NASA Contractor Report 181866 

ON PROCESSING DEVELOPMENT FOR FABRICATION OF 0 FIBER REINFORCED COMPOSITE - I1 

Tan-Hung Hou 

PRC Systems Services 

A Division Of Planning Research Corporation 

Hampton, Virginia 23666 

Gene J. W. Hou and Jeen S. Sheen 

Department of Mechanical Engineering & Mechanics 

Old Dominion University 

Norfolk, Virginia 23508 ' 

Contract NAS 1 - 18000 

July 1989 v 

NASA 

National Aeronautics and 

Space Administration 

Langley Research Center 

Hampton, Virginia 23665-5225 

(HASA-CR-381866) 08 PEOCBSSI1oG DEVELOPHENT N 89- 269 17 

FOR FABBICBTXIOY OF FIBER BEIZIPORCBD 

COEPOSITE, PART 2 (Planning Research Corp.) 

CSCL 11D 56 P Onclas 

63/24 0224023 

-L- 
- ON PROCESSING DEVELOPMENT FOR FABRICATION OF FIBER 

REINFORCED COMPOSITE - I1 

.. FOREWORD ................................................................... .ll 

ABSTRACT ........................................................... 1 

INTRODUCTION ........................................................... 2 

THERMAL ANALYSIS 

Problem Statement ........................................................... 4 . 

Diffusion-Reaction System Equations ......................................... 5 

THERMAL DESIGN SENSITIVITY ANALYSIS ................................... 10 

OPTIMAL CURE CYCLE DESIGN ................................................. 14 

Numerical Examples 

Example 1 ............................................................ 

Example 2 .......................................................... 19 

2.0 

Example 4 .......................................................... 21 

DISCUSSION ........................................................ .23 

Example 3 .......................................................... 

CONCLUSIONS AND REMARKS ............................................................ 

REFERENCES ......................................... ;. .............. .27 

TABLES .......................................................... 29 

FIGURES .......................................................... 34 

I 
FOREWORD 

This work was sponsored by and performed at the Polymeric Materials Branch (PMB), 

NASA Langley Research Center (LaRC). Mr. Robert M. Baucom (PMB) was the Technical 

Monitor for this investigation. 

High performance fiber reinforced composite materials have found increasing usages in 

the aerospace and automobile industries in recent years. Typically, these composite materials 

are available as Sheet Molding Compound (SMC) or in prepreg forms, and can be processed 

by press or Autoclave molding. For successful processing of high quality composite 

laminates, an effective design of the cure cycle is the foremost important factor. The design of 

the cure cycle is often influenced by material properties such as: resin flow, chemorheology, 

volatile escaping mechanism, heat transfer between the process environment and the specimen, 

fiber deformation, and the kinetics of the chemical reaction of resin, etc. This report presents 

an effective cure cycle design by means of the optimization technique. The design is 

implemented by Computer Aided Design (CAD) methodology. 

This work has been accepted for publication in the International Polymer Processing, 

Volume IV, 1990. One previous publication which deals with the same subject matter is: 

Autoclave Processing For Composite Laminate : An Analysis Of Resin Flows And Fiber 

Compactions For Thin Laminates, NASA Contractor Report CR-178011, November, 1985. 

The authors would like to acknowledge financial support provided by NASA LaRC 

under the Contract NAS 1-18000 to the Planning Research Corporation, Hampton, Virginia, 

and the Research Grant NAG1-561 to the Department of Mechanical Engineering & 

Mechanics, Old Dominion University, Norfolk, Virginia, during the course of this 

investigation. 

ii 
ON PROCESSING DEVELOPMENT FOR FABRICATION OF FIBER 

REINFORCED COMPOSITE - 11' 

Tan-Hung Hou112 

PRC Systems Services, Aerospace Technologies Division 

Planning Research Corporation 

Hampton, Virginia 23666 

Gene J. W. Hou1 and Jeen S. Sheen1 

Department Of Mechanical Engineering & Mechanics 

Old Dominion University, Norj6olk, Virginia 23508 

ABSTRACT 

Fiber-reinforced composite laminates are used in many aerospace and automobile 

applications. The magnitudes and durations of the cure temperature and the cure pressure applied 

during the curing process have significant consequences for the performance of the finished 

product. The objective of this study is to exploit the potential of applying the optimization 

technique to the cure cycle design. Using the compression molding of a filled polyester Sheet 

Molding Compound (SMC) as an example, a unified Computer Aided Design (CAD) 

methodology, consisting of three uncoupled modules, (Le., Optimization, Analysis and Sensitivity 

Calculations), is developed to systematically generate optimal cure cycle designs. Various 

optimization formulations for the cure cycle design are investigated. The uniformities in the 

distributions of the temperature and the degree of cure within the specimen cured under the optimal 

cycles are compared with those resulting from conventional isothermal processing conditions with 

pre-warmed platens. Recommendations with regards to further research in the computerization of 

the cure cycle design are also addressed. 

*Portions of this work was presented as paper No. AIAA 87-0751-CP at the AIAA/ASME/ASCE/AHS 28th 

Structures, Structural Dynamics and Materials Conference, Monterey, California, April 6-8, 1987. Adjunct 

Assistant Professor, Associate Professor, and Graduate Research Assistant, respectively, ODU. 2Supervisor, 

Polymeric Materials Unit. 

1 
INTRODUCTION 

High performance polymeric composites are used increasingly in the aerospace and 

automobile industries. Such materials are typically composed of long or chopped fibers embedded 

in a thermosetting resin matrix. The composite parts and structures are often manufactured by 

curing the prepreg or unmolded material. The cure process is accomplished by exposing the 

material to elevated (cure) temperatures and (cure) pressures for a predetermined length of time. 

The cure temperature provides the heat required for initiating and maintaining the chemical 

reactions in the resin during the curing process. Once the reactive mamx resin is heated, 

polymerization reactions start to occur. The heat comes from two sources, Le., from the exotherm 

generated from the reactions and by conduction and convection from the surrounding environment. 

At the certain stage during the processing, the cure pressure is applied to squeeze out the excess 

resin inside the laminate. Consequently, the individual plies are consolidated and the vapor 

bubbles are compressed. 

The magnitudes and durations of the cure temperature and the cure pressure applied during 

the curing process have significant consequences on the performance of the finished product. 

