Optimization of Carbon Fiber Reinforced Plastic Curing Parameters for Aerospace Application

Abstract

The use of carbon fiber reinforced plastic (CFRP) is increasing in engineering applications such as aerospace, automobiles, defense, and construction. Excellent strength-to-weight ratio, high impact toughness, and corrosion resistance make CFRP highly suitable for aerospace applications. Curing temperature, curing time, and autoclave pressure are among the most important curing parameters affecting the properties of CFRP. Tensile strength, impact toughness, and hardness of CFRP were selected as desirable properties for optimization. A 2³ full factorial design of experiment (DOE) was employed by varying curing temperature (120 and 140 °C), curing time (90 and 120 min), and autoclave pressure (3 and 7 bar) while keeping the number of experiments to a minimum level. The cured samples were subjected to tensile strength, impact toughness, and hardness tests at room temperature as per relevant ASTM standards. Analysis of variance (ANOVA) was used, and it was found that tensile strength, impact toughness, and hardness were influenced most significantly by temperature and time. The maximum tensile strength and hardness were achieved for curing cycle parameters of 140 °C, 120 min, and 7 bar, and impact toughness was maximized for 140 °C, 120 min, and 3 bar. A concept of composite desirability function was used to achieve simultaneous optimization of conflicting tensile strength and impact toughness properties for the specific application of aircraft skin.

1. Introduction

Carbon fiber reinforced plastics (CFRPs) have proven to be the most suitable alternative to aluminum alloys for structural applications in the aerospace industry. Due to their superior properties, the use of CFRPs has increased in recent years [1,2]. Some of the properties suitable for aerospace applications are high strength-to-weight ratio, impact toughness, hardness, dimensional stability, corrosion resistance, fatigue resistance, noise reduction, low radar cross-section, and the capability to be molded into large and complex shapes [3,4,5,6].

Tensile strength, impact toughness, and hardness are some of the desired properties for the skin of an aircraft. Tensile strength is the most fundamental requirement for the design of any structural component. The structure of commercial and military aircraft is semi-monocoque in construction. The entire skin of the fuselage, wings, and empennage is divided into regular geometric units. Each unit of the skin can be considered as a thin plate subjected to aerodynamic pressure. The required strength for most of the aircraft skin can be estimated by Equation (1) [7,8].

$${\sigma }_{max}=\frac{\beta q{b}^2}{t^2}$$

(1)

where

• ${\sigma }_{max}$ is maximum stress in the skin patch (MPa);
• β is a plate dimensions ratio (dimension less);
• q is uniformly distributed aerodynamic pressure on the skin of the selected portion (MPa);
• b is a short dimension of the skin patch (mm);
• t is the thickness of the skin patch (mm).

Besides being dependent on the dimensions, the maximum allowable stress is a function of aerodynamic pressure acting on the skin panel and it must be below the yield strength of the material. Furthermore, a fracture is less likely to occur if the maximum applied stress is below the tensile strength of the skin panel. Adequate impact toughness of composite makes the skin damage tolerant and enables it to sustain normal impact loads such as runway debris [9], bird strikes, gale strikes during normal operation, and tool drops during maintenance [10]. The impact toughness is also correlated with Mode I and II interlaminar crack growth resistance [9,11] (Section 3.2.2) influencing the structural integrity of the material. The hardness of the aircraft skin helps to resist indentation, scratching, and abrasion. Prepreg polymer matrix composites (PMCs) are generally used for the construction of aircraft skin due to the superior quality of the finished product. It is well established that the mechanical properties of prepreg PMCs are strongly dependent on the curing cycle (CC) [12,13,14,15]. The CC can be programmed for desired levels of processing parameters. The effect of various CC parameters such as autoclave pressure [16,17,18,19], vacuum application time, curing temperature, curing time [20,21,22,23,24,25], heating/cooling rate [26], and the number of stages for curing [27] has been investigated in the literature. Amongst these, temperature, time, and pressure are the most influential in dictating the mechanical properties of CFRP [20,23,24,25,28,29,30]. Temperature and time are interlinked as there is always an optimal temperature for a selected time to obtain an optimum mechanical property. It is often desirable to know those optimum values of temperature and time [31,32]. Autoclave pressure has also been found to heavily influence the volume fractions of the voids in the matrix [17,18]. Increasing the pressure causes a decrease in matrix voids thus increasing mechanical properties. A combination of certain (optimal) values of temperature, time, and autoclave pressure results in optimum values of mechanical properties of composites that have been studied in the literature. For example, Singh et al. investigated the effects of curing parameters on tensile, compressive, and flexural characteristics of CFRP [33]. The authors compared experimental results to find out the optimal curing parameters for the resulting optimized properties. Similarly, the optimization of surface finish, void formation, void distribution, tensile strength, flexural strength, stiffness, and mass has also been investigated in literature [23,32].

