRESIN.NPLIES.ICURE 
COMMON/TIMES/ TIME,DTIME(2),ATIME,BTIME,CTIME,POSA,POSB,ITIME 

’* CALCULATES THE DEGREE OF CURE AND RESIN VISCOSITY ** 

IF (IVSWH.EQ.O) THEN 
TEMP = 0.0D0 
RETURN 
ELSE 

IF (IRESIN.EQ.1) CALL H35016 
IF (IRESIN.EQ.2) CALL S1282 
VISCFL= FVISC 
END IF 

RETURN 

END 


APPENDIX A 


35 



non 


7.5 Subroutine FTEMP 


** FUNCTION FTEMP 


FUNCTION FTEMP(TVAU) 

IMPLICIT REAL*8 (A-H,0-Z) 

COMMON/TEMPS/ TIMEI N (300) ,TAUTO(300),NTEM PS 
IF(TVAL.GT.T1MEIN(I + 1)) 1 = 1 + 1 
IF(I.GE.NTEMPS) GO TO 2 
IF(TVAL.NE.TIMEIN(I)) GO TO 1 
FTEMP = TAUTO(l) 

RETURN 

2 FTEMP = TAUTO(NTEMPS) 

RETURN 

1 FTEMP = TAUTO(I) + (TAUTO(l + l)-TAUTO(l))/ 

1 (TIMEIN(I + 1)-TIMEIN(I))‘(TVAL-TIMEIN(I)) 
RETURN 
END 


APPENDIX A 


36 



oooo 


7.6 Subroutine H35016 


** CALCULATES THE TEMPERATURE, DEGREE OF CURE, AND VISCOSITY OF ** 
** HERCULES 3501-6 


SUBROUTINE H35016 
C 

IMPLICIT REAL*8 (A-H.O-Z) 

COMMON NODMAT(200,9),RPERM(10,2,2),VISCFL,RHOFL, 

1 KSTRG(600),STI F(8,8),VELSTO(200,2) 

COMMON/M ATLS/ A(5), COM PP.RLGTH, WIDTH, RVOL.RM ASS, 

1 TUNCPT.ZETA,DIAFI,RHOFI, 

2 RKCC.PORO.THK.TEMP, 

3 FRATE, ALPHA, FVISC, GAS, PZERO, IVSWH.IRESIN.NPLIES.ICURE 
C 

RHOFL = 1.26D3 
PREX1 = 3.5019D7 
PREX2 = -3.3571 D7 
PREX3 = 3.2665D3 
ACT1 = 8.0788D1 
ACT2 = 7.7918D1 
ACT3 = 5.6647D1 
BRR = 4.7000D-1 
RMULN1 = -3.0166D1 
VACT1 = 9.0905D1 
VISK = 1.4100D1 
C 

IF (ALPHA. LE.0.3D0) THEN 
RK1 = PREX1*DEXP(-ACT1/GAS/(TEMP + 273.15)) 

RK2= PREX2*DEXP(-ACT2/GAS/(TEMP + 273.15)) 

FRATE = (RK1 + RK2‘ALPHA)*(1.D0-ALPHA)*(BRR-ALPHA) 

ELSE 

RK3 = PREX3*DEXP(-ACT3/GAS/(TEMP + 273.15)) 

FRATE = RK3*(1. DO-ALPHA) 

END IF 
C 

FVISC = DEXP(RMULN1 + VACT1/GAS/(TEMP + 273.15) + VISK* ALPHA) 
C 

RETURN 

END 


APPENDIX A 


37 


o o o o 


7.7 Subroutine SI 282 


** CALCULATES THE TEMPERATURE, DEGREE OF CURE, AND VISCOSITY OF ** 
** SHELL RSL1282/9470 32.4PHR 


SUBROUTINE S1282 
C 

IMPLICIT REAL‘8 (A-H.O-Z) 

COMMON NODMAT(200,9),RPERM(10,2,2),VISCFL,RHOFL, 

1 KSTRG(600),STIF(8,8),VELSTO(200,2) 

COMMON/MATLS/ A(5), COM P P, R LGTH, WIDTH, R VOL, R MASS, 

1 TUNCPT,ZETA,DIAFI,RHOFI, 

2 RKCC,PORO,THK,TEMP, 

3 FRATE, ALPHA, FVISC, GAS, PZERO, IVSWH.IRESIN.NPLIES.ICURE 
C 

TEMP = TEMP + 273.15D0 
RHOFL = 1.158D3 
C 

AA = -1.3119D-5 
B= 0.016357D0 
C = -6.7848D0 
D = 936.8D0 
E = -2.0306D-5 
F= 0.025619D0 
G = -10.7646D0 
H = 1507.694D0 
R = 8.314D0 
CAPU = 44786.58683D0 
RMUINF = 7.56525D-9 
AMU = 1076.6816D0 
EMU = 16702. 90914D0 
C 

IF (TEMP.LE.383.0D0) THEN 
RM = 0.5776D0 
RN = 2.034D0 
A1 = 50.663D0 
El = 35305. 6D0 
A2 = 292.037D0 
E2 = 30485. 075D0 

RKMU = AMU*DEXP(-EMU/R/TEMP) 

GO TO 20 
END IF 
C 

IF (TEMP.LE.408.0D0) THEN 
RM = D + TEMP*(C + TEMP*(B + TEMP*AA)) 

RN = H + TEMP* (G + TEMP*(F + TEMP* E)) 

A1 = 50.663D0 
El = 35305.6D0 
A2 = 292.037D0 


APPENDIX A 


38 



E2 = 30485. 075D0 

RKMU = AMU*DEXP(-EMU/R/TEMP) 

GO TO 20 
END IF 
C 

IF (TEMP.LE.422.0D0) THEN 
RM = D + TEMP*(C + TEMP‘(B + TEMP*AA)) 

RN = H + TEMP‘(G + TEMP*(F + TEMP*E)) 

A1 = 50.663D0 

El = 35305.6D0 

A2 = 7.6908482D 1 3 

E2 = 1 19686.623D0 

RKMU = AMU*DEXP(-EMU/R/TEMP) 

GO TO 20 
END IF 
C 

IF (TEMP.LE.450.0D0) THEN 
RM = D + TEMP‘(C + TEMP*(B + TEMP*AA)) 

RN = H + TEMP*(G + TEMP*(F + TEMP‘E)) 

A1 =4.9876D21 

El = 196823.000 

A2 = 9.0382D0 

E2= 15230.7028D0 

RKMU = AMU*DEXP(-EMU/R/TEMP) 