Thus, it is not a trivial task to properly design a cure cycle (temperature and pressure profiles). The 

material should be cured uniformly and completely with the lowest void content; the temperature 

inside the laminate must not exceed some maximum value; and the cure process should be 

completed within the shortest amount of time. In the past, most cure cycle designs for newly 

developed composite systems have been based on the technique of laboratory trial and error. Such 

an approach has long been recognized as costly and inefficient. Several simulation models have 

been developed recently for curing various thermoplastic [ 11 and thermosetting [2 - 41 matrix 

composites. These developments represent a significant advancement in computerizing the cure 

cycle design. The next logical step is then to develop a methodology which could be used to 

search for the optimal cure cycle for a given fiber/resin composite system. This paper reports and 

discusses the initial results from such an investigation which uses a unified Computer-Aided 

2 
Design (CAD) method for the cure cycle design, that incorporates an optimal design technique with 

an analytical model for a composite curing process. 

The curing process of interest is the compression molding of a polyester sheet molding 

compound (SMC). The finite element method is employed to convert the initial-boundary value 

problem into a set of first order differential equations which are solved simultaneously by the DE 

program [5]. The equations for thermal design sensitivities are then derived by using the direct 

differentiation method and are solved by the DE program. Finally, a recursive quadratic 

programming algorithm with an active set strategy, called a linearization method [6], is used to 

design the optimal cure cycle which is subjected to the given design performance requirements. 

The difficulties of casting the cure cycle design process into a proper mathematical form are 

recognized, and various optimal design problems are formulated to address these aspects. The 

optimal solutions of these formulations are compared and discussed, and the processing and 

material parameters which play major roles in the cure cycle design for a given composite system 

are identified. Recommendations with regard to the computerizing of the cure cycle design are also 

addressed. 

3 
THERMAL ANALYSIS 

Problem Statement 

The formulation of a complete analytical model for the curing process in the manufacture 

of fiberhesin composite laminates is rather complicated [3]. Such an analytical model should be 

able to address: 

a) the heat transmission between the surrounding environment and the specimen, 

b) the heat generated by the chemical reaction of the resin, 

c) the temperature distribution within the laminate, 

d) the phase changes of the resin during cure as commonly characterized by the 

chemoviscosity and the degree of cure, and 

e) the resin flow problems associated with the consolidation process among the prepreg 

plies and volatile removal from the specimen. 

The major parameters which play important roles in modeling the cure process may be 

identified as the temperature, the degree of cure of the resin, the resin viscosity, the resin flow 

properties, the thickness of the specimen and the material properties, such as density, heat 

conductivity, etc. Most parameters are varied continuously with respect to the time and spatial 

location. 

To focus on the optimization aspects of the present study, several assumptions which 

simplify the formulation of the curing process are introduced as follows: 

1) the temperature and the degree of cure of the specimen are uniformly distributed in a 

plane parallel to the tool plates. As a result, the parameters of the problem are functions 

of the time and the position along the thickness of the specimen only. 

4 
2) the resin content in the material is assumed to be low SO that there is only a small amount 

of excess resin. Consequently, the resin flow model as well as the pressure cycle are not 

considered. 

3) the material properties which depend on the fiber-resin ratios are assumed to remain 

constant during the entire cure cycle, 

4) the volatiles escaping mechanism is not considered, and 

5) there is no deviation between the environment (tool) temperature and the temperature on 

the surfaces of the material adjacent to the tool plates. The temperature distribution and 

the degree of cure are the only two state variables which are governed by diffusionreaction system equations. 

After these simplifications, a CAD scheme for the cure cycle design is developed in the 

following sections for the curing process of the compression molding for a filled polyester SMC 

[2]. Similar procedures are also applicable to the curing of continuous fiber reinforced composite 

lamination process. 

Diffusion-Reaction System Equations 

The SMC curing process is modeled by a diffusion-reaction mechanism. The diffusionreaction system equations consist of a one-dimensional unsteady heat-conduction equation with its 

boundary and initial conditions, and a kinetics model of the curing reaction for the reactive resin 

system. A computational algorithm, based on the Finite Element Method and a numerical 

integrator, is developed to analyze the thexmo-chemical reaction. 

The temperature distribution T(z,t) and the degree of cure a(z,t) of the resin inside the 

composite laminate depend on the rate at which heat is transmitted from the environment. The 

temperature distribution inside the composite laminate can be calculated by using the law of 

conservation of energy together with an appropriate expression for the cure kinetics. By neglecting 

energy transferred by convection, the energy equation may be expressed as 

5 
pcT = kT" + pH, d 

with the boundary conditions, 

T' (0,t) = 0, OStST, 

OItS2, 

and the initial condition, 

where p and c are the density and the specific heat of the composite material, respectively, k is the 

thermal conductivity in the direction perpendicular to the plane of composite material, 2h is the total 

thickness, Tc(t) is the cure cycle in OK, z is the time in seconds needed for the completion of one 

cure cycle, and Hr is the total or ultimate heat of reaction. Moreover, the dot (.) on the top of a 

symbol indicates the time, t, derivative and the superscripts, (I) and ("), denote the first and second 

spatial, z, derivative respectively. According to the assumptions discussed previously, all 

coefficients in Eqs. (1) - (3) are treated as constants. Note that the cure temperature TJt) appears 

in Eq. (2) as the boundary conditions; and the last term in Eq. (l), pH, a, is the rate of heat 

generated by the chemical reaction as characterized by the degree of cure a. 

The degree of cure, a, is defined as the fraction of heat, H(t), released up to time, t, for the 

resin system under cure: 

6 
Both H(t) and H, in Eq. (4) can be measured experimentally by Differential Scanning Calorimetry 

(DSC). For an uncured material, a approaches zero, and for a completely cured material, a 

approaches one. The reaction rate, a, depends strongly on the curing temperature. As an example, 

the cure rate equation of a stepwise isothermal curing process is used for a polyester SMC [2] as 

follows: 

where al, a2, dl, d2, m and n are constants, R is the universal gas constant, and K1 and K2 are 

exponential functions of the temperature. Some observations of interest are noted: (1) The state 

equations of the cure process are coupled with two state variables, namely, the temperature 

distribution T(z,t) and the degree of cure a(z,t), and (2) The non-homogeneous boundary value, 

T,(t), is to be considered as the design variable in the design optimization problem. Using the 

following replacement for the temperature T(z,t): 

T(z,t) = T(z,t) + T,(t), 

the heat-conduction problem stated in Eqs. (1) - (3) can be simplified as an equation of T(z,t) 

(74 pcT = kT” - ~cT, + pHr f(a,T,T,) , 

with the homogeneous boundary conditions, 

- 

T’(0,t) = 0, OIt12, (7.b) 

7 
- 

T(h,t) = 0, OStST, (7.c) 

and the initial condition, 

where the function f is defined in Eq. (5). From here on, ?; is abbreviated as T for further 

simplification. Because the initial temperature TJz) is the same as the initial cure temperature for 

most applications, Eqs. (7) may have a homogeneous initial condition as well. 