DOE is a systematic data collection and analysis tool that is used to determine the effects of curing parameters on the properties. Determination of optimum CFRP properties requires DOE in the curing parameters space followed by experimentation. An efficient DOE helps to minimize the number of experiments and saves time and resources. This was achieved by exploiting available information about the curing process (Section 2) which was then used in selecting the levels of curing parameters. This helped to choose the starting point in the likely vicinity of the optimum property, which made the optimization efficient, requiring a lower number of experiments. In contrast, other advanced optimization techniques such as artificial neural networking (ANN) cannot be used for optimization with a smaller number of experiments. The results predicted by ANN do not always describe the most effective improvement. For example, the main effects of a process parameter cannot be described as statistically significant with clarity. However, these limitations of ANN can be overcome if used with DOE and response surface methodology (RSM) as a hybrid model [34]. DOE provides a high level of control over the variables, allowing researchers to utilize as many variations as they want without destroying the validity of the research design, leading to excellent results.

Some of the standard design of experiments (DoE) techniques, i.e., full factorial [24], fractional factorial, central composite [35], and Taguchi design [20], were used for experimentation in various optimization schemes. Generally, it is a common practice to develop intricate mathematical objective functions between curing parameters and properties for optimization using numerical methods [23,32,36]. In the case of multiple properties optimization, the mathematical modeling of the objective function becomes even more complex. This requires the use of a heuristic algorithm to find out the optimum parameter at the cost of accuracy and precision [22,36]. However, most of the referred studies are generic and not targeted at a specific engineering application.

For aerospace engineering applications such as the skin of an aircraft (aimed in this work), mechanical properties such as tensile strength and impact toughness have generally conflicting objective functions. Hence, engineering decisions about trade-off amongst various available options becomes a necessity. In this work, an aerospace-specific multiple properties optimization scheme for a CFRP with a minimal number of experiments is presented. A full factorial 2³ DoE was used for the design and execution of experiments. A reference CC and seven other CCs were designed using existing knowledge of composite properties. The mechanical tests for tensile strength, impact toughness, and hardness were conducted. ANOVA was used to identify significant curing parameters and interactive terms, with a 95% confidence level [37,38]. Regression equations and three-dimensional surface plots were then developed between significant curing parameters and properties of CFRP. The concept of composite desirability function was used to trade-off between conflicting properties of tensile strength and impact toughness [39,40,41,42]. With the existing knowledge of some of the composite properties, the approach presented in this paper can be used to quickly reach optimization point without expanding large experimental resources.

2. Materials and Methods

The composite material used for this research work is a prepreg unidirectional carbon fiber reinforced plastic. The matrix of the understudy composite is a di-glycidyl ether of bisphenol A (DGEBA) epoxy system, a class of thermoset polymer. DGEBA is used as a binding matrix in high-performance fiber-reinforced composites and it is known for excellent mechanical properties, dimensional stability, chemical resistance, and ease of processing [19,43]. During curing, the epoxy converts into a hard rigid solid by chemical cross-linking. A two-stage CC is recommended by the prepreg CFRP manufacturer. The glass transition temperature with the maximum degree of conversion (T_g∞) is 140 °C according to the manufacturer. Stage-1 comprises 1–3 °C/min heating rate from ambient temperature to 80 °C and holding for 30 min. During stage-1, polymerization initiates. Stage-2 recommends increasing curing temperature at the same heating rate from 80 °C to 120 °C for an additional time of 120 min to accelerate the polymerization process under autoclave pressure of 7 bar. After 120 min, a cooling rate of 2–5 °C/min is recommended to bring the laminate to 30 °C. A vacuum (−0.8 bar) is recommended inside the laminate bag during curing. Figure 1 presents a manufacturer-recommended curing cycle (MRCC) comprising curing temperature (T_c = 120 °C), curing time (t_c = 120 min), and autoclave pressure (P_au = 7 bar). This research work is confined to the second stage of curing (MRCC) only. It is pertinent to mention that MRCC results in a set of CFRP properties for general-purpose application. The MRCC needed modification to achieve optimum properties for an aircraft skin application.