GO TO 20 
END IF 
C 

20 RK1 =A1*DEXP(-E1/R/TEMP) 

RK2 = A2*DEXP(-E2/R/TEMP) 

C 

FRATE = (RK1 + RK2*ALPHA**RM)*(1.0D0-ALPHA**RN)/60 
FVISC = RMUINF*DEXP(CAPU/R/TEMP + RKMU*ALPHA) 

C 

TEMP = TEM P-273. 15D0 
C 

RETURN 

END 


APPENDIX A 


39 



7.8 Subroutine GLOBL 


c — 

C ** COMPUTES THE GLOBAL STIFFNESS MATRIX AND GLOBAL LOAD VECTOR 

SUBROUTINE GLOBL (ITRUN) 

C 

IMPLICIT REAL‘8 (A-H.O-Z) 

COMMON NODMAT(200,9),RPERM(10,2,2),VISCFL,RHOFL, 

1 KSTRG(600),STIF(8,8),VELSTO(200,2) 

COMMON/ONE/ X(600),Y(600),CENTX(200),CENTY(200) 

COMMON/TWO/ NEQ,IBWTH,STIFF(600,50),RHSV(600) 

COMMON/FOUR/ PRESS(600) 

COMMON/FIVE/ NOEL,NNODES,NMATR,NTIMES 
DIMENSION LM(16),Z(8,8),WK(8) 

C 

ISTOP = 0 
ITRUN = 0 
C 

C ** INITIALIZE OVERALL STIFFNESS MATRIX AND OVERALL LOAD VECTOR ** 
C 

DO 50 I = 1.NEQ 
RHSV(I) = 0.0D0 
DO 50 J = 1,IBWTH 
50 STIFF(I.J) = 0.0D0 
C 

C ** COMPUTE ELEMENT STIFFNESSES AND LOADS " 

C 

DO 55 M = 1,NOEL 
IF (NODMAT(M,9).GT.O) GO TO 60 
ITRUN = ISTOP + 1 
WRITE(6,1) ITRUN 
GO TO 55 

60 CALL ASTIF(M.AREA) 

C 

IF (AREA.LE.0.0D0) THEN 
WRITE(6,2) M,AREA 
ITRUN = ISTOP +1 
GO TO 55 
END IF 
C 

C ** ASSEMBLE STIFF MATRIX AND LOAD VECTOR ’* 

C 

DO 65 1 = 1,8 
II = NODMAT(M.I) 

C 

DO 65 J = 1,8 
JJ = NODMAT(M,J)-ll 4- 1 
IF(JJ)65,65,70 

70 IF(IBWTH-JJ) 75,80,80 


APPENDIX A 



75 WRITE(6,3) M 

ITRUN = ISTOP + 1 
GO TO 65 

80 STIFF(IIJJ) = STIFF(II,JJ) + STIF(I,J) 

65 CONTINUE 

55 CONTINUE 
C 

C ** INTRODUCE BOUNDARY CONDITIONS TO THE STIFFNESS AND RHS ** 

C 

M = 1 

110 IF (KSTRG(M).GE.0.AND.KSTRG(M).LT.4) GO TO 115 
ITRUN = ISTOP + 1 
WRITE(6,1) ITRUN 
M = M + 1 
GO TO 120 
C 

C NODAL UNKNOWN (NO BOUNDARY CONDITION SPECIFIED) ** 

C 

115 IF (KSTRG(M).EQ.O) THEN 
M = M + 1 
GO TO 120 
END IF 
C 

C ** NODAL FLOW RATES SPECIFIED ** 

C 

IF (KSTRG(M).EQ.2) THEN 
M = M + 1 
ITRUN = 1 
GO TO 120 
END IF 
C 

C ” NODAL PRESSURES SPECIFIED ** 

C 

IF ((KSTRG(M).EQ.1).OR.(KSTRG(M).EQ.3)) THEN 
CALL BOUNC(PRESS(M),M) 

M = M + 1 
END IF 
C 

120 IF (M.LE.NNODES) GO TO 110 
C 

IF (ITRUN. EQ.0) GO TO 95 
WRITE(6,1) ITRUN 
95 RETURN 

C ** FORMATS FOR SUBROUTINE GLOBL ** 

1 FORMAT (//' **** SOLUTION WILL NOT BE PERFORMED BECAUSE OF', 15, 
1' DATA ERRORS'/) 

2 FORMAT (//' **“ ERROR ELEMENT', 15,' HAS THE AREA OF',1 PE10.4//) 

3 FORMAT (//' **** BAND WIDTH EXCEEDS ALLOWABLE', 15//) 

END 


APPENDIX A 


41 



ooO o o uoo ooo^ ^ o uoo 


7.9 Subroutine ASTIF 


** COMPUTES THE ELEMENT STIFFNESS MATRIX AND ELEMENT LOAD VECTOR ’* 


SUBROUTINE ASTIF(M.AREA) 

IMPLICIT REAL*8 (A-H,0-Z) 

COMMON NODMAT(200,9),RPERM(10,2,2),VISCFL,RHOFL, 

1 KSTRG(600),STI F(8,8),VELSTO(200,2) 

COMMON/ONE/ X(600),Y(600),CENTX(200),CENTY(200) 
COMMON/THREE/ XJ,B(2,8),BT(8,2),RN(8) 

COMMON/FOUR/ PRESS(600) 

COMMON/FIVE/ NOEL,NNODES,NMATR,NTIMES 
DIMENSION TT(4),SS(4),R(2,2),TEMP0(2 I 2),TEMP1(2,8), 

I TEMP2(8,8) 

DATA SS/-1.D0,1.D0 I 1.D0,-1.D0/ I TT/-1.D0,-1.D0,1.D0,1.D0/ 

II = NODMAT(M.I) 

JJ = NODMAT(M,2) 

KK = NODMAT(M,3) 

LL = NODMAT(M,4) 

MM = NODMAT(M,5) 

NN = NODMAT(M,6) 

IJ = NODMAT(M,7) 

IK = NODMAT(M,8) 

MATL = NODMAT(M,9) 

** ANISOTROPIC PERMEABILITY MATRIX ** 

R(1,1) = RPERM(MATL,1,1) 

R ( 1 ,2) = R PERM (MATL, 1,2) 

R(2,1) = RPERM(MATL,2,1) 

R (2,2) = RPERM(MATL,2,2) 