The finite element discretization is introduced herein to convert the initial-boundary value 

problem, Eqs. (5) and (7), into a set of first order matrix equations. Quadratic and linear 

polynomials are used to interpolate the states of temperature and the degree of cure, respectively. 

Notation T2i-1, T2i and ai denote the temperature, the temperature gradient and the degree of cure, 

respectively, at node i: 

where the unknowns are the vector of temperature (T} = (TI, T2, ..., T2n}T and the vector of the 

degree of cure, {a}= (al, a2, ..., an}T for n = NE + 1 as the total number of nodes. The 

matrices [C], [Kj and FrJ result from the finite element discretization of the terms and T" in 

Eq. (7.a) and the term & in Eq. (5). Moreover, the vector (P} is associated with the term Tc in 

Eq. (7.a) and the vectors (Q} and {R] appearing in Eq. (8) are the discretized forms of the terms 

pertaining to f(a,T) in Eqs. (5) and (7.a). Note that Tl(t) and T2n(t) are always zeros in the 

analysis according to the boundary conditions of T(h,t) = 0 and T'(0,t) = 0, respectively. The 

initial conditions for each of the components in (T} and ( a) are 

8 
and T2i(O) = ai(0) = 0 where i is the nodal number. Moreover, To represents the temperature of 

the composite at the onset of the cure process and this is usually uniformly distributed. The 

detailed derivation of the matrix equations, Eqs. (8), is given in Ref. [7]. The above equations, 

coupled with each other through the non-linear terms on the right side of Eqs. (8), can be solved 

simultaneously by using the computer program DE [5]. 

The DE program is one of predictor-corrector integration algorithms using the Adams 

family of formulas. The truncation error is controlled by varying both the step size and the order 

of the polynomial approximation. The DE program is quite easy to use and has the capability of 

managing moderately stiff differential equations which happen frequently in the chemical kinetics 

problems. To maintain a unified accuracy in the analysis, the computation of two state variables, 

namely, the temperature and the degree of cure, are subjected to the same error tolerance in this 

study. Numerical solutions of several examples designed to verify Eqs. (8) with existing analytical 

solutions can be found in Ref. [7]. 

9 
THERMAL DESIGN SENSITIVITY ANALYSIS 

The derivatives of functionals of responses with respect to the design variables are often 

referred to as design sensitivity derivatives. Most general optimization algorithms require such 

derivatives which can be used to approximate constraints and to choose a search direction to obtain 

a set of improved design variables. It is then necessary to have a reliable means to calculate the 

design sensitivity derivatives. 

To focus on the study of thermal design sensitivity analysis in this section, the cure 

uniformity is simply represented by the least-square integral of the deviation between the pointwise 

temperature and the averaged temperature as 

The above functional defines a global sense of temperature uniformity across the thickness of the 

composite during the cure process. It is expected that the temperature uniformity within the curing 

specimen will translate into the uniformity of the curing reaction. Other mathematical expressions 

of the cure uniformity will be discussed in the following section of optimal cure cycle design. On 

the other hand, the following pointwise inequality may be used to force the cure reaction to reach 

certain predetermined value, q , at the end of cure cycle: 

where z is the total time required to complete one cure cycle. The numerical techniques to calculate 

the design derivatives of the functional Q0 and the state variable a, and 2, will be addressed 

hereafter. Note that the design variable b is a parameter associated with the cure cycle (temperature 

profile). 

do0 

10 
In general, there are four ways to calculate the thermal design derivatives, namely, the finite 

difference method, the Green's function approach, the direct differentiation method (the behavior 

space approach), and the adjoint variable method (the dummy load method). The last two methods 

are often mentioned in the literature [8 - lo]. Both methods lead to a set of linear equations that 

have a similar structure to the original system. However, based on the numerical study [ 1 11, it has 

been concluded that the direct differentiation method is superior to the adjoint variable technique in 

terms of accuracy and physical interpretation of results. Thus, the thermal design sensitivity is 

calculated by using the direct differentiation method in this study. 

The direct differentiation method is an approach that takes derivatives of differential 

equations with respect to a single design variable directly. For a given functional, Eq. (9), and the 

governing equations of the diffusion-reaction system, Eqs. (5) and (7), the direct differentiation 

results in the following equations in terms of design derivatives dT 5 and % as: 

and, 

af dTc 

aTc db ' 

+ pH,--- 

da af da af CfT af dT, -=-- +-- +--. 

db aa db aT db aT, db 

11 
It is assumed that T(z,b,t) and a(z,b,t) have enough regularity in the time-spatial domain and in the 

design space. Thus, the order of the differentiation is interchangeable. 

Based on the same finite element discretization as used in solving the original diffusionreaction system discussed previously, Eqs. (11) - (13) can be converted into a set of matrix 

equations 

and 

(15.a) 

(15.b) 

The construction of the above equations is discussed in Ref. [5]. 

Note that the coefficient matrices of Tb and ab in Eqs. (15) are identical to those of (T} 

and {a} defined in Eqs. (8). Therefore, the same numerical scheme and numerical tolerance can 

be applied to solve both Eqs. (8) and (15) simultaneously for state variables ((T} and {a}) and 

design derivatives ({ Tb} and (ab}). In this way, the state variables and the design derivatives 

achieve the same numerical accuracy, though an additional set of equations such as Eqs. (15) is 

needed in this approach for each design variable b. 

1-1 

Once {T}and (Tb) are available, the design derivative given in Eq. (14) can be easily 

obtained by the numerical integration. Another suggestion is to rewrite the integral form of Eq. 

(14) as a differential equation of 0 given as 

The above equation of @o,b can then be solved simultaneously with equations of ({ T}, {a)) and 

((Tb) and {ab}). In this way, one extra design derivative @o,b for each design variable is 

12 
introduced in the design sensitivity andysis. However, the accuracy of $o,b is secured. Equation 

(16) is used in the next section to compute Q0,b 

13 
OPTIMAL CURE CYCLE DESIGN 

The optimal design of cure cycles is studied here to find the optimal cure cycle such that the 

specimen is cured as uniformly as possible, and that a certain preset degree of cure is achieved at 

the end of the curing process. 

Numerical results presented in this section have been obtained by a recursive quadratic 

programming algorithm with an active set strategy, called a linearization method [6]. The 

linearization method, with its active set strategy, minimizes the number of constraints which must 

be considered in each design iteration. The detailed derivation of this algorithm can be found in 

Refs. [6,12]. The concept of this algorithm is that, rather than directly solving the optimal criteria, 

a small perturbation for each design variable is determined in each iteration to reduce the objective 

function and correct the violation. Note that, in this approach, the reduction of the objective 

function and the correction of the constraint violations are approximated by the design gradients. 