2.1. Selection of Curing Parameter Levels

To investigate the optimum properties for aircraft skin material, the properties region around MRCC was explored experimentally. For this purpose, one of the levels of the curing parameters was selected as defined in MRCC. The other level was selected either above or below the MRCC level, keeping in view the known relationship of curing parameters with the property.

2.1.1. Curing Temperature Levels

One of the T_c levels was selected from MRCC, i.e., 120 °C. The second level of T_c was selected as 140 °C, the glass transition temperature (T_g∞) of the understudy CFRP matrix epoxy. However, above T_g∞, the resin begins to char which adversely affects the properties of CFRP [44] making T_g∞ a practical constraint for experimentation.

2.1.2. Curing Time Levels

The effect of increasing T_c and t_c on the properties of CFRP is similar [21]. Since 140 °C was selected as a higher level of T_c, selection of a longer period of t_c than MRCC-defined time could likely result in property degradation of the CFRP matrix. Therefore, another level of t_c was selected as 90 min which is shorter than the MRCC t_c value (120 min).

2.1.3. Autoclave Pressure Levels

The high level for experimentation was selected according to MRCC, i.e., 7 bar [45]. The first level of P_au was selected lower than MRCC-defined P_au, i.e., 3 bar, to explore the probability of improvement in impact toughness, which increases with decreasing P_au [19].

Table 1. Summary of designed curing parameters levels for experimentation.

Parameters	Symbols (Units)	Levels
		−1	1
Curing temperature	Tc (°C)	120	140
Curing time	tc (min)	90	120
Autoclave pressure	Pau (bar)	3	7

shows the summarized designed curing parameters levels for experimentations.

2.2. Samples Preparation and Experimentations

CFRP UD lamina of thickness 0.125 mm was selected for preparing composite laminate for mechanical testing. Zund 1600 cutting plotter was used to cut laminae at 45° and 0° orientations, as shown in Figure 2. For good strength along the axial direction of a test coupon, stacking sequence [0/+45/0/0/0/−45/0]₃ was selected to prepare laminate for the tensile test coupon, whereas [0/+45/0/0/0/−45/0]₁₂ laminate was prepared for impact toughness and hardness test coupons. Both these laminates were prepared in the ISO class 8 cleanroom.

The laminates were subjected to eight different CCs according to 2³ full factorial design as shown in

Table 2. 2³ full factorial design and mechanical tests results. MRCC parameters and corresponding properties are represented by bold numbers.

CC	Tc (°C)	tc (min)	Pau (bar)	Tensile Strength (MPa)	Impact Toughness (J)	Hardness (HRB)
1	120	90	3	1044.8	02.45	46.0
1	120	90	3	1078.4	02.42	48.2
1	120	90	3	1060.8	02.53	44.8
2	140	90	3	1083.2	03.61	52.4
2	140	90	3	1153.6	05.84	50.7
2	140	90	3	1137.6	03.93	50.2
3	120	120	3	1041.6	08.08	48.4
3	120	120	3	1142.4	07.19	48.2
3	120	120	3	1224.0	08.52	51.5
4	140	120	3	1364.8	17.43	56.2
4	140	120	3	1417.6	16.97	54.5
4	140	120	3	1384.0	17.80	56.1
5	120	90	7	1110.4	03.37	45.5
5	120	90	7	1177.6	03.10	49.2
5	120	90	7	1148.8	03.20	48.4
6	140	90	7	1212.8	05.20	52.9
6	140	90	7	1094.4	05.85	53.1
6	140	90	7	1048.0	05.86	55.4
7 *	120	120	7	1204.8	11.19	48.2
7 *	120	120	7	1345.6	11.00	49.5
7 *	120	120	7	1327.5	12.03	52.0
8	140	120	7	1446.4	16.40	59.1
8	140	120	7	1422.4	16.97	56.8
8	140	120	7	1432.0	16.19	60.8

* MRCC/CC7.

. It shows all eight combinations of three curing parameters. Vacuum bagging of laminates was carried out to avoid void formation during curing and exposure of epoxy to air, as shown in Figure 3. The curing was performed in an Irop Parma autoclave, as shown in Figure 4a,b.