** INITIALIZING FOR THE BIG INTEGRATION LOOP ** 

5 DO 70 I - 1,8 
DO 70 J =1,8 
0 STIF(I,J) = 0.0D0 

AREA = (X(II)-X(MM))'(Y(KK)-Y(IJ))-(X(KK)-X(IJ))*(Y(II)-Y(MM)) 
CENTX(M) = (X(ll) + X(KK) + X(MM) + X(IJ))/4.0D0 
CENTY(M) = (Y(ll) + Y(KK) + Y(MM) + Y(l J))/4.0D0 

** THE NUMERICAL INTEGRATION LOOP ** 

DO 75 II =1,4 
C 

S = SS(II)*0.577350269189626D0 


APPENDIX A 


42 



ooo 


T = TT(II)*0.577350269189626D0 

** CALCULATE THE B AND BT MATRICIES AT THE GAUSS POINTS ’* 

CALL FINDB(M,S,T) 

C 

CALL MULT (R,B,2,2,8,TEMP1) 

CALL MULT (BT,TEMP1 ( 8,2,8,TEMP2) 

C 

DO 80 1 = 1,8 
DO 80 J = 1,8 

80 STIF(I,J) = STIF(I,J) + TEMP2(I,J)*XJ 
C 

75 CONTINUE 
RETURN 
END 


APPENDIX A 


43 


DUO O O^O OOO QUO 


7.10 Subroutine FINDB 


** DETERMINES THE B MATRIX EVALUATED AT THE POINTS S AND T 


SUBROUTINE FINDB (M,S,T) 

IMPLICIT REAL‘8 (A-H.O-Z) 

COMMON NODMAT(200,9),RPERM(10,2,2),VISCFL,RHOFL, 

1 KSTRG(600),STIF(8,8),VELSTO(200,2) 

COMMON/ONE/ X(600),Y(600),CENTX(200),CENTY(200) 
COMMON/THREE/ XJ,B(2,8),BT(8,2),RN(8) 

DIMENSION RNCS(8),RNCT(8),RNCX(8),RNCY(8),XX(8),YY(8) 

DO 50 1 = 1,8 
RNCX(I) = O.ODO 
RNCY(I) — O.ODO 
XJ = O.ODO 


OMT= 1.0D0-T 
OPT = 1.0D0 + T 
OMS = 1.0D0-S 
OPS = 1.0D0 + S 
TSPT = 2.0D0*S + T 
TSMT = 2.0D0*S-T 
TTPS = 2.0D0*T + S 
TTMS = 2.0D0*T-S 

** SHAPE FUNCTIONS ** 

RN(1) = 0.25D0*OMS*OMT*(-S-T-1.0D0) 
RN(2) = 0.5D0‘(1.0D0-S'S)*OMT 
RN(3) = 0.25D0‘OPS*OMT*(S-T-1.0D0) 
RN(4) = 0.5D0*(1.0D0-T*T)*OPS 
RN(5) = 0.25DO*OPS*OPT*(S + T-.1.0D0) 
RN(6) = 0.5D0‘(1.0D0-S*S)*OPT 
RN(7) = 0.25DO*OMS*OPT*(-S +T-1.0D0) 
RN(8) = 0.5D0*(1.0D0-T*T)*OMS 


*‘ N i , s ** 

RNCS(1) = 0.25D0'OMT*TSPT 
RNCS(2) = -S*0MT 
RNCS(3) = 0.25D0'OMT*TSMT 
RNCS(4) = 0.5DO*OMT’OPT 
RNCS(5) = 0.25D0*OPT*TSPT 
RNCS(6) = -S‘OPT 
RNCS(7) = 0.25D0‘OPT*TSMT 
RNCS(8) = -0.5DO*OMT*OPT 


APPENDIX A 


44 



c 

C ** N i , t ** 

C 

RNCT(1) = 0.25D0*OMS*TTPS 
RNCT(2) = -0.5DO‘OMS*OPS 
RNCT(3) = 0.25D0‘OPS*TTMS 
RNCT(4) = -T*OPS 
RNCT(5) = 0.25D0* OPS’TTPS 
RNCT(6) = 0.5DO*OMS*OPS 
RNCT(7) = 0.25D0*OMS*TTMS 
RNCT(8) =-T*OMS 
C 

DO 55 1 = 1,8 
XX(l) = X(NODMAT(M,l)) 

55 YY(l) = Y(NODMAT(M,l)) 

C 

DO 60 1 = 1,8 
DO 60 J = 1,8 

60 XJ = XJ + XX(I)*YY(J)*(RNCS(I)*RNCT(J)-RNCT(I)*RNCS(J)) 

C 

DO 65 1 = 1,8 
DO 65 J = 1,8 

RNCX(I) = RNCX(I) + YY(J)/XJ*(RNCS(I)*RNCT(J)-RNCT(I)*RNCS(J)) 
65 RNCY(I) = RNCY(I) + XX(J)/XJ*(RNCT(I)*RNCS(J)-RNCS(I)*RNCT(J)) 
C 

c 

DO 75 1 = 1,8 
B(1 ,1) = RNCX(I) 

B(2,l) = RNCY(I) 

BT (1,1) — RNCX(I) 

75 BT(I,2) = RNCY(I) 

C 

C 

RETURN 

END 


APPENDIX A 


45 



o o o 


7.11 Subroutine BOUNC 


** COMPILES THE BOUNDARY CONDITIONS INTO THE KNOWN LOAD VECTOR ** 


SUBROUTINE BOUNC (U,N) 

C 

IMPLICIT REAL*8 (A-H.O-Z) 

COMMON/TWO/ NEQ,IBWTH,STIFF(600,50),RHSV(600) 
C 

DO 50 M = 2.IBWTH 
K = N-M + 1 
IF (K.LE.O) GO TO 55 
RHSV(K) = RHSV(K)-STIFF(K,M)*U 
STIFF(K.M) = 0.0D0 
55 K = N + M-1 

IF (K.GT.NEQ) GO TO 50 
RHSV(K) = RHSV(K)-STIFF(N,M)*U 
STIFF(N,M) = 0.0D0 
50 CONTINUE 
C 

STIFF(N.I) = 1.0D0 

RHSV(N) = U 
C 

RETURN 

END 


APPENDIX A 


46 



o o o 


7.12 Subroutine SOLVR 


** SOLVES THE SYSTEM OF EQUATIONS IN HALF-BANDWIDTH STORAGE 


SUBROUTINE SOLVR 
C 

IMPLICIT REAL*8 (A-H.O-Z) 