In the linearization method it has been proved [13] that a local optimal solution is found when the 

I* norm of the perturbation of design variables approaches zero. The complete flow chart of 

optimal cure cycle design is listed in Fig. 1. As shown in the figure, the proposed CAD method 

consists of three uncoupled modules; namely, Optimization, Analysis, and Sensitivity Calculation. 

Once the analysis capability of any cure process is established, the Optimization and Sensitivity 

Calculation modules can be added onto it to constitute a unified CAD methodology which can 

generate optimal cure cycles under various constraints systematically. 

Problem Statement 

As mentioned, optimal design techniques have been successfully applied to various 

transient problems. In general, an optimal design problem consists of the design variables, the 

objective functions, the constraint functions, and the state equations which describe the physical 

model of interest. 

14 
In our study, the process of interest is the compression molding of a filled polyester resin 

reinforced by chopped glass fibers SMC [2]. The state equations are limited to a heat conduction 

equation, Eq. (l), and an empirical equation which addresses the chemical-kinetics reaction of 

resin, Eq. (5). Since this study excludes the resin flow and the effects of the pressure cycle, the 

selection of the cure cycle is then limited to the following considerations: 

a) The maximum temperature inside the composite laminate at any instant during the cure 

cycle can not exceed 500 "K, 

b) At the end of the curing cycle, the degree of cure of the reactive resin system is 

required to reach at least 0.85, and 

c) The specimen should be cured uniformly at any instant during the entire cycle. 

The first two requirements may be formulated as constraints 

$1 : T(t) I500 'K, OItSz, 

Here the curing period, z, is predetermined by the user, and is not considered as a design variable 

in the current design formulation. However, it is not difficult to include z as an additional design 

variable in the proposed formulation. The last requirement can be met by formulating it as the 

objective function of the optimal design. Since the degree of cure is a function of temperature, a 

uniform distribution of temperature across the thickness will tend to insure the uniformity of the 

cure within the specimen. The objective of the optimal design may then be set to achieve 

uniformity of the temperature across the section of the material during the cure process. The 

objective function Q0 is thus defined as the greatest value of the standard derivation of temperature 

distribution which happens during the cure process 

15 
It follows that the minimum of the objective function, $JT,,t) = 0, corresponds to a uniform 

temperature distribution inside the composite at any time during the cure process. To sum up, the 

optimal cure cycle design is defined as follows: 

The optimal cure cycle (temperature profile) is designed, subject to the limitations regarding 

the maximum temperature and the state of cure, so as to achieve a uniform temperature distribution 

along the cross section of the material at any time during the entire cure cycle. 

The mathematical formulation of the stated optimal design problem is a minimax problem given as 

Minimum Maximum T2dz - (! Tdzrh] Tdt) OIt57 

subject to the constraints stated in Eqs. (17) - (18) where the temperature T(t) and the degree of 

cure a(t) are the solutions of state equations. 

It is known that the objective function of a minimax problem is discontinuous in the design 

space [ 141. To avoid computational difficulty, one may modify the optimal design problem to a 

standard form by introducing an extra design variable bo and an additional constraint $3 as follows: 

subject to 

$1 : T(t) I500 OK, 

$2 : a(~) 2 0.85, 

16 

OStIT, 
OStST. 

The design function Tc(t) can now be parameterized by a linear combination of design 

parameters and given functions. In this presentation, the design function is simply represented by 

a combination of linear polynomials and sinusoids 

where To is the room temperature and bl, b2, b3, and b4 are to be determined by the optimal design 

algorithm. As a result, the design space becomes finite dimensional, and the design sensitivities 

(or gradients) of temperature T(t) and state of cure a(t) are taken as derivatives with respect to 

design parameters bl, b, b3, and b4. For example, the design derivatives of constraint functions, 

Eqs. (21) and (22), can be derived as 

and 

h 

o T cdz ab. - (a Tdz) (a ;dz)/h] . 1 

aT aa 

for i =1-4. It is obvious that the design sensitivities of - and - are needed for the calculation of 

the above function gradients. Note that the pointwise constraints, $1 and $3, are imposed at every 

time grid point in this study. With the information of thermal sensitivities, the optimal cure cycle 

TJt) of the above problem can be found numerically by using a gradient-based mathematical 

abi abi 

17 
programming technique. As discussed in the last section, the direct differentiation method is 

employed hereafter to compute the required thermal design derivatives. 

Numerical Examples 

To show the applicability of the proposed CAD scheme for the optimal cure cycle design, 

four examples associated with various problem formulations are discussed and presented in this 

section. 

Example 1. 

The objective function q0 defined by Eq. (19) is minimized to find an optimal cure cycle 

design for processing a typical chopped glass fiber reinforced polyester SMC with a thickness of 

10 mm by compression molding. The total processing time is limited to 100 seconds. The 

maximum temperature allowed inside the SMC is 500 OK; and the degree of cure, a, is required to 

reach at least 0.85 at the end of the cure cycle. 

. 

The physical and kinetics properties of the SMC material are given in Table 1 [2]. The 

optimization algorithm requires 22 iterations to obtain the optimal solution for this case. Numerical 

results for the optimal design are listed in Table 2. Fig. 2 shows the cure cycles computed at 

iterations 1, 11, and 22, respectively. It should be noted that the cure cycles designed in this 

example are always made to start from room temperature which is different from the common 

practice with pre-warmed press platens employed in the compression molding process. The initial 

cure cycle (iteration 1) has two peaks and a valley at around 20, 85 and 60 sec., respectively. 

During the iterations toward the optimal solution, the initial heating rates are seen to decrease 

gradually; and a single peak near 70 sec is obtained eventually for the iteration 22 solution. The 

values of the objective function are shown in Fig. 3. The optimal cure cycle indeed delivers a 

more uniformly distributed temperature. The optimal solution has reduced the maximal value of 

temperature deviation from 2,700 to 378 units. 

18 
-Temperature distributions across the thickness of the SMC at selected instants of 20, 60 

and 100 sec during the cure process are compared for iterations 1, 11 and 22, shown in Fig. 4(a), 

(b) and (c), respectively. As noted previously in Fig. 2, the lower initial heating rate helps the 

optimal cure cycle (iteration 22) achieve a more uniform temperature distribution at the early 20 

sec. into the cure process. At the 60 sec., the cure cycle of the eleventh iteration yields a better 

distribution profile as seen in Fig. 4(b), which is due to the negative heating rates (cooling) 

between 30 to 50 sec. as seen in Fig. 2. On the other hand, the higher initial heating rate provided 

by the cure cycle of iteration 1 (Fig 2) has strongly triggered the kinetics reaction in the first 20 sec. 

into the cure process, and consequently results in a highly non-uniform temperature distribution 

between 30 to 50 sec., in spite of the provision of subsequent steep cooling rate within the same 

time interval in the cure cycle as shown in Fig. 2. In other words, within the processing time, the 

heat exchanges offered by the steep cooling rate of the cure cycle did not effectively offset the extra 

heat generated by the chemical reactions between this time period. 