A total of 3 coupons were prepared from each of the laminate cured at 8 different CCs. Thus, 24 coupons for mechanical tests, i.e., tensile test (ASTM D3039), Charpy impact test (ASTM D6110), and Rockwell hardness test (ASTM D785), were prepared. The tensile test was conducted on a 300 kN UTM at a strain rate of 2 mm/min (Figure 5a and Figure 6a), impact toughness was conducted on Charpy impact testing machine model JBS300 (Figure 5b and Figure 6b), whereas hardness tests were conducted on a Rockwell hardness testing machine model TH300 (Figure 5c and Figure 6c). The mechanical test results are summarized in Table 2.

3. Results and Discussions

3.1. Analysis of Variance (ANOVA)

ANOVA was performed at a 95% confidence interval [46] to study the influence of curing parameters on tensile strength, impact toughness, and hardness. ANOVA results, summarized in

Table 3. ANOVA results for tensile strength. The table shows the significance (p-value < 0.05) of individual factors T_c, t_c, and P_au, and their interaction (T_c t_c) and (T_c P_au) on the property of tensile strength.

Source	DF	Adj SS	Adj MS	F-Value	p-Value
Model	5	402,449	80,490	25.85	0.000
Linear	3	339,145	113,048	36.30	0.000
Tc	1	69,346	69,346	22.27	0.000
tc	1	240,544	240,544	77.24	0.000
Pau	1	29,255	29,255	9.39	0.007
2-way inter	2	63,304	31,652	10.16	0.001
Tc × tc	1	47,926	47,926	15.39	0.001
Tc × Pau	1	15,378	15,378	4.94	0.039
Error	18	56,054	3114
Lack-of-Fit	2	5895	2947	0.94	0.411
Pure Error	16	50,159	3135
Total	23	458,503
R-sq = 88%, R-sq(adj) = 84%, R-sq(pred) = 78%

,

Table 4. ANOVA results for impact strength. It was observed that all main effects and three-way interactions were found significant (p-value < 0.05) for the impact toughness of the CFRP.

Source	DF	Adj SS	Adj MS	F-Value	p-Value
Model	7	722.798	103.257	304.35	0.000
Linear	3	669.428	223.143	657.72	0.000
Tc	1	135.233	135.233	398.60	0.000
tc	1	526.500	526.500	1551.88	0.000
Pau	1	7.695	7.695	22.68	0.000
2-Way inter	3	44.813	14.938	44.03	0.000
Tc × tc	1	38.837	38.837	114.47	0.000
Tc × Pau	1	5.812	5.812	17.13	0.001
tc × Pau	1	0.165	0.165	0.49	0.496
3-Way inter	1	8.556	8.556	25.22	0.000
Tc × tc × Pau	1	8.556	8.556	25.22	0.000
Error	16	5.428	0.339
Total	23	728.226
R-sq = 99%, R-sq(adj) = 99%, R-sq(pred) = 98%

and

Table 5. ANOVA results for hardness. It was observed that only the main effect of T_c, t_c, and P_au had a significant effect on the hardness of the CFRP.

Source	DF	Adj SS	Adj MS	F-Value	p-Value
Model	3	361.37	120.456	41.20	0.000
Linear	3	361.37	120.456	41.20	0.000
Tc	1	255.45	255.454	87.37	0.000
tc	1	82.51	82.51	28.22	0.000
Pau	1	23.4	23.404	8.00	0.010
Error	20	58.48	2.924
Lack-of-Fit	4	14.25	3.561	1.29	0.316
Pure Error	16	44.23	2.765
Total	23	419.85
R-sq = 86.1%, R-sq(adj) = 84%, R-sq(pred) = 80%

, were further used for the development of prediction models and optimization. Prediction models for individual responses were developed using the backward elimination method (α = 0.1). F-value shows the most contributory curing parameters towards the response variable. A p-value less than 0.05 shows the statistical significance of curing parameters on the response variable. The results showed that the individual factors T_c, t_c, and P_au, and their interaction (T_c t_c) and (T_c P_au), have a significant effect on tensile strength.

For impact toughness, all main effects, as well two- and three-way interactions, were found significant, except (t_c P_au). For hardness, only the main effect of T_c, t_c, and P_au had a significant effect. The T_c, t_c, and P_au has also been indicated as significant curing parameters in the literature [20,22,27,36,44].

