# The influence of key processing parameters on thermoset laminate curing

Adam Fisher, Arjun Radhakrishnan, James Kratz, Arthur Levy

► To cite this version:

Adam Fisher, Arjun Radhakrishnan, James Kratz, Arthur Levy. The influence of key processing parameters on thermoset laminate curing. Composites Communications, 2023, 42, pp.101686. 10.1016/j.coco.2023.101686. hal-04183958v2

HAL Id: hal-04183958

https://hal.science/hal-04183958v2

Submitted on 4 Feb 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# The influence of key processing parameters on thermoset laminate curing

Adam Fisher<sup>a, b</sup>, Arjun Radhakrishnan<sup>a</sup>, James Kratz<sup>a, *</sup>, Arthur Levy<sup>b</sup>

<figure><img src="image_2.png" /></figure>

## ARTICLE INFO

### Keywords:

- Thermoset laminate
- Curing
- Sensitivity analysis
- Variability
- Processing

## ABSTRACT

The many uncertainties in thermoset composite laminate processing can have undesirable consequences. It is impractical to address the uncertainties individually. A methodology is introduced in this study that ranks parameters by an influence metric to give insights into how to reduce variability in cure time most effectively. The presented example considers a range of parameters from the material, geometry, and processing conditions within a thermochemical model of composite laminate curing. Due to the nonlinearities in the process, the influence metric must include representative parameter uncertainty. In the example considered here of a high-performance aerospace grade epoxy system, dwell temperature and diffusion terms in the cure kinetics model were most influential. This was a result of a long dwell period and a post-vitrification final degree of cure. Therefore, the best investment to reduce curing variability is processing equipment with repeatable and uniform temperature.

## 1. Introduction

The demand for composite materials within the aerospace industry has exploded in recent decades, with a trend of replacing metallic primary structures with high-performance thermosetting epoxy composites. In thermoset composite processing it is common for conditions to differ from those assumed/prescribed, this can occur in both the materials and the processing environment. This variability can cause higher scrappage, reducing efficiency and increasing costs. Potter [1] introduced a taxonomy of offending variability sources, listing more than sixty that are present during composite manufacturing. Given the high number of variables identified, it may not be practical to address them all and no method was given to determine which to prioritise.

Sensitivity analysis coupled with numerical simulation provides an effective tool for determining which parameters have the most influence on a given process. Loos et al. [2] showed that a thermochemical model coupling heat transfer and cure kinetics was capable of modelling composite curing. Building on these concepts, sensitivity analysis has been used on a cure kinetics model to determine which parameters to consider in more detail [3], efficiency was improved by only selecting the most influential parameters. This approach can be extended to consider parameters of the whole process, by applying sensitivity analysis to a suitable thermochemical model.

In this study, a methodology is presented to identify which

parameters to prioritise to increase the robustness of thermoset laminate processing. The parameters are ranked by an influence metric, similar to sensitivity, but accounts for real-world uncertainty. Values of the metric, based on the time to reach a degree of cure, are derived from a Finite Elements (FE) solution to coupled 1-Dimensional (1D) through thickness transient heat transfer and cure kinetics equations. Uniquely, the analysis considers the influence of key parameters, from the process, the material, and the geometry on composite curing. The numerical element of the approach is demonstrated by considering a flat plate, representative of epoxy laminate processed by vacuum bag moulding in an oven. Recommendations are provided based on the results.

## 2. Method

### 2.1. Predicting parameter influence

The metric of influence considered the rate of change of cure time with respect to the parameters listed in Table 1. Where, cure time was defined as the time for a degree of cure to be passed at every location through the thickness [2]. The parameters were classified as related to the process, geometry, or material, as well as cure kinetics, conductivity, and specific heat capacity fitting parameters. To accommodate the different units among the parameters, each gradient was multiplied by the standard deviation of the corresponding parameter, giving the

<footnote><sup>a</sup> Bristol Composites Institute, University of Bristol, Queen's Building, University Walk, Bristol, BS8 1TR, United Kingdom</footnote>

<footnote><sup>b</sup> Nantes Université, CNRS, Laboratoire de thermique et énergie de Nantes, LTeN, UMR 6607, F-44000, Nantes, France</footnote>

<footnote>* Corresponding author.
E-mail address: james.kratz@bristol.ac.uk (J. Kratz).</footnote>
influence metric the units of cure time.