The distributions of the degree of cure a across the SMC thickness are shown in Figs. 5 

and 6 for the cure cycles of iteration 1 and 22. In both cases, the cure of the resin starts from the 

surface regime and extends into the core of the SMC. The cure cycle of iteration 1 requires the 

shortest time (60 sec.) to complete the cure reaction of the material with a > 0.85. The lower cure 

temperatures provided by the optimal cure cycle (iteration 22) at the initial 40 seconds into the cure 

process can hardly trigger the chemo-kinetics reactions of the resin matrix as seen from Fig. 6. 

However, the rate of the cure speeds up in the next 40 seconds and eventually the degree of cure 

exceeds the 0.85 limit throughout the SMC material at the end of the cure cycle. 

Example 2. 

The effect of the length of cure cycle is investigated here. Example 2 is formulated to be 

identical to the problem stated in Example 1, except that the total processing time, 2, is extended to 

150 seconds. 

19 
The optimal cure cycle (iteration 22, Fig. 2) of Example 1 is used as the initial trial cure 

cycle (iteration 1, Fig. 7) studied here. The algorithm needs another 25 iterations to reach the 

optimal solution for this problem. Table 3 lists the numerical results for the optimal design. The 

starting (iteration 1) and optimal (iteration 25) cure cycles are compared in Fig. 7. It is noted that 

the cure cycle of Example 2 possesses even slower initial heating rates, and the cooling period is 

no longer needed over the entire cure cycle. The value of the objective functions are also compared 

in Fig. 8, and a drop of maximum temperature deviation from 250 to 110 units is noted. The 

temperature distributions across the SMC thickness at selected instants during the cure process for 

the two optimal cure cycles of Examples 1 and 2 are compared in Figure 9. The distribution of the 

degree of cure for the optimal cure cycle of this example is shown in Fig. 10. The cure behavior 

basically shows the same characteristics as the optimal solution of Example 1. The extension of the 

total curing time, therefore, only enables an optimally designed cure cycle to achieve an 

insignificant improvement in the temperature uniformity. 

Example 3. 

Example 3 is identical to the problem stated in Example 1, except that a new objective 

function, Eq. (24) (see below), which defines the maximum deviation in the cure state, is 

minimized; and the total processing time is extended to 150 seconds. 

It was rationalized in the past two examples that a uniform state of cure within the specimen 

could be achieved when a perfectly uniform temperature distribution at any time of the cure cycle 

was maintained. However, numerical results showed that the uniform degree of cure was not 

realized even though the temperature uniformity (as indicated by the objective functions Qo) had 

been improved greatly. This could be due to the fact that the degree of cure is quite sensitive to the 

temperature non-uniformity. In this example, the objective function Eq. (19) and the constraint 

Eq. (22) are therefore replaced by the following forms, respectively; 

20 
The optimal cure cycle of Example 2 is used as the initial trial solution in this case. Fiftyfive more iterations are required in order for the algorithm to converge to a optimal solution. The 

optimal cure cycle shown in Fig. 11 has the characteristic of a ramp-hold-ramp feature. Numerical 

results are listed in Table 4. The values of the objective functions of Eq. (24) for the starting and 

the (final) optimal cure cycles are compared in Fig. 12. The optimal solution reduces the maximum 

deviation in the degree of cure, as expected. However, the differences are, again, not significant. 

The distribution of the degree of cure, shown in Fig. 13, for the optimal cure cycle of Example 3, 

is similar to that of Example 2 (Fig. 10). The temperature distribution under the optimal cure cycle 

is shown in Fig. 14. These results indicate that the change of the objective function from Eq. (19) 

to Eq. (24) has only minor effects on the uniformity in the distribution of the degree of cure, even 

though the profiles of the optimal cure cycle designs are quite different. 

Example 4. 

Example 4 is identical to the problem stated in Example 1, except that a new objective 

function, Eq. (26), which defines the maximum deviation in the state of cure is minimized; the total 

processing time allowed is 150 seconds and the initial cure temperature is no longer restricted to 

room temperature, and is regarded as an additional design variable. 

In this example, the objective function Eq. (19) and the constraint Eq (22) are replaced by 

the following forms, respectively; 

21 
Q0 : Maximum (cq, - aJ, 

OltlT 

(Q : (a, - a,) I b, Oltlz. 

Here the objective function becomes the difference of the degree of cure between the outer 

surface, a,, and the center plane, a,. The optimal cure cycle of Example 3 (iteration 55, Fig. 11) 

is used as the initial trial solution. The optimal design algorithm does not really achieve 

convergence. However, after the forty-sixth iteration, the changes of the design variables become 

relatively small, and all the constraints are satisfied. The feasible design of the forty-sixth iteration 

is then regarded as the final design. Numerical results of this example are listed in Table 5. This 

example has five design variables in total that introduce two hundred and eighty-two equations in 

the form of Eqs. (8) or (15) to be solved. It took the algorithm around 196,800 CPU seconds 

(54.6 CPU hours) on the IBM 4381 computer to obtain the final solution. 

The cure cycles and the values of the objective function of Eq. (26) for iterations 1 

(corresponding to the optimal solution of Example 3), iteration 46, and that of reference [2] are 

shown in Figs. 15 and 16, respectively. Note that the cure cycle given by reference [2] is a 

constant temperature profile with T, = 423 "K. The cure cycle obtained from the forty-sixth 

iteration has the characteristic of a ramp-hold-ramp feature similar to that of Example 3. It is 

recognized that the higher onset cure temperature of the optimal cure cycle benefits the cure cycle 

design by initiating the chemical reaction as quickly as possible so as to achieve a better uniformity 

in the state of cure distribution (see Fig. 16). Similar to the previous case, the optimal solution of 

this example did improve the uniformity of the state of cure, although such improvement is not 

very significant. The final results of the temperature distribution and the degree of cure distribution 

at selected instants are shown in Figs. 17 and 18, respectively. 

22 
DISCUSSION 

After studying four different optimization design formulations, the uniformity of cure was 

not seen to improve significantly. This result is attributed to the physical aspects of the problem. In 

the curing of thermosetting resin matrix, there are two heat sources involved, namely, the heat flux 

from the processing tool platens and the heat generated by the kinetics reactions of the material. 