Equations (2)–(4) show the prediction model developed for tensile strength (TS), impact toughness (IT), and hardness (HD) of understudy CFRP. The equations adequacy was analyzed by a lack-of-fit test. The coefficient of determination, i.e., R-square (R-sq), adjusted R-square (R-sq(adj)), and predicted R-square (R-sq(pred)), are summarized in Table 3, Table 4 and Table 5. The lack-of-fit test shows the adequacy of the relationship between modeled curing parameters and responses/properties. The p-value of lack-of-fit is an indicator of the regression model adequacy. As the p-values of lack-of-fit for TS, IT, and HD are greater than 0.05, it shows that lack-of-fit is insignificant. In other words, prediction models are properly formulated, and the important parameters and their interaction terms are included. The R-sq, R-sq(adj), and R-sq(pred) of TS, IT, and HD equations show that the regression model describes the experimental values with good approximation. The validation of the regression models is appended in Appendix A to this article. Validation was carried out by selecting curing parameters other than those used in Table 2, and the regression models output was compared with that of experimental results [47].

TS = 2970 − 19.58T_c − 32.05t_c + 182P_au + 0.2979T_ct_c − 1.266T_cP_au

(2)

IT = 180.6 − 2.098t_c − 1.575T_c − 23.98P_au + 0.01843T_ct_c + 0.18445T_cP_au + 0.2615P_aut_c − 0.00199T_c P_aut_c

(3)

HD = −6.27 + 0.3263T_c + 0.1236t_c + 0.494P_au

(4)

Adequacy of ANOVA depends upon normal distribution and constant variance of residuals for each response/property. The normal probability plots of residuals for each property (TS, IT, and HD) are shown in Figure 7a–c, respectively. For all responses, the residuals data fall near the fitted line, which indicates a normal distribution of the data. Further, the normal distribution of the residuals is validated by Ryan–Joiner (RJ) normality test. A p-value of the test greater than the alpha value of 0.05 shows that the data follow a normal distribution. As the p-value of the RJ test for TS, IT, and HD are greater than 0.05, it further supports the assumption that residuals are normally distributed. The residuals are spread randomly above and below the fitted line for all responses with no recognizable patterns (uneven distribution and curve patterns), therefore it also satisfies the assumption of constant variance of the data points (Figure 8a–c).

3.2. Surface Plots

The surface plot conveniently expresses the relationship between curing parameters and responses/properties. The surface plots between properties (TS, IT, and HD) and curing parameters (T_c, t_c, and P_au) were generated based upon regression Equations (2)–(4). There are three curing parameters for each of the properties. Therefore, two surface plots were drawn for each of the properties at two constant values of P_au (3 and 7 bar), to elaborate the complete behavior of each property.

3.2.1. Optimum Tensile Strength

The experimental results of the understudy CFRP tensile strength (Table 2) were transformed into regression Equation (2) and surface plots (Figure 9). Equation (2) was used to predict TS within the upper and lower limit of curing parameters (T_c, t_c, and P_au).

The two surface plots of tensile strength at constant P_au of 3 and 7 bar are shown in Figure 9. It was observed from the surface plots of Figure 9b that the MRCC resulted in tensile strength of 1274.8 MPa at CC7 (120 °C, 120 min, 7 bar), whereas the enhanced tensile strength of 1420 MPa was achieved at CC8 (140 °C, 120 min, 7 bar) in our study. With increasing T_c, more epoxide rings of the CFRP matrix open and larger molecules are formed [48], giving rise to a higher degree of cross-linking [49]. During cross-linking, the unordered amorphous state of the CFRP matrix transforms into an ordered glassy state which results in a higher tensile strength [49,50] of the epoxy matrix. On the contrary, for insufficiently high values of T_c, matrix resin would not cure fully, resulting in reduced mechanical properties [51]. As we used a high T_c of 140 °C (equal to T_g∞), an increase of 11.4% in strength was observed as compared to the tensile strength at MRCC. The result of optimal curing parameters along with optimum tensile strength is summarized in

Table 6. A comparative summary of non-optimum and optimum properties. This table compares MRCC (non-optimal) curing parameters and non-optimum properties with optimal curing parameters and optimum properties.