Using the standard deviations as the step size for the gradients, the influence metric represented parameter variability in addition to the sensitivity of cure time. Given the standard deviations were not infinitesimally small, the influence metric approximates the gradient of the secant about the nominal cure time. This corresponds to the average rate of change over the interval. By combining sensitivity and variability, the influence metric indicates the likely cure time variability each parameter will cause.

Where possible the standard deviations were derived from data available in-house or in the literature. The dwell temperature, heat transfer coefficient and ramp rate from measurements in an industrial oven [4], fibre volume fraction from acid digestion of M21 composite panels, part thickness from measurements of IMA/M21 prepreg thickness [5] and the cure kinetics parameters from the fitting of Differential Scanning Calorimeter (DSC) data [3]. The two curves created by the conductivity model when the values of the fitting parameters were simultaneously shifted by 6%, up and down, bounded 68.2% of the laser flash analysis data points used to fit the model [3], corresponding ±1 standard deviation from the mean. The same procedure was applied to the specific heat capacity fitting parameters, giving standard deviations equal to 5% of the parameter values. Manufacturer data suggested a 0.35 mm tolerance is typical for a 6 mm thick metal sheet [6], assuming a normal distribution, the standard deviation for tool thickness was derived from a distribution with a 95% confidence interval of ±0.35 mm from the mean.

An approach analogous to the central difference method, with step size equal to one standard deviation, was used to calculate the average rates of change. The matrix of influence metric values (unit corrected average rates of change) was written as,

<table><caption>**Table 1**

Parameters with description, units, nominal values and standard deviations.</caption><thead><tr><th>Parameter</th><th>Description</th><th>Units</th><th>Nominal Value Φ<sub>i</sub></th><th>Standard Deviation σ<sub>i</sub></th></tr></thead><tbody><tr><td>A<sub>1</sub></td><td>Cure kinetics</td><td>s<sup>-1</sup></td><td>420615</td><td>333</td></tr><tr><td>E<sub>1</sub></td><td>Cure kinetics</td><td>Jmol<sup>-1</sup></td><td>78890</td><td>355</td></tr><tr><td>A<sub>2</sub></td><td>Cure kinetics</td><td>s<sup>-1</sup></td><td>57440</td><td>33</td></tr><tr><td>E<sub>2</sub></td><td>Cure kinetics</td><td>Jmol<sup>-1</sup></td><td>68978</td><td>1086</td></tr><tr><td>A<sub>D</sub></td><td>Cure kinetics</td><td></td><td>2.60E+20</td><td>2.80E+17</td></tr><tr><td>E<sub>D</sub></td><td>Cure kinetics</td><td>Jmol<sup>-1</sup></td><td>87455.74</td><td>419</td></tr><tr><td>m</td><td>Cure kinetics</td><td></td><td>0.6</td><td>0.0032</td></tr><tr><td>n<sub>1</sub></td><td>Cure kinetics</td><td></td><td>0.8</td><td>0.026</td></tr><tr><td>n<sub>2</sub></td><td>Cure kinetics</td><td></td><td>3.2</td><td>0.031</td></tr><tr><td>b</td><td>Cure kinetics</td><td></td><td>1.98</td><td>0.014</td></tr><tr><td>w</td><td>Cure kinetics</td><td></td><td>1.65E-04</td><td>7.40E-07</td></tr><tr><td>g</td><td>Cure kinetics</td><td></td><td>0.058235</td><td>3.80E-04</td></tr><tr><td>Dwell temperature</td><td>Process</td><td>K</td><td>453.15</td><td>5</td></tr><tr><td>Ramp rate</td><td>Process</td><td>Kmin<sup>-1</sup></td><td>2</td><td>0.16</td></tr><tr><td>Heat transfer coefficient</td><td>Process</td><td>Wm<sup>-2</sup>K<sup>-1</sup></td><td>50</td><td>4</td></tr><tr><td>Total heat of reaction</td><td>Material</td><td>Jkg<sup>-1</sup></td><td>4.15E+05</td><td>11602</td></tr><tr><td>Fibre volume fraction</td><td>Material</td><td></td><td>0.6</td><td>0.008</td></tr><tr><td>Part thickness</td><td>Geometry</td><td>m</td><td>0.005</td><td>0.00023</td></tr><tr><td>Tool thickness</td><td>Geometry</td><td>m</td><td>0.006</td><td>0.00018</td></tr><tr><td>A</td><td>Heat capacity</td><td>Jkg<sup>-1</sup>K<sup>-1</sup></td><td>2.9</td><td>0.15</td></tr><tr><td>B</td><td>Heat capacity</td><td>Jkg<sup>-1</sup>K<sup>-1</sup></td><td>1840</td><td>92</td></tr><tr><td>C</td><td>Heat capacity</td><td>JK<sup>-1</sup></td><td>0.15</td><td>0.0075</td></tr><tr><td>Δ</td><td>Heat capacity</td><td>Jkg<sup>-1</sup>K<sup>-1</sup></td><td>-260</td><td>-13</td></tr><tr><td>s</td><td>Heat capacity</td><td>°C</td><td>0.65</td><td>0.033</td></tr><tr><td>A<sub>r</sub></td><td>Conductivity</td><td>Wm<sup>-1</sup>K<sup>-2</sup></td><td>-1.50E-03</td><td>-7.5E-05</td></tr><tr><td>B<sub>r</sub></td><td>Conductivity</td><td>Wm<sup>-1</sup>K<sup>-1</sup></td><td>0.392</td><td>0.020</td></tr><tr><td>C<sub>r</sub></td><td>Conductivity</td><td>Wm<sup>-1</sup>K<sup>-2</sup></td><td>-1.00E-03</td><td>-5.00E-05</td></tr><tr><td>D<sub>r</sub></td><td>Conductivity</td><td>Wm<sup>-1</sup>K<sup>-1</sup></td><td>0.734</td><td>0.037</td></tr></tbody></table>