COMMON/TWO/ NEQ,IBWTH,STIFF(600,50),RHSV(600) 
C 

NRS = NEQ-1 
NR = NEQ 
C 

DO 50 N = 1,NRS 
M = N-1 

MR = MINO(IBWTH.NR-M) 

PIVOT = STIFF(N.I) 

C 

DO 50 L = 2,MR 
C = STIFF(N,L)/PIVOT 
1= M + L 
J = 0 

c 

DO 55 K = L,MR 
J= J + 1 

55 STIFF(I.J) = STIFF(I,J)-C*STIFF(N,K) 

C 

50 STIFF(N.L) = C 
C 

DO 60 N = 1,NRS 
M = N-1 

MR = MINO(IBWTH.NR-M) 

C = RHSV(N) 

RHSV(N) = C/STIFF(N,1) 

C 

DO 60 L = 2,MR 
1= M + L 

60 RHSV(I) = RHSV(I)-STIFF(N,L)*C 

C 

RHSV(NR) = RHSV(NR)/STIFF(NR,1) 

C 

DO 65 1 = 1, NRS 
N = NR-I 

M = N-1 

MR = MINO(IBWTH.NR-M) 

C 

DO 65 K= 2, MR 
L= M + K 

65 RHSV(N) = RHSV(N)-STIFF(N,K)*RHSV(L) 

C 


APPENDIX A 


47 



RETURN 

END 


APPENDIX A 


48 



non 


7.13 Subroutine STRESS 


** COMPUTES THE SECONDARY VARIABLES 


SUBROUTINE STRESS 
C 

IMPLICIT REAL*8 (A-H.O-Z) 

COMMON NODMAT(200,9),RPERM(10,2,2),VISCFL,RHOFL, 
1 KSTRG(600),STIF(8,8),VELSTO(200,2) 

COMMON/ONE/ X(600),Y(600),CENTX(200),CENTY(200) 
COMMON/TWO/ NEQ,IBWTH,STIFF(600,50),RHSV(600) 
COMMON/THREE/ XJ.B(2,8),BT(8,2),RN(8) 

COMMON/FIVE/ NOEL,NNODES,NMATR,NTIMES 
DIMENSION VELO(2),TEMPO(2,8),PERM(2,2),ESOLU(8) 

C 

DO 50 M = 1.NOEL 

CALL FI NDB(M, 0. 5773502691 89626D0.0.0D0) 

MATL = NODMAT(M,9) 

C 

DO 55 1 = 1,2 
DO 55 J = 1,2 

55 PERM(I,J) = RPERM(MATL,I,J) 

C 

CALL MULT (PERM, B.2, 2, 8, TEMPO) 

DO 60 1 = 1,8 
II = NODMAT(M.I) 

60 ESOLU(I) = RHSV(II) 

CALL MULT (TEMPO,ESOLU,2,8,1,VELO) 

C 

VELO(1) = -VELO(1)/VISCFL 
VELO(2) = -VELO(2)/VISCFL 
C 

VELSTO(M,1) = VELO(1) 

VELSTO(M,2) = VELO(2) 

C 

50 CONTINUE 
C 

RETURN 

END 


APPENDIX A 


49 


ooo ooo ooo 


7.14 Subroutine RECON 


** RECONFIGURES THE MESH FOR THE NEXT TIME STEP 


SUBROUTINE RECON 
IMPLICIT REAL‘8 (A-H.O-Z) 

COMMON NODMAT(200,9),RPERM(10,2,2),VISCFL,RHOFL, 

1 KSTRG(600),STIF(8,8),VELSTO(200,2) 

COMMON/ONE/ X(600) I Y(600),CENTX(200),CENTY(200) 

COMMON/FOUR/ PRESS(600) 

COMMON/FIVE/ NOEL,NNODES,NMATR,NTIMES 
COMMON/M ATLS/ A(5),COMPP,RLGTH,WIDTH,RVOL,RMASS, 

1 TUNCPT.ZETA.DIAFI.RHOFI, 

2 RKCC,PORO,THK,TEMP, 

3 FRATE, ALPHA, FVISC, GAS, PZERO, IVSWH,IRESIN,NPLIES,ICURE 
COMMON/TIMES/ TIME,DTIME(2),ATIME,BTIME,CTIME,POSA,POSB,ITIME 

** NEW NODAL POSITIONING ** 

PI = DACOS(-I.ODO) 

MATL = NODM AT(NOEL,9) 

I = NNODES + 1 
J = l + 1 
K = J + 1 
L = K+ 1 
M = L+1 


** UPDATEING THE TIME 

IF (MATL.GT.1) THEN 
POS = (X(NNODES)-X(8))/THK 
DTIME(MATL) = DTIME(I) + ATIME'POS 
IF (POS.GE.POSA) DTIME(MATL) = BTIME 
IF (POS.GE.POSB) DTIME(MATL) = CTIME 
END IF 

TIME = TIME + DTIME(MATL) 

C 

X(l) = X(NNODES-I) + 0.5DO*DTIME(MATL)*VELSTO(NOEL,1) 
X(J) = X(I) 

X(K) = X(NNODES-I) + DTIME(MATL)*VELSTO(NOEL,1) 

X(L) = X(K) 

X(M) = X(K) 

C 

Y(l) = Y(NNODES-2) 

Y(K)= Y(l) 

Y(M) = Y(NNODES) 

Y(J) = Y(M) 

Y(L) = Y(NNODES-I) 

C 


APPENDIX A 


50 



ooo o ooo oo 


" CONNECTIVITY MATRIX OF NEW ELEMENT ** 

NODMAT(NOEL+ 1,1) = NNODES-2 
NODMAT(NOEL+ 1,2) = I 
NODMAT(NOEL+ 1,3) = K 
NODMAT(NOEL + 1,4) = L 
NODMAT(NOEL+1,5) = M 
NODMAT(NOEL+ 1,6) = J 
NODMAT(NOEL + 1,7) = NNODES 
NODMAT(NOEL+ 1,8) = NNODES-1 
IF (NOEL.EQ.1) MATL = MATL + 1 
NODMAT(NOEL + 1,9) = MATL 

** MOVING BOUNDARY CONDITIONS *" 

KSTRG(K) = KSTRG(NNODES-2) 

KSTRG(L) = KSTRG(NNODES-I) 

KSTRG(M) = KSTRG(NNODES) 
KSTRG(NNODES) = 0 
KSTRG(NNODES-I) = 0 
KSTRG(NNODES-2) = 0 
KSTRG(I) = 0 
KSTRG(J) = 0 

PRESS(K) = PRESS(NNODES-2) 

PRESS(L) = PRESS(NNODES-I) 