	Non-Optimal Curing Parameter	Non-Optimum Properties	Optimal Curing Parameters	Optimum Properties	Improvement (%)
Tensile Strength (MPa)	120 °C 120 min 7 bar (MRCC/CC7)	1274.8	140 °C 120 min 7 bar (CC8)	1420	11.4
Impact Toughness (J)		10.9	140 °C 120 min 3 bar (CC4)	17.4	59.6
Hardness (HRB)		51.2	140 °C 120 min 7 bar (CC8)	57.6	12.5

.

3.2.2. Optimum Impact Toughness

Similar to the experimental results of understudy CFRP tensile strength, the results of impact toughness (Table 2) were transformed into regression Equation (3) and the surface plots (Figure 10). This equation and the surface plot were used to predict impact toughness within the upper and lower limit of curing parameters (T_c, t_c, and P_au) of experiments.

It was observed from the surface plots of Figure 10b that MRCC produced an average impact toughness of 10.9 J. However, the maximum impact toughness of 17.4 J was produced at CC4 (140 °C, 120 min, 3 bar), as shown in Figure 10a. Unlike the result of the maximum tensile strength, the maximum impact toughness was achieved at a different set of curing parameters. The increased void and resin content of the CFRP matrix at lower P_au (3 bar) was the likely reason for the maximum impact toughness. The increased void content, at lower P_au promotes multiple cracking mechanisms, which raises the impact toughness of CFRP [11,20,52]. The higher impact toughness is related to a higher Mode I and II interlaminar crack growth resistance due to multiple crack failure mechanisms as a result of increased void contents at lower P_au [9,11] This improves the structural integrity and damage tolerance of the material, which is a fundamental requirement for material used in aircraft. As we used a smaller cure P_au value of 3 bar, an increase of 59.6% in impact toughness was observed, as compared to the impact toughness at MRCC. A similar set of values of impact toughness (5–13 J) has been observed for CFRP laminate in the literature [53]. The summary of optimal curing parameters along with optimum impact toughness is provided in Table 6.

3.2.3. Optimum Hardness

The experimental results of the understudy CFRP hardness (Table 2) were transformed into regression Equation (4) and the surface plot (Figure 11). The equation and the surface plot were used to predict hardness within the upper and lower limit of curing parameters (T_c, t_c, and P_au) of experiments.

The MRCC (120 °C, 120 min, 7 bar) produced a hardness of 51.2 HRB, whereas the maximum hardness of 57.6 HRB was observed at CC8 (140 °C, 120 min, 7 bar) (Figure 11b). A similar trend of increasing hardness with an increase in either T_c or t_c is found in the literature for CFRP [21]. Both tensile strength and hardness were maximum at the same curing condition, i.e., CC8. Hardness is resistant to plastic deformation and is somewhat related to the highest point in the stress–strain curve. Since both tensile strength and hardness address the same physical phenomenon, maximum hardness was also observed under the same curing conditions as tensile strength. As we used a higher T_c of 140 °C, an increase of 12.5% in hardness was observed, as compared to hardness at MRCC. The result of optimal curing parameters along with optimum hardness is summarized in Table 6.

3.3. Multi-Response Optimization of CFRP Mechanical Properties

The outcome of experimental results shows that maximum tensile strength and impact toughness was achieved at two different CCs. To solve such issues of multiple responses, the desirability function was introduced by Harrington [41]. Derringer and Suich [39] further modified the concept later and suggested using a composite desirability function to solve multiple response optimization problems [10,40,54,55,56]. According to this approach, each of the properties was converted into an individual desirability value “d_i” which varied over a range of 0 to 1, (0 ≤ d_i ≤1). The value of d_i increased with the desirability of the corresponding property. For the maximization of three properties (tensile strength, impact toughness, and hardness), Equation (5) was used to calculate the desirability of an individual property.

$$d_i=\{\begin{array}{cc}0;& y_i<L\\ {\left[\frac{\left(y_i-L\right)}{\left(T-L\right)}\right]}^{w_i};& L\le y_i\le T\\ 1;& y_i>T\end{array}$$

(5)

where

• d_i is the desirability of an individual response,
• y_i is the actual property value,
• L is the lower bound of the property,
• T is the target property value,
• w_i is the weight of the desirability function.

The individual desirability di was then combined by using the geometric mean, as expressed in Equation (6):

$$D={({{\displaystyle \prod }}_{I=1}^n{d}_i)}^{\frac{1}{n}}$$

(6)

where

• D is the composite desirability,
• n is the number of responses.