$$S^* = S\sigma \qquad (1)$$

where S is the matrix of average rates of change for a given degree of cure and σ is a diagonal matrix containing the standard deviations. Each element of S* took the form,

$$S_i^* = \sigma_i S_i = \sigma_i \left[ \frac{t_c(\Phi_i + \sigma_i) - t_c(\Phi_i - \sigma_i)}{2\sigma_i} \right] = \frac{t_c(\Phi_i + \sigma_i) - t_c(\Phi_i - \sigma_i)}{2} \qquad (2)$$

where t_c is the cure time, and Φ_i is the nominal parameter value. The values of Φ_i and σ_i for each parameter are shown in Table 1.

## 2.2. Numerical implementation

Coupled cure kinetics and transient heat transfers equations were solved in 1D using FE in COMSOL Multiphysics. The 1D assumption was based on the high conductivity of the fibres causing a much lower Biot number in-plane than through the thickness, this assumption has been shown to produce reliable results [2,3]. The cure kinetics for the M21/IMA prepreg with 13 fitting parameters was implemented as a distributed ordinary differential equation in COMSOL [3]. The cure kinetics model had both kinetic and diffusion terms (Equations (5) and (6)) because this specific material vitrifies, i.e., the glass transition temperature of the resin will exceed the process dwell temperature. The cure kinetics model is given in Equations (3)–(7). A non-zero value for initial degree of cure was required to escape the singular stationary point of the model; a convergence analysis showed negligible changes in cure time at values below 0.0001.

$$\frac{d\alpha}{dt} = k_1(1 - \alpha)^{n_1} + k_2\alpha^m(1 - \alpha)^{n_2} \qquad (3)$$

$$\frac{1}{k_i} = \frac{1}{k_{iC}} + \frac{1}{k_D}, \quad i = 1, 2 \qquad (4)$$

$$k_{iC} = A_i e^{\left(\frac{-\epsilon_i}{k_D}\right)}, \quad i = 1, 2 \qquad (5)$$

$$k_D = A_D e^{\left(\frac{-\epsilon_D}{k_D}\right)} e^{\frac{g}{T}} \qquad (6)$$

$$f = w(T - T_g) + g \qquad (7)$$

Heat transfer was modelled using the 'Heat Transfer in Solids' physics in COMSOL. The cure cycle is the recommended cycle for M21 [7], a 2°Cmin<sup>-1</sup> ramp from 20 °C to a dwell at 180 °C which continued until 95% cure. The part and tool are assumed initially to be at 20 °C. Fig. 1 shows a schematic of a curing assembly, the dotted line highlights the simplified form assumed in the model. Under the applied vacuum, it was assumed the contact resistance between the elements was negligible [8]. The properties of the consumables were from Ref. [9] and the thicknesses from Ref. [10]. The same convective boundary condition was applied to each end, with a heat transfer coefficient of 50 Wm<sup>-2</sup>K<sup>-1</sup>, representative of an industrial oven [4].