PRESS(M) = PRESS(NNODES) 

” UPDATING THE SITUATION ** 

NNODES = NNODES + 5 
NOEL = NOEL + 1 

RETURN 

END 


APPENDIX A 



ooo 


7.15 Subroutine MULT 


** MULTIPLIES TWO TENSORS TO GET A THIRD 


SUBROUTINE MULT(A,B,L,M,N,C) 
C 

IMPLICIT REAL*8 (A-H.O-Z) 
DIMENSION A(L,M),B(M,N),C(L,N) 
C 

DO 50 1 = 1, L 
DO 50 K = 1,N 
SUM = 0.0D0 
DO 55 J = 1,M 

55 SUM =SUM + A(I,J)*B(J,K) 

50 C(I,K)=SUM 
C 

RETURN 

END 


APPENDIX A 



ooo ooo ooo 


7.16 Subroutine CURE 


** HEAT TRANSFER AND KINETICS OF THE CUREING RESIN 

SUBROUTINE CURE 
IMPLICIT REAL‘8 (A-H.O-Z) 

REAL*8 KTZ,KTFL,KTFI,KTZI,MDOT,MULN1,KTOOL,KPRES, 

1 LAMTOL.LAMPRE 

DIMENSION AA(300),B(300),C(300),D(300),U(300),T(300), 

1 CALPHA(300),VISC(300),SAVEM(300),RM(300), 

3 Z(300),ZRATIO(300) 

COMMON NODMAT(200,9),RPERM(10,2,2),VISCFL,RHOFL, 

1 KSTRG(600),STIF(8,8),VELSTO(200,2) 

COMMON/M ATLS/ A(5), COMPP.RLGTH, WIDTH, RVOL.RM ASS, 

1 TUNCPT.ZETA.DIAFI.RHOFI, 

2 RKCC,PORO,THK,TEMP, 

3 FRATE, ALPHA, FVISC, GAS, PZERO, IVSWH,IRESIN,NPLIES,ICURE 
COMMON/TIMES/ TIME,DTIME(2),ATIME,BTIME,CTIME,POSA,POSB,ITIME 
COMMON/TEMPS/ TIMEIN(300),TAUTO(300),NTEMPS 

DATA BMASS,FRACZ,XMASS, 

1 FRACX,ZB,TMN,FRACT,SAVE/8*0.0D0/ 

DATA SAVEM/30CT0.0D0/ 

** READ DATA SET ** 

READ(5,*) NTOOL.NPRESS.IFREQ.IRED 
READ(5,‘) CPFL.CPFI.KTFL.KTFI.HR 
READ(5,‘) DELT.VEL 

READ(5,‘) ZTOOL,KTOOL,RHOTOL,CPTOOL, 

1 ZPRES,KPRES,RHOPRE,CPPRES,NBLEED 

** CALCULATE CONSTANTS FOR TIME = 0 FOR EACH LAYER ” 

VFR = PORO 

RHO - RHOFI + (RHOFL-RHOFI)‘VFR 

RMF = RHOFL*PORO/(RHOFL*PORO + (1,ODO-PORO)‘RHOFI) 

CP = CPFI + (CPFL-CPFI)'RMF 
Cl - (1.0D0-VFR)/3.14159D0 
BB = 2.0D0*(KTFL/KTFI-1 .0D0) 

C2 = DSQRT(1.0D0-(BB*BB*C1)) 

C3 = C2/(1.0D0+ BB'DSQRT(CI)) 

KTZ = (1.0D0-2.0D0*DSQRT(C1))*KTFL + KTFL/BB* 

1 (3.14159D0-4.0D0/C2*DATAN(C3)) 

TDIFF= KTZ/(RHO*CP) 

ITOP = 0 
IEDGE = 0 
N1 = NTOOL+ 1 
N2 = N1 +NPLIES 
N3 = N1 + 1 


APPENDIX A 


S3 



ooo ooooo ooo ooo 


N4 = NTOOL + NPLIES 
N5 = N2+ 1 

N6 = NTOOL + NPLIES + NPRESS 
NTOT = N6 + 1 
DO 50 1 = 1, NTOT 
50 T(l) = TEMP 

** CALCULATE INITIAL MASS AND AREA OF EACH LAYER ** 


RMFI = 0.4 

AREAZ = RLGTH'WIDTH 

FMI = ZETA‘AREAZ 

FMFI = 1.0-RMFI 

TMI = FMI/FMFI 

RMI = TMI-FMI 

DELZ = THK/FLOAT(NPLIES) 

ZMIN = DELZ 

Al = -(TDIFF‘DELT/(DELZ*DELZ)) 

Bl = 1. 0-2.0* Al 

VFFF= FMI/(RHOFI‘AREAZ*ZMIN) 

VFRF = 1.0-VFFF 

TMNF = RHO*AREAZ*ZMIN 

RMIN = TMNF-FMI 

BRR = 0.47 

TMNI = TMI*NPLIES 

BTHICK = FLOAT(NBLEED)*0.2540E-02 

HTCT = VEL 

HTCB = HTCT 

** PRINT DATA SET ** 

WRITE(6,200) CPFL.KTFL.HR 

WRITE(6,205) CPFI.KTFI 

WRITE(6,210) RHO.CP.KTZ 

WRITE(6,21 1) ZTOOL,RHOTOL,CPTOOL,KTOOL 

WRITE(6,212) ZPRES,RHOPRE,CPPRES,KPRES 

WRITE(6,225) DELT.VEL 

WRITE(6,230) IFREQ.IRED 

** CALCULATE VECTORS A,B,C** 

** TOOL PLATE** 

DELZT = ZTOOL/FLOAT(NTOOL) 

TDIFT = KTOOL/(RHOTOL*CPTOOL) 

LAMTOL = DELT/(DELZT*DELZT) 

CTOOL = 2.0*TDI FT* LAMTOL 

** AIR/TOOL INTERFACE 1 = 1** 


APPENDIX A 


54 



C(1) = -CTOOL 
C 

C** INTERIOR TOOL PLATE 2<l<NTOOL** 

C 

DO 10 I = 2.NTOOL 
AA(I) = -TDIFT*LAMTOL 
B(l) = 1.0 + 2.0*(-AA(l)) 

10 C(I) = AA(I) 

C 

C** TOOL PLATE/COMPOSITE INTERFACE l = N1** 

C 

CONI =2.0*TDIFF*DELT/(DELZ*DELZ) 

CON2= KTOOL/(CTOOL‘DELZT) 