The results are summarized in

Table 7. Desirability and composite desirability values of the three responses. The highest desirability value of IT was observed at CC4, whereas the highest desirability value of TS, HD and composite desirability values were observed at CC8 (represented by bold letters).

CCs	Desirability Value of TS	Desirability Value of IT	Desirability Value of HD	Composite Desirability Value
1	0.008	0.002	0.075	0.000
1	0.091	0.000	0.213	0.000
1	0.047	0.007	0.000	0.000
2	0.103	0.077	0.475	0.001
2	0.277	0.222	0.369	0.008
2	0.237	0.098	0.338	0.003
3	0.000	0.368	0.225	0.000
3	0.249	0.310	0.213	0.005
3	0.451	0.397	0.419	0.025
4	0.798	0.976	0.713	0.185
4	0.929	0.946	0.606	0.178
4	0.846	1.000	0.706	0.199
5	0.170	0.062	0.044	0.000
5	0.336	0.044	0.275	0.001
5	0.265	0.051	0.225	0.001
6	0.423	0.181	0.506	0.013
6	0.130	0.223	0.519	0.005
6	0.016	0.224	0.663	0.001
7 *	0.403	0.570	0.213	0.016
7 *	0.751	0.558	0.294	0.041
7 *	0.706	0.625	0.450	0.066
8	1.000	0.909	0.894	0.271
8	0.941	0.946	0.750	0.222
8	0.964	0.895	1.000	0.288

* MRCC/CC7.

. The highest desirability values obtained for TS are at CC8 (140 °C, 120 min, 7 bar), i.e., 1, 0.941, and 0.964, with the maximum TS of 1420 MPa. For IT, the highest desirability values are at CC4 (140 °C, 120 min, 3 bar), i.e., 1, 0.947, and 0.977, with the maximum IT of 17.4 J. For hardness, optimal CC was found to be the same as for TS, with desirability values of 1, 0.894, and 0.750. The maximum HD value obtained at optimal CC8 is 57.6 HRB. Optimization of TS and IT at different CCs is consistent with the findings of Odian and d’Almeida [49,50].

To overcome the issue of two different optimal CC, and simultaneous optimization of mechanical properties, the concept of composite desirability was applied using Equation (6). The results are tabulated in Table 7.

There were two CCs at which maximum properties were achieved, i.e., CC4, where maximum IT was achieved, and CC8, where maximum TS and HD were achieved. Hence, the composite desirability function at these two CCs was compared. The largest composite desirability values (i.e., 0.271, 0.222, and 0.288 (avg = 0.260)) were obtained at CC8, with TS of 1420 MPa, IT of 16.5 J, and HD of 57.6 HRB. The summary of the composite desirability function is appended in

Table 8. Composite desirability function value for two options of CCs.

Option	Tc (°C)	tc (min)	Pau (bar)	Tensile Strength (MPa)	Impact Toughness (J)	Hardness (HRB)	Average Composite Desirability
CC8 *	140	120	7	1420 †,‡	16.5 †	57.6 †,‡	0.260
CC4	140	120	3	1400	17.4 ‡	55.7	0.187

* Optimal CC. ^† Optimum property. ^‡ Maximum property.

.

4. Conclusions

The experimental work resulted in improved properties at the designed CC8, as compared to properties observed at MRCC/CC7. The TS and HD were maximized to 1420 MPa (11.4% improvement) and 57.6 HRB (12.5% improvement) when cured at CC8 (140 °C, 120 min, 7 bar), but the IT was maximized to 17.4 J (59.6% improvement) at CC4 (140 °C, 120 min, 3 bar).

Due to the detection of two different optimal CC (CC4 and CC8) for optimum properties (TS, IT, and HD), a composite desirability function was used to determine simultaneous optimum properties. The composite desirability function yielded TS of 1420 MPa, IT of 16.5 J, and HD of 57.6 HRB as optimum properties at CC8 as optimal CC for understudy CFRP, suitable for aircraft skin application.

The statistical analysis (ANOVA) concluded that T_c and t_c are the most significant curing parameters for influencing TS, IT, and HD of CFRP.

5. Future Work

The porosity in the CFRP has a remarkable effect on the tensile strength, impact toughness, and hardness as well the Mode I and II interlaminar crack growth resistance of CFRP laminate. For aerospace application, structural integrity and damage tolerance of the used material matters a lot. It is therefore suggested to include microstructural analysis of CFRP laminate to validate the effect of porosity on the understudy properties of CFRP.