A 60% fibre volume fraction was assumed for the composite laminate. The thermal properties in the composite domain were representative of the through thickness direction. The density and specific heat capacity were homogenised using rule of mixtures according to fibre volume fraction and fibre weight fraction respectively [3]. The specific heat capacity model for the resin, with 5 fitting parameters, is shown in Equation (8). The thermal conductivity model (Equation (9)), has 4 fitting parameters [3]. All the fitting parameter values are given in Table 1.

$$c_{pr} = A_{rcp} T + B_{rcp} + \frac{\Delta_{rcp}}{1 + \exp\left(C_{rcp}(T - T_g - s)\right)} \qquad (8)$$
<figure><img src="image_3.png" /><figcaption>Fig. 1. The layup schematic assumed in the Finite Elements model, including thicknesses and boundary condition.</figcaption></figure>

$$K_{33} = A_{kr}T\alpha + B_{kr}\alpha + C_{kr}T + D_{kr} \quad (9)$$

The described model conditions are typical of aerospace composite manufacturing. The results give an indication of the parameters likely to be most influential.

## 3. Results and discussion

Fig. 2 shows how the absolute value of the influence metric depends on the final targeted degree of cure. The parameters are ranked by the absolute value of the influence metric at 0.95° of cure, a typical end point when targeting full cure. For clarity, the results have been separated into subplots with similar values. Presenting the metric value versus targeted degree of cure is relevant for preliminary cure steps, such as those prior to co-curing and co-bonding where the level of partial cure effects the adhesion [11,12].

Fig. 3 focuses on the influence of dwell temperature, ramp rate and heat transfer coefficient. Dwell temperature has non-zero influence before the dwell is reached, because for a given temperature ramp rate, dwell temperature influences the duration of the ramp. The high 180 °C dwell temperature and slow 2°Cmin⁻¹ ramp rate in this example resulted in an influence that grew slowly during the initial stages of the process, but increased rapidly at high degrees of cure, as the dwell became a more significant proportion of the cure cycle. As shown in Fig. 3, beyond a degree of cure of 0.6, dwell temperature surpasses temperature ramp rate as the dominant influence on cure time. A similar trend is expected for other aerospace grade epoxies, among which 180 °C dwell

<figure><img src="image_4.png" /><figcaption>Fig. 2. The absolute influence metric value for each parameter for degrees of cure up to 0.95. The parameters are ranked by the metric values at 0.95 cure.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. The absolute gradients values for the process parameters during the curing reaction.</figcaption></figure>

temperatures are common. For lower temperatures or higher ramp rates, the influence metric for dwell temperature would be more significant earlier in the process.

Dwell temperature can be used to illustrate the need for case specific nominal values. Fig. 4 shows that cure progresses as a sigmoid function of time, the rate starts to slow around gelation, the plateau coincides with vitrification [13], these occur at degrees of cure of approximately 0.7 and 0.9 respectively for M21 at 180 °C [3]. At a higher dwell temperature vitrification occurs earlier in the plateau, so in terms of degree of cure, cure rate remains higher for longer, as demonstrated in Fig. 4. Therefore, for cases such as this, where final glass transition temperature exceeds the dwell temperature, the influence of dwell temperature will be large and may not be representative of the reaction pre-vitrification.

From Fig. 2, the influence of the cure kinetics parameters was often highly weighted towards the end of the curing reaction; therefore, the high rankings of these parameters are not applicable to all processes. As shown in Fig. 5, this is particularly true for the parameters representing post-vitrification diffusion limiting effects (b, g, E₀). Away from a degree of cure of 0.85, the influence of diffusion limiting effects drops more sharply than reaction effects. The results indicate that although accurately characterising DSC measurements is critical for process reliability at high degrees of cure, it becomes less important away from vitrification, for this system, below a degree of cure of 0.85.