CON3 = KTZ/(CON1*DELZ) 

AA(N1) = -KTOOL/DELZT 

B(N1) = CON2*(1.0 + CTOOL) + CON3*(1.0 + CONI) 
C(N1) =-KTZ/DELZ 
C 

C** INTERIOR OF COMPOSITE N3<KN4” 

C 

DO 60 I = N1,N2 
CALPHA(I) = ALPHA 
60 VISC(I) = VISCFL 
ZIN = DELZ'NPLIES 
Z(N1) = 0.0D0 
ZRATIO(NI) = 0.0D0 
DO 11 I = N3,N2 
Z(l) = Z(l-1) + DELZ 

11 ZRATIO(I) = Z(I)/ZIN 
DO 65 I = N3.N4 

AA(I) = Al 
B(l) = Bl 
65 C(l) = Al 
C 

C“ COMPOSITE/PRESSURE PLATE INTERFACE l = N2** 
C 

TDIFP = KPRES/(RHOPRE*CPPRES) 

DELZP = ZPRES/FLOAT(NPRESS) 

LAMPRE = DELT/(DELZP‘DELZP) 

CPFLES = 2.0'TDIFP* LAMPRE 
CON4 = 2.0‘TDIFF‘DELT/(DELZ‘DELZ) 

CON5 = KTZ/(CON4*DELZ) 

CON6 = KPRES/(CPFLES" DELZP) 

AA(N2) = -KTZ/DELZ 

B(N2) = CON5‘(1 .0 + CON4) + CON6*(1 .0 + CPFLES) 
C(N2) = -KPRES/DELZP 
C 

C** INTERIOR PRESSURE PLATEN5< I < N6*“ 

C 

DO 12 I = N5.N6 
AA(I) = -TDIFP‘LAMPRE 


APPENDIX A 


55 


ooo ooo ooo ooo 


B(l) = 1.0 + 2.0‘(-AA(l)) 

12 C(l) = A A( I) 

** PRESSURE PLATE/AIR INTERFACE l = NTOT 
AA(NTOT) = -CPFLES 
** INITIALIZE COUNTERS ** 

ICOUNT = 0 

000 TIME = TIME + DELT 
ICOUNT = ICOUNT + 1 
I PR I NT = 0 

** SET TEMPERATURES AT BOUNDARIES ** 

TAIR = FTEMP(TIME.ITIME) 

** COMPUTE VALUE OF VECTORS U AND D ** 

B(1) = 1.0 + CTOOL*(1 .0 + HTCB*DELZT/KTOOL) 

D(1) = CTOOL*HTCB*DELZT*TAIR/KTOOL + T(1) 

C 

DO 13 I = 2.NTOOL 

13 D(l) — T(l) 

C 

TEMP = T(N1) 

ALPHA = CALPHA(N1 ) 

CALL RESIN(2) 

U(N1) = RHOFL*VFR*HR*FRATE/CP/RHO 
D(N1) = CON3‘U(N1)‘DELT + (CON2 + CON3)‘T(N1) 

C 

DO 14 I = N3,N4 
TEMP = T(I) 

ALPHA = CALPHA(I) 

CALL RESIN(2) 

U(l) = RHOFL*VFR*HR‘FRATE/CP/RHO 

14 D(I) = T(I) + U(I)*DELT 
C 

TEMP = T(N2) 

ALPHA = C ALPH A(N2) 

CALL RESIN(2) 

U(N2) = RHOFL*VFR*HR*FRATE/CP/RHO 
D(N2) = CON5*U(N2)‘DELT + (CON5 + CON6)*T(N2) 

C 

DO 15 I = N5,N6 

15 D(l) = T(I) 

C 

B(NTOT) = 1.0 + CPFLES*(1.0+ DELZP'HTCT/KPRES) 
D(NTOT) = CPFLES*DELZP*HTCT*TAIR/KPRES + T(NTOT) 
C 


APPENDIX A 


56 



OOO OOO .*00000 ooo ooo ooo oo 


* COMPUTE NEW TEMPERATURES ** 

CALL TRIDAG(1,NT0T,AA,B.C,D,T) 

* COMPUTE NEW DEGREE OF CURE AND RESIN VISCOSITY ** 

DO 20 I = N1,N2 
TEMP = T(I) 

ALPHA = CALPHA(I) 

CALL RESIN(2) 

CALPHA(I) = CALPHA(I) + FRATE'DELT 
VISC(I) = VISCFL 
20 CONTINUE 

'* PRINT RESULTS EVERY I FREQ TIME STEPS ** 

IF((ICOUNT/IFREQ)*IFREQ.EQ.ICOUNT) IPR1NT = 1 
IF(TIME.GE.TIMEIN(NTEMPS)) IPRINT = 2 
IF(IPRINT.EQ.O) GO TO 1040 

'* PRINT RESULTS ** 

WRITE(6,245) TIME.TAIR 

WRITE(6,250) (l,Z(l),T(l),CALPHA(l),VISC(l), 

1 ZRATIO(l),l = N1,N2,IRED) 

WRITE (6,253) T(1),T(NT0T) 

NASDF= N2-N1 

WRITE(8,251) (TIME,T(I),CALPHA(I),VISC(I), 

1 ZRATIO(l),l = N1,N2,NASDF) 

IF(IPRINT.EQ.2) GO TO 999 
GO TO 1000 

'* CALCULATE NEW VALUES FOR VECTORS A.B.C.U ** 

“TOOL PLATE/COMPOSITE INTERFACE l = N1 

040 CONI =2.0*TDIFF*DELT/(DELZ*DELZ) 

C0N3= KTZ/(C0N1*DELZ) 

B(N1) = CON2*(1.0 + CTOOL) + C0N3*(1 .0 + CONI) 

C(N1) = -KTZ/DELZ 

'* INTERIOR OF COMPOSITE N3< I < N4** 

DO 40 I = N3,N4 

AA(I) = -2.0‘TDIFF*DELT/(DELZ*DELZ*2.0D0) 

B(l) = 1.0 + (2.0*TDIFF*DELT/(DELZ*DELZ)) 

C(l) = -2.0*TDIFF*DELT/(DELZ*DELZ*2.0D0) 

40 CONTINUE 

** COMPOSITE/PRESSURE PLATE INTERFACE l = N2*‘ 


APPENDIX A 


57 



o o o 


C0N4 = 2.0‘TDIFF*DELT/(DELZ*DELZ) 

C0N5 = KTZ/(C0N4*DELZ) 