The conduction is the dominant mechanism for the heat transfer in this case. It can be seen from 

Eq. (5) that the objective of current cure cycle design, namely, to have a uniform cure inside the 

laminate at all times during the entire cure cycle, can be achieved when a uniform temperature 

profile exists across the lamanate. However, a uniform temperature profile without gradient will 

not yield any heat conduction. Thus the heat generated by the kinetics reactions inside the laminate 

can not be transfered outward effectively. As a result, the current optimal design algorithm tends to 

raise the temperature of the laminate, through the heat conduction from the tool platens, at a very 

slow pace. Such a curing process will require a long cure time 2. For practical considerations, 

however, only finite lengths of cure time were investigated in this study. 

It is interesting to note that the resultant optimal cure cycle in each of the four examples 

studied above can be broadly divided into three stages as follows: 

STAGE 1 This is the initial stage of the cure. The laminate was warmed up uniformly 

with no apparant reactions triggered. The cure cycle was inclined to raise temperature to expedite 

the curing process and to meet the design constraints (the cure time 2, for example). The degree of 

cure at the surface, 06% is greater than that at the center, ac. 

STAGE 2 The influx of heat triggered the reactions inside the laminate. However, the 

small temperature gradient across the laminate prevented effective outward heat conduction, and 

further kinetics reactions were triggered such that, in a short period of time, large extent of cure 

was reached. This process is evident by noting a sharp decrease of (a, - a,). For the optimal 

design of Example 4, this period started at 120 and ended at 140 seconds ( Figure 16). 

23 
STAGE 3 This is the latter stage of cure. The entire laminate had reached the desired 

degree of cure. The cure cycle was inclined to lower the temperature to facilitate more effective heat 

conduction outward from the laminate. 

It is evident that the optimal cure design algorithm tends to stretch the period of STAGE 1 

as long as possible for the reasons discussed above. 

In summary, one may conclude that (i) a uniform cure across the laminate at all time during 

the cure cycle can only be achieved with an infinite length of cure time. Obviously this is not a 

practical cure cycle, a more realistic design objective needs to be identified, and (ii) a more uniform 

temperature profile across the laminate could be achieved if more effective heat transfer 

mechanisms were adopted in the process. The technique of employing internal heating sources [ 151 

may provide extra flexibilities for the cure cycle design in this aspect. 

Finally, it is recognized that SMC molding process has a relatively short cycle time and 

molding temperature can not be varied easily during curing. The selection of SMC as a preliminary 

case study for the CAD methodology reported here is simply because of the consideration of the 

amount of CPU times required to reach convergence of the algorithm. Neverthless, the 

optimization technique presented here can be easily applied to the curing process with long cycle 

time ( i.e. Autoclave curing) without any difficulties. 

24 
CONCLUSIONS AND REMARKS 

A unified CAD methodology is introduced in this paper to design the optimal cure cycle in 

compression molding operation for a fiber reinforced composite laminate SMC. The process for 

curing the fiber reinforced composite laminate is simplified as a diffusion-reaction system and a 

kinetics model is used for the reactive resin system. The proposed CAD methodology consists of 

three uncoupled modules; namely, Optimization, Analysis, and Sensitivity Calculations. Once the 

analytical capability of any curing process is established, the Optimization and Sensitivity 

Calculation modules can be added onto it to constitute a unified CAD methodology which can 

systematically generate the optimal cure cycle designs subjected to various constraints . 

Four optimal design formulations for the optimal cure cycle design for the compression 

molding of a chopped fiber SMC were studied. The numerical examples showed that the proposed 

CAD approach was valid in different situations. It did improve the degree of cure uniformity 

within the laminate. This study also indicated that the total processing time, the initial heating rate 

and the initial cure temperature have significant effects on the cure uniformity. Enlarging the 

design space by increasing the total processing time and adding more design variables can further 

improve the cure cycle design. The long CPU time required in the present optimization 

formulation was a concern. To shorten the CPU time one may use other numerical algorithms, 

such as an unconditional by stable one, which can increase the time step. Other kinds of 

optimization algorithms, such as the I-DESIGN [16] which does not need the line search to 

accelerate the optimization process, should also be considered. 

The proposed CAD scheme can be extended to design an optimal cure cycle for the 

fabrication of long fiber reinforced composite laminates ( i.e., autoclave processing). It is noted 

that, to optimally design a realistic cure process for a resin-fiber composite, some modifications in 

Analysis module over this simplified SMC model are required. For example, the resin flow 

properties, the material inhomogeneities such as voids, fiber segregation, local fiber orientation, 

etc., and the heat convection through the surrounding environment should be considered in the 

25 
Analysis module. The total processing time should be regarded as a design variable to enlarge the 

design space. Moreover, some experiments are necessary to verify the results of the optimal cure 

cycle designed. 

In summary, it is clear that the CAD methodology is a valid technique to enhance the 

capability of designing the optimal cure cycles for the curing process of fiber reinforced composite 

laminates. However, in order to improve its applicability, further studies in modeling, 

computational efficiency and optimization formulation are needed to explore. 

26 
REFERENCES 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

Lee, W. I. and Springer, G. S., "A Model of the Manufacturing Process of Thermoplastic 

Matrix Composites", J. Comp. Matl. Vol. 21, pp. 1017-1055, 1987. 

Barone, M. E., and Caulk, D. A., "The Effect of Deformation and Thermoset Cure on 

Heat Conduction in a Chopped-Fiber Reinforced Polyester during Compression Molding," 

International Journal Heat Mass Transfer, Vol. 22, pp. 1021-1032, 1979. 

Loos, A. C., and Springer, G. S., "Curing of GraphiteEpoxy Composites," AFWAL-TR83-4040, March 1983. 

Loos, A. C., and Dara, P. H., "Modeling the Curing Process of Thick-Section Autoclave 

Cured Composites," Department of Engineering Science and Mechanics, Virginia 

Polytechnic Institute and State University, Blacksburg, VA, December 1986. 

Shampine, L. F. and Gordon, M. K., Computer Solution of Ordinarv Differential 

Eauations: The Initial Value Problem, W. H. Freeman and Co., San Francisco, 1975. 

Choi, K. K., Haug, E. J., Hou, J. W., and Sohoni, V. N., "Pshenichny's Linearization 

Method for Mechanical System Optimization," ASME Journal of Mechanisms, 

Transmissions. and Automation in Desip, No. 1, Vol. 105, pp. 97-103, 1983. 

Sheen, J. S., "Optimal Cure Cycle Design of a Resin-Fiber Composite Laminate," Master 

Thesis, Department of Mechanical Engineering and Mechanics, Old Dominion University, 

Norfolk, VA, August 1986. 

Haug, E. J., Mani, N. K., and Krishnaswami, P., "Design Sensitivity Analysis and 

Optimization of Dynamically Driven System," Computer- Aided Analvsis and OD~I 'mization 

of Mechanical Svstem Dvnamics, (Ed. E. J. Haug) Springer-Verlag, Berlin, Germany, pp. 