In contrast to dwell temperature and the cure kinetics parameters, the influence of many process and geometry parameters is less concentrated towards higher degrees of cure. Hence, when only considering high degrees of cure the importance of these parameters can be overlooked. This is particularly true for heat transfer coefficient which as

<figure><img src="image_6.png" /><figcaption>Fig. 4. Degree of cure (DOC) with time for dwell temperatures of 180 and 185 °C. Arrows mark gel time (0.7 DOC) and vitrification time (0.9 DOC) with the two dwell temperatures.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Influence metric of the cure kinetics parameters during the cure reaction.</figcaption></figure>

indicated by Fig. 3, is only influential initially, when there is a temperature difference between the geometry and the imposed cure cycle, not applicable to the long dwell in this example. The contrasting distributions of parameter influence illustrates how the most effective parameters for reducing process variability can change with the targeted degree of cure.

## 4. Conclusion

A methodology that ranked parameters by an influence metric, based on cure time, to determine which parameters contribute most to variability in thermoset curing processes was presented. The ranking appeared to be dependent on the final degree of cure targeted.

Based on the methodology shown here, the results from the influence study can be used to optimise design and manufacturing processes for composite curing. For example, if material properties dominate, investment in better material characterisation instruments for deriving material models and verifying incoming batches would lead to more consistent parts. If the process equipment drives variability, an oven with more uniform temperature and convection heat-transfer coefficients might be a better investment. For geometry, metrology equipment or tighter tool tolerances might be the best approach. Based on our analysis, process equipment with temperature uniformity and repeatability is the best investment to minimise variability in curing.

### Data access statement

The acid digestion data is available in the supplementary information.

### Funding

This work was supported by the EPSRC Future Composites Manufacturing Research Hub under Grant EP/P006701/1.

### CRediT authorship contribution statement

**Adam Fisher:** Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing – original draft, Writing – review & editing, Visualization. **Arjun Radhakrishnan:** Conceptualization, Resources, Writing – review & editing, Supervision. **James Kratz:** Conceptualization, Writing – review & editing, Supervision, Project administration, Funding acquisition. **Arthur Levy:** Conceptualization, Methodology, Formal analysis, Writing – review & editing, Supervision, Project administration, Funding acquisition.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

No data was used for the research described in the article.

### Acknowledgements

The authors wish to thank Dr Vincent Maes of the University of Bristol for proof reading and providing suggestions on formatting.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.coco.2023.101686.

### References

[1] K. Potter, Understanding the origins of defects and variability in composites manufacture, in: International Conference on Composite Materials (ICCM)-17, 2009. Edinburgh, UK.

[2] A.C. Loos, G.S. Springer, Curing of epoxy matrix composites, J. Compos. Mater. 17 (2) (1983) 135–169.

[3] T. Mesogitis, J. Kratz, A.A. Skordos, Heat transfer simulation of the cure of thermoplastic particle interleaf carbon fibre epoxy prepregs, J. Compos. Mater. 53 (15) (2019) 2053–2064.

[4] A. Fisher, A. Levy, J. Kratz, Effects of heat transfer coefficient variations on composite curing, J. Compos. Mater. (2022).

[5] M. Matveev, et al., A numerical study of variability in the manufacturing process of thick composite parts, Compos. Struct. 208 (2019) 23–32.

[6] METALEX, Aluminium Plate Thickness Tolerences. Poole, UK.

[7] H. Corporation, HexPly® M21 180°C (350°F) Curing Epoxy Matrix Product Data Sheet, 2020.

[8] J.H. Oh, D.G. Lee, Cure cycle for thick glass/epoxy composite laminates, J. Compos. Mater. 36 (1) (2002) 19–45.

[9] S.T. Peters, Handbook of Composites, Springer Science & Business Media, 2013.

[10] Diatex Vacuum, Bagging materials [cited 2023 21/07/2023]; Available from: https://composite-integration.co.uk/products/vacuum-bagging-materials-2/.

[11] M. O'Leary, et al., The effect of semi-curing on infused laminate interfacial properties, in: The 20th European Conference on Composite Materials (ECCM20), 2022.

[12] N. Motsch-Eichmann, et al., Experimental investigation of modified co-curing process for carbon fiber/epoxy-laminates, J. Micromech. Mol. Phys. 6 (3) (2021) 1–12.

[13] P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, 1953.