AA(N2) = -KTZ/DELZ 

B(N2) = C0N5*(1 .0 + CON4) + CON6*(1 .0 + CPFLES) 

C 

GO TO 1000 

** FORMAT STATEMENTS ** 

200 FORMAT (////8X, 'RESIN PROPERTIES'/ 

1 "10X/CP =',E13.5/ 

2 ",10X,'KT =',E13.5/",10X,'HR = ',E13.5) 

205 FORMAT (//8X, 'FIBER PROPERTIES'/ 

1 ",10X,'CP =',E13.5/ 

2 ",10X,'KT =',E13.5) 

210 FORMAT (//8X/PLY PROPERTIES'/ 

5 ' MOX/RHO = ',E13.5/",10X,'CP = ',E13.5/ 

6 ",10X,'KTZ =',E13.5) 

211 FORMAT (//8X/TOOL PLATE PROPERTIES'/ 

1 ", 10X, 'THICK =',E13.5/",10X,'RHO = ',E13.5/ 

2 ",10X,'CP =',E13.5/",10X,'KT =',E13.5) 

212 FORMAT (//8X, 'PRESSURE PLATE PROPERTIES'/ 

1 ", 10X, 'THICK =',E13.5/",10X,'RHO =',E13.5/ 

2 ",10X,'CP =',E13.5/",10X,'KT =',E13.5) 

225 FORMAT (//8X, 'PROGRAM CONSTANTS'/ 

2 ",10X,'DELT =',E13.5/",10X,'VEL =',E13.5) 

230 FORMAT (//8X/OPTIONS7 

1 ".10X/IFREQ =',14/ 

2 ",10X,'IRED = ',I4) 

245 FORMAT (////8X/TIME =',E13.6,5X,'TAIR =',F6.1/ 

2 /4X,'I',5X,'Z(I)',9X,'T(I)',7X, 

3 'CALPHA(I)',5X,'VISC(I)',7X,'Z/ZI') 

250 FORMAT (' 'I4.4E13.6.F9.5) 

251 FORMAT (' '.4E14.6.F7.3) 

253 FORMAT (/' '.8X/TTOOL = ',E13.6,5X,'TPLATE =',E13.6) 
999 STOP 
END 


APPENDIX A 


58 



ooo ooo poo 


7.17 Subroutine TRIDAG 


** SUBROUTINE TRIDAG 

SUBROUTINE TRIDAG(ISTART,IEND,A,B,C,D,T) 

IMPLICIT REAL*8 (A-H.O-Z) 

DIMENSION A(1).B(1),C(1),D(1),T(1).BETA(300),GAMMA(300) 

** CALCULATE VECTORS BETA AND GAMMA ** 

BETA(ISTART) = B(ISTART) 

GAMM A(ISTART) = D(ISTART)/BETA(ISTART) 

ISP1 = ISTART+1 

DO 10 I = ISP1.IEND 

BETA(I) = B(I)-A(I)*C(I-1)/BETA(I-1) 

10 GAMMA(I) = (D(I)-A(I)*GAMMA(I-1))/BETA(I) 

** CALCULATE TEMPERATURES ** 

T(IEND) = GAMMA(IEND) 

LAST = IEND-ISTART 
DO 20 J = 1.LAST 
I = IEND-J 

20 T(l) = GAMMA(I)-C(I)*T(I + 1)/BETA(I) 

RETURN 

END 


APPENDIX A 


59 


oo oo oo oo oo oo oooo 


7.18 Subroutine HCONV 


CALCULATES THE CONVECTIVE HEAT TRANSFER COEFFICIENT 
V = VELOCITY(M/S),PHI = VELOCITY CORRECTION FACTOR 


SUBROUTINE HCONV(TT,TB,HT,HB,PCURE,V,XLEN) 

IMPLICIT REAL*8 (A-H.O-Z) 

REAL*8 MUAIR 

TR = ((TT-273.)* 1 .8 + 32.) + 460, 

PSI = PCURE/6894.8 

**SPECICIFIC HEAT (J/KG-K) 

CPAIR = 1008.3 

"VISCOSITY (N-SEC/M2) 

MUAIR - 490.728E-9*TR**1.5/(TR + 198.72) 

"THERMAL CONDUCTIVITY (W/M-K) 

TKAIR - (2.E-5*(TR-460.) + .0133)*1.731 

'•DENSITY (KG/M 3) 

RHOAIR = 1 .326*2.03591 ‘PSI/TR* 16.02 

'•REYNOLDS NUMBER 

REL = RHOAIR‘V‘XLEN/MUAIR 

'•PRANDTL NUMBER 

PR = CPAIR*MUAIR/TKAIR 
IF(PR.GE..1.AND.REL.LT.500000.) GO TO 316 
I F(PR.LT.,1. AND.REL.LT. 500000.) GO TO 317 
IF(PR.GE..5.AND.REL.GE. 500000.) GO TO 318 
IF(PR.LT..5.AND.REL.GE.500000.) GO TO 319 

316 HT = (1.133‘(REL‘PR)**.5*PR*‘.33)*TKAIR/XLEN*PHI 
GO TO 320 

317 HT= (1.133*(REL*PR)**.5)*TKAIR/XLEN*PHI 
GO TO 320 

318 HT = (0.36*PR**.33*(REL**.8-23200.))*TKAIR/XLEN*PHI 
GO TO 320 

319 WRITE(6,321)PR,REL 

321 FORMAT(/,130('*'),/,'THE TOP CONVECTIVE HEAT TRANSFER COEFFICIEN', 
IT IS OUT OF REALISTIC BOUNDS'/ PR = \E10.4,' REL = '.E10.4,/, 

2130('*'),/) 

320 CONTINUE 

TR = ((TB-273.) * 1 .8 + 32.) + 460. 

CPAIR = 1008.3 

MUAIR = 490. 728E-9*TR**1.5/(TR + 198.72) 

TKAIR = (2.E-5*(TR-460.) + .0133)*1.731 
RHOAIR = 1.326*2.03591*PSI/TR‘16.02 
XLEN = .305 


APPENDIX A 


60 



REL = RHOAIR*V*XLEN/MUAIR 
PR = CPAIR*MUAIR/TKAIR 
I F(PR.GE..1. AND.REL.LT. 500000.) GO TO 326 
I F(PR.LT..1. AND.REL.LT. 500000.) GO TO 327 
IF(PR.GE..5.AND.REL.GE.500000.) GO TO 328 
IF(PR.LT..5.AND.REL.GE.500000.) GO TO 329 

326 HB = (1.133*(REL*PR)‘*.5*PR**.33)*TKAIR/XLEN*PHI 
GO TO 330 

327 HB = (1.133*(REL*PR)“.5)*TKAIR/XLEN*PHI 
GO TO 330 

328 HB = (0.36*PR**.33*(REL**.8-23200.))*TKAIR/XLEN*PHI 
GO TO 330 

329 WRITE(6,331)PR,REL 

331 FORM AT(/,130("'),/, 'THE BOTTOM CONVECTIVE HEAT TRANSFER 
1'COEFFICIENT IS OUT OF REALISTIC BOUNDS',' PR = ',E10.4,' REL = 
2E10.4,/,130('*'),/) 

330 CONTINUE 
RETURN 
END 


APPENDIX A 


61 



BIBLIOGRAPHIC DATA 1. Report No. 