555-632, 1984. 

Hsieh, C. C., and Arora, J. S., "Design Sensitivity Analysis and Optimization of 

Dynamics Response," ComDuter Methods in Amlied Mechanics and En pineering, No. 2, 

Adelman, H. M., Haftka, R. T., Camarda, C. J., and Walsh, J. L., "Structural Sensitivity 

Analysis: Methods, Applications and Needs," NASA TM-85827, June 1984. 

Vol. 43, pp. 195-219, 1984. 

Hou, J. W., and Sheen, J. S., "Numerical Studies of the Thermal Design Sensitivity 

Calculation for a Reaction-Diffusion System with Discontinuous Derivatives," En~neering 

ODtimization, Vol. 11, pp. 103-1 19, 1987. 

Belegundu, A. D., and Arora, J. S., "A Recursive Quadratic Programming Method with 

Active Set Strategy for Optimal Design," International Journal for Numerical Method in 

Engineering, Vol. 20, No. 5, pp. 803-816, May 1984. 

Pshenichny, B. N. and Danilin, Y. M., Numerical Methods in External Problems, MIR 

Publishers, Moscos, 1978. 

27 
14. 

15. 

16. 

Taylor, J. E., and Bendose, M. P., "An Interpolation for Min-Max Structural Design 

Problems Including a Method for Relaxing Constraints," International Journal of Solid 

Structures, No. 4, Vol. 20, pp. 301-314. 

Maffezzoli, A. M., Kenny, J. M. and Nicolais, L., "Welding of PeeWCarbon Fiber 

Composite Laminates", SAMPE Journal, No. 1, Vol. 25, Jan/Feb 1989. 

Arora, J. S., Thanedar, P. B., and Tseng, C. H., User's Manual for Program I-DESIGN" 

Technical Report No. 85-10, Optimal Design Laboratory, College of Engineering, The 

University of Iowa, Iowa City, Iowa 52242, 1985. 

28 
Table 1. Material Properties of A Filled Polyester SMC [21 

P 

k 

a1 

a2 

C 

dl 

d2 

m 

n 

R 

Hr 

1900kg m-3 

1.0 J g-1 k-1 

0.53 W m-1 k-1 

4.9 x 1014 sec-1 

6.2 x 105 sec-1 

140 kJ mole-1 

51 kJ mole-1 

1.3 

2.7 

8.83138 J mole-' K-1 

84 J g-1 

29 
Table 2. Convergence History of The Optimum Design (Example 1) 

~ 

Para meter Initial Value Final Value 

Design Variables: 

Cost Function 

12 norm 

Computer Time 

(CPU sec. CDC 855) 

No. of Iterations 

100.00 115.74 

100.00 100.52 

100.00 -5.16 

100.00 6.83 

2700.00 378.33 

33.62 0.0054 

_-- 108,140.00 

22 --- 

30 
Table 3. Convergence History of The Optimum Design (Example 2) 

Para meter Initial Value Final Value 

Design Variables: 

Cost Function 

12 norm 

Computer Time 

(CPU sec. CDC 855) 

No. of Iterations 

115.74 162.32 

100.52 30.98 

-5.6 1 -0.18 

6.83 5.00 

250.00 110.86 

40.8 8 0.0147 

156,370.00 

25 

31 
Table 4. Convergence History of The Optimum Design (Example 3) 

Para meter Initial Value Final Value 

Design Variables: 

Cost Function 

12 norm 

Computer Time 

(CPU sec. CDC 855) 

No. of Iterations 

162.32 200.42 

30.98 25.04 

-0.18 46.99 

5.00 -5.28 

46.9 1 33.85 

5.29 0.19 

32 
Table 5. Convergence History of The Optimum Design (Example 4) 

Parameter Initial Value Final Value 

Design Variables: 

Cost Function 

12 norm 

Computer Time 

(CPU sec. IBM 4381) 

No. of Iterations 

300.00 

168.39 

47.41 

40.67 

-0.99 

0.8032 

11 1.40 

395.85 

106.59 

-46.92 

23.42 

-24.29 

0.6992 

4.08788 

196,800.00 

46 

33 
0 P Ti MI ZATl ON 

I h 

Objective I and constraint I 

I 

I 

I 

I 

.I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

1 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

-I 

I 

I 

I Finite element 

r------+---- - -7 

I 

ANALYSIS 

approximation I 

I 

I 

-function evaluation I: 

I 

Implementation of I 

boundary conditions I 

L 

I 

I 

I 

Numerical integration I 

of state equations I 

SENSITIVITY 

Evaluation of design 

gradients of objective 

and constraint functions 

I !- I Numerical integration I 

design gradients I 

I 

I I of equations for I 

4 I 

f 

I I 

I Recursive quadratic I 

I programming 

1 

I r I 

I 

I New design variables 

Figure 1. 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

Flow chart of the proposed CAD methodology which includes the Analysis, the 

Sensitivity and the Optimization modules. 

34 
0 0 0 0 0 0 0 0 

0 In 0 In 0 In 0 In 

co In In 4 4 m m cy 

0 

'00 

0 

b 

0 

m 

0 

cy 

0 

35 
'I I 

I' 

I !I 

0 

0 

00 

N 

0 

0 * 

N 

0 

0 

0 

N 

0 

0 

(0 

c 

0 0 0 ~ 

0 0 

00 * 

0 

NOIlVIA3 a 3UnlVU3d W3 1 

36 
0 

00 

In 

aaa 

www 

--- +++ 

II 

i 

I 

I 

I 

I 

I 

I 

I 

0 

0 

0 

00 

zt 

0 0 

00 00 

m N 

In 

zt 

m 

cy 

F 

0 

0 

00 

4 

0 

00 

0 

m 

m 6J 

\ 

In 

0 0 0 

00 00 00 

zt m cy 

In 

* 

0 

N 

F 

0 

0 

aa 

ln 

0 

(D 

II 

CI 

LI 

n 

LI 

E 

E 

U 

=E 

0 

LL 

a Y E 

cu 

0 

37 
W 

3 

0 

IA 

0 

W 

w 

U 

c3 

W 

0 

a 

1.0 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0.0 

-0.1 

80 sec 

ec 

20 sec 1 

0 1 2 3 4 5 

DISTANCE FROM MIDPLANE (mm) 

Figure 5. Distribution of the degree of cure at iteration 1 (Example 1). 

38 
W 

3 

0 

LL 

0 

W 

W 

t3 

W 

0 

a 

a 

1.0 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0.0 

-0.1 

-- 1C" 

20 sec 

0 1 2 3 4 5 

DISTANCE FROM MIDPLANE (rnrn) 

Figure 6. Distribution of the degree of cure at iteration 22 (Example 1). 