SHEET CCMS-89-1 1, VPI-E-89-14 

4, Title and Subtitle 

RTM User's Guide 


2 . 


3. 


5. 


6 . 


Recipient's Accession Nc 


Report Date 
May 1989 


7. Author(s) 

Steven J. Claus and Alfred C. Loos 


8. Performing Organization F 
No. VPI-E-89-14 


9. 


Performing Organization Name and Address 


10. Project/Task/Work Unit 


Virginia Polytechnic Institute and State University 
Engineering Science and Mechanics Department 
Blacksburg, VA 24061-0219 

12. Sponsoring Organization Name and Address 
Applied Materials Branch 
National Aeronautics and Space Administration 
Langley Research Center 
Hampton, VA 23665-5225 

15. Supplementary Notes 


11, Contract/Grant No. 
NAG-1-343 


13. Type of Report Sc Period 
Covered 


14. 


16. Abstracts 

RTM is a Fortran '77 computer code which simulates the infiltration of textile reinforcements and the kJnetic 
thermosetting polymer resin systems. The computer code is based on the process simulation model deveic 
by the author [1]. The compaction of dry, woven textile composites is simulated to describe the increase in [ 
volume fraction with increasing compaction pressure. Infiltration is assumed to follow D'Arcy's law for Newto 
viscous fluids. The chemical changes which occur in the resin during processing are simulated with a the* 
kinetics model. The computer code is discussed on the basis of the required input data, output files and s< 
comments on how to interpret the results. An example problem is solved and a complete listing is included. 


17. Key Words and Document Analysis. 17a. Descriptors 

resin transfer molding, processing modeling, composites processing, textile composites, porous flow 


17b. Ident if iera /Open-Ended Terms CFJOINAI* PAGE IS 

OF POOR QUA I TTY 

I 


17c. COSATI Field/Group 
18. Availability Statement 


19,. Security Class (This 
Report) 


UNCLASSIFIED, 

‘ /*! ~ /TL ■ 


20. Security Class (This 

‘Unclassified 


21. No. of Pages 

68 


22. Price 





















VIRGINIA TECH CENTER FOR 
COMPOSITE MATERIALS AND STRUCTURES 


The Center for Composite Materials and Structures 
is a coordinating organization for research and 
educational activity at Virginia Tech. The Center was 
formed in 1982 to encourage and promote continued 
advances in composite materials and composite 
structures. Those advances will be made from the 
base of individual accomplishments of the forty 
members who represent ten different departments 
in two colleges. 

The Center functions through an Administrative 
Board which is elected yearly and a Director who 
is elected for a three-year term. The general purposes 
of the Center include: 

• collection and dissemination of information 
about composites activities at Virginia Tech, 

• contact point for other organizations and 
individuals, 

• mechanism for collective educational and 
research pursuits, 

• forum and agency for internal interactions at 
Virginia Tech. 

The Center for Composite Materials and Structures 
is supported by a vigorous program of activity at 
Virginia Tech that has developed since 1963. Research 
expenditures for investigation of composite materials 
and structures total well over seven million dollars 
with yearly expenditures presently approximating two 
million dollars. 


Research is conducted in a wide variety of areas 
including design and analysis of composite materials 
and composite structures, chemistry of materials and 
surfaces, characterization of material properties, 
development of new material systems, and relations 
between damage and response of composites. 
Extensive laboratories are available for mechanical 
testing, nondestructive testing and evaluation, stress 
analysis, polymer synthesis and characterization, 
material surface characterization, component 
fabrication, and other specialties. 

Educational activities include eight formal courses 
offered at the undergraduate and graduate levels 
dealing with the physics, chemistry, mechanics, and 
design of composite materials and structures. As of 
1984, some 43 Doctoral and 53 Master's students have 
completed graduate programs and several hundred 
Bachelor-level students have been trained in various 
aspects of composite materials and structures. A 
significant number of graduates are now active in 
industry and government. 

Various Center faculty are internationally recog- 
nized for their leadership in composite materials and 
composite structures through books, lectures, 
workshops, professional society activities, and 
research papers. 


Aerospace and Ocean 

Engineering 
Raphael T. Haftka 
Eric R. Johnson 
Rakesh K. Kapania 

Chemical Engineering 
Donald G. Baird 

Chemistry 
John G. Dillard 
James E. McGrath 
Larry Taylor 
Thomas C. Ward 
James P. Wightman 

Civil Engineering 
Richard M. Barker 

Electrical Engineering 
loannis M. Besieris 
Richard O. Claus 


MEMBERS OF THE CENTER 

Engineering Science 

and Mechanics 
Robert Czarnek 
David Dillard 
Norman E. Dowling 
John C. Duke, Jr. 

Daniel Frederick 
O. Hayden Griffin, Jr. 

Zafer Gurdal 
Robert A. Heller 
Edmund G. Henneke, II 
Michael W. Hyer 
Robert M. Jones 
Liviu Librescu 
Alfred C. Loos 
Don H. Morris 
John Morton 
Ali H. Nayfeh 
Daniel Post 


J. N. Reddy 
Kenneth L. Reifsnider 

C. W. Smith 

Wayne W. Stinchcomb 
Surot Thangjitham 

Industrial Engineering and 
Operations Research 
Joel A. Nachlas 

Materials Engineering 
$. B. Desu 

D. P. H. Hasselman 
Robert E. Swanson 

Mathematics 
Werner E. Kohler 

Mechanical Engineering 
Charles E. Knight 
John B. Kosmatka 
J. Robert Mahan 
Craig A. Rogers 
Curtis H. Stern 


Inquiries should be directed to: 


Center for Composite Materials and Structures 
College of Engineering 
Virginia Tech 

Blacksburg, VA 24061-0230 
Phone: (703) 231-4969