39 
-In 

cy 

zz 

00 

a4 

ww 

t-t- 

_- I-F 

dca 

-- 

0 

4 

v F 

0 

-to 

0 

-4 

0 

-cy 

I I I 1 I I 

0 0 0 0 0 0 

Ln 0 In 0 In 0 

In In 4 4 c1 c1 cy 

In 0 

-ru 

m 

a, 

l-0 

40 
PIn 

N 

I I I I I I I 

0 0 0 0 0 0 0 

0 In 0 In 0 In 

m N N P F 

N 0 IlV I A3 a 3 tl n 1V t13 d W 3 1 

0 

0 

P 

0 

00 

0 

ro 

0 

cy 

0 

u 

0, 

ln 

Y 

W 

I 

I- 

- 
nn rCU 

22 

EpE 

QQ 

xx 

ww 

oo 

)r- 

+-In 

N 

zz 

-- I-+ 

1 // 

// 

0 0 0 0 0 

0 v) 0 v) 0 

v) 4t 4t m m 

In 

4t 

m 

N 

F 

0 

U 

Q, 

m 

0 

v) 

I1 

v 

c 

CI 

U 

0 

Q, 

m 

0 

Q, 

II 

4 

CI 

n 

0 0 0 0 0 

0 v) 0 tn 0 

ln 4t 4 0 0 

0 

Q, 

m 

0 

lD 

II 

0 0 0 0 0 

0 v) 0 In 0 

In 4t 4 m 0 

(>i .I 3tlnlvki3d w(31 

CI 

€ 

E 

W 

Z 

U 

1 

a 

- 

a 

I 

- 

a 

LL 

0 

5 

M .-- 

L4 

42 
1.0 

0.9 

0.8 

0.7 

W 

3 

0 

0 

W 

a 

W 

a 0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

sec 1 

~ 

I 

I 

90 sec 

30, 60 sec 

-0.1 \ I 1 1 1 1 

0 1 2 3 4 5 

DISTANCE FROM MIDPLANE (mm) 

Figure 10. Distribution of the degree of cure at iteration 25 (Example 2). 

43 
r I I I I I 

0 0 0 0 0 0 

0 In 0 In 0 In 

0 

In 

In ln 4 4 m m N 

(>I.) 3UnlVU3dW31 

44 
F 

IU 

W 

Ia 

- 

ln 

ln 

lU 

W 

Ia 

- 

ln 

0 

0 

-4 

0 

0 

m (v 

0 0 

0 0 

. 0 

0 

0 

0 

0 

45 
1.0 

0.9 

0.8 

0.7 

a 0.6 

LL 0.5 

0 

W 0.4 

a 

0 

W 

0 0.3 

0.2 

0.1 

0.0 

-0.1 

0 

150 sec 

60 

30 

1 1 1 1 1 

1 2 3 4 5 

DISTANCE FROM MIDPLANE (mm) 

sec 

sec 

Figure 13. Distribution of the degree of cure at iteration 55 (Example 3). 
550 

500 

Y 

W 

U 

3 

E 

W 

a. 

I: 

W 

t- 350 

2 400 

300 

250 

0 

150 sec 

120 sec / - 

90 sec 

/ 

60 sec 

30 sec 

1 2 3 4 

DISTANCE FROM MIDPLANE (rnrn) 

5 

\\ t 

Figure 14. Profiles of temperature distribution (Example 3). 

47 
CON 

d, 

F4 - 

ccv 

OOC 

. 

\ 

\ 

\ 

-I 

I/ 

r I I 

0 0 0 In 0 In 0 In 0 

In 4 4 0 m 

0 0 0 0 

In 

N In 

$ 

cu 

0 
0 

/ 

/ 

/ 

I 

\ 

\ 

\ 

\ 

\ 

\ 

\ 

I 

-0 

-0 

cy 

F 

-0 

a 

Q) 

2 1 

m 

c 

0 

> 

6) 

a 

.r( -2 

49 
W 

3 

0 

LL 

0 

w 

w 

0 

W 

0 

a 

a 

0.9 4 / 

0.8 4 150 sec 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0.0 

-0.1 4 1 1 1 1 1 

0 2 1 3 4 5 

DISTANCE FROM MIDPLANE (mm) 

Figure 17. Distribution of the degree of cure at iteration 46 (Example 4). 

50 
550 

500 

450 

400 

350 

300 

250 

120 sec 

1 2 3 4 5 

DISTANCE FROM MIDPLANE (mm) 

Figure 18. Profiles of temperature distribution at iteration 46 (Example 4). 

51 
Report Documentation Page 

NASA CR-181866 

17. Key Words (Suggested by Author(s)l 

Sheet Molding Compound (SMC) 

Cure Cycle, Optimization, Compression 

Molding, Sensitivity Analysis, Computer 

Aided Design (CAD) 

7. Authorls) 

18. Ditribution Statement 

Unclassified - Unlimited 

Subject Category - 24 

Tan-Hung HOU, Gene J. W. Hou and Jeen S. Sheen 

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of pages 

Unclassified Uncl assi fi ed 54 

9. Performing Organization Name and Address 

Planning Research Corporation 

303 Butler Farm Road 

Hampton, VA 23666 

National Aeronautics and Space Administration 

Langley Research Center 

Harnpton, VA 23665-5225 

12. Sponsoring Agency Name and Address 

15. Supplementary Notes 

Langley Technical Monitor: R. M. Baucom 

22. Price 

A04 

3. Recipient's Catalog No. 

5. Report Date 

July 1989 

6. Performing Organization Code 

8. Performing Organization Report No. 

10. Work Unit No. 

505 -63-01 -01 

11. Contract or Grant No. 

NAS1-18000 

13. Type of Repon and Period Covered 

Contractor Report 

14. Sponsoring Agency Code 

16. Abstract 

:iber-reinforced composite laminates are used in many aerospace and automobile 

ipplications. The magnitudes and durations of the cure temperature and the cure pressure 

ipplied during the curing process have significant consequences for the performance of the 

inished product. The objective of this study is to exploit the potential of applying the 

Iptimization technique to the cure cycle design. Using the compression molding of a filled 

,olyester Sheet Molding Compound (SMC) as an example, a unified Computer Aided 

Iesign (CAD) methodology, consisting of three uncoupled modules, (Le., Optimization, 

inalysis and Sensitivity Calculations), is developed to systematically generate optimal cure 

:ycle designs. Various optimization formulations for the cure cycle design are investigated. 

'he uniformities in the distributions of the temperature and the degree of cure within the 

ipecimen cured under the optimal cycles are compared with those resulting from 

:onventional isothermal processing conditions with pre-warmed platens. Recommendaions with regards to further research in the computerization of the cure cycle design are 

rlso addressed.