Fundamentals of Infrared Heating and Their Application in Thermosetting Polymer Curing: A Review

Abstract

Thermosetting polymers offer a wide range of applications in modern industries, including coatings, the automotive and aerospace industries, and furniture manufacturing. The curing process, which is a key step in the application of such materials, has become a research hotspot. More specifically, significant research efforts have been devoted toward shortening the curing cycle and reducing curing energy consumption without affecting product quality. Two common curing methods, namely, infrared (IR) curing and hot air convection curing, have been commonly employed. IR curing technology demonstrates certain advantages, such as high energy efficiency and adaptability, compared to traditional convection curing technology. Moreover, it has achieved desirable results in engineering applications and research. In this review, the current research on IR curing technology is presented in detail based on two fundamental aspects: the heat transfer process and the curing process. This article provides a comprehensive overview of the IR curing heat transfer process in terms of IR heating equipment, heat transfer monitoring devices, heat transfer models, and heat transfer simulation methods. Moreover, it summarizes and compares the basic research methods, equipment, and theoretical models involved in the curing process. In addition, it describes the non-thermal effect and its impact on the properties of cured products. This study describes the author’s perspective and opinions on the research direction in IR radiation-based curing technology. This literature review concludes that IR curing technology has strong research value and application prospects, particularly in fields requiring low-temperature rapid curing of thermosetting polymers.

1. Introduction

Thermosetting polymers play a pivotal role in various industrial sectors due to their exceptional mechanical strength, chemical resistance, and thermal stability. Their high cross-linking density endows them with a superior modulus, strength, durability, and resistance to heat and chemicals, making the curing process a crucial stage in their production [1]. With the continuous growth in the demand for advanced materials in industries such as aerospace, automotive, and electronics, increasing emphasis has been placed on developing efficient and sustainable curing methods for such polymers. Although traditional curing techniques are well established, they are often associated with challenges related to energy consumption and processing time [2].

The common curing methods mainly include convection curing and radiation curing. Traditional convection curing has some problems, such as long curing time, low energy utilization rate and large heat loss of curing furnace. Most of the existing studies have carried out reasonable optimization of oven by means of numerical simulation, so as to reduce energy consumption. Satit et al. [3] used computational fluid dynamics (CFD) modeling and simulation methods to conduct a large-scale study of temperature distribution and flow patterns in a convective paint oven. The validated CFD model is used to investigate the temperature distribution and the flow pattern for two proposed options: eliminating stored heat and rearranging airflow. Yi et al. [4] developed a CFD model to investigate the thermal-transfer efficiency of the existing hot -air convection ovens in a continuous production lines. The increase of the line speed was investigated by varying the temperature, velocity of airflow, and modifications of nozzles. Through simple modifications the line speed can be increased, al-lowing the reduction of cycle time.

Compared to the traditional heat convection curing technology, IR technology offers the advantages of high energy density, low thermal inertia, and high adaptability in the curing field, providing an effective solution for fast and low-energy curing of thermoset-ting polymers [5]. For instance, Dilmurat et al. [6] assessed the curing mechanism, current application status, and primary advantages and disadvantages of various curing processes for advanced polymer composites. C. F. JASSO et al. [7] used four different curing methods: traditional convection oven, long wave infrared (IR) radiation oven, medium wavelength infrared radiation oven, and open curing conditions without oven heating at room temperature to cross-link the general unsaturated polyester resin. The results show that the medium-wavelength IR oven as a curing condition provides the highest conversion, glass transition temperature (Tg) and mechanical properties of the best choice. Subasri et al. [8] prepared decorative hydrophobic coatings, and the coating is cured using near infrared curing technology. The densified coatings were characterized for their thickness, roughness, contact angles and adhesion. The results show that the properties of the near-infrared radiation cured pigmented coatings were found to be comparable with those of the conventionally cured coatings. Compared to conventional curing, the coating can be cured quickly using near-infrared radiation (NIR), thus minimizing processing time. Barletta et al. [9] conducted an experimental study to analyze the degree of chemical conversion of the pigmented basecoat, the overall coating morphology and its thermal, mechanical and tribological properties based on infrared radiation time and power. The result shows that the intermediate range of curing time and IR power investigated leads to properly cured basecoats and subsequently to better morphological, mechanical and tribological behavior of the whole coating system. Kumar et al. [10] investigated infrared radiation (IR) post curing process for glass fiber reinforced polymer composite laminates as an alternative to conventional thermal cure. The result shows that IR curing results in volumetric heating and the entire composite laminate will be uniformly heated resulting in uniform curing of all the layers and hence the stresses are reduced. More uniform crosslinking takes place and hence there is no uncured resin patches with in the laminate. In addition, IR utilizes only 25% of total time as compared to conventional curing method. IR curing process has drastically reduced the curing time. Among these methods, IR curing technology has emerged as highly valuable technique. The application of IR radiation has demonstrated a potential in improving the curing process of thermosetting polymers via deep penetration into the material and controlled heating within the polymer matrix.

Although these studies have clarified the advantages and benefits of IR, there is a lack of review and analysis. To provide a comprehensive summary and comparative analysis of the heat transfer and curing processes involving IR curing, articles from the WOS database concerning other curing techniques were searched and screened using “thermosetting polymers”, “curing process”, and “heat transfer” as the topic index terms. In total, 298 articles were obtained after screening. A comparison of the number of articles published per year is presented in Figure 1. It can be found that this direction has always maintained a relatively stable research progress and has become more popular since 2016. In order to identify current research hotspots, this study presents a clustering time analysis through citespace 6.3. R2, as shown in Figure 2. Based on the analysis of the node types to select keywords, the literature was divided into 10 clusters according to research topics, and #0 nanocomposites cluster includes the most literature studies. The lines in Figure 2 represent the citation relationship, each node represents a keyword and the time it first appeared, the size of the circle represents the citation intensity of the literature, and the circle represents the time it was cited. Notably, clustering focuses more on the materials characteristic such as nano material and polymers and less on studies involving IR curing.

In addition, research on curing thermoset composites by infrared irradiation is oriented. The search was conducted using “thermoset”, “curing process”, and “infrared” as index terms, and the core collection was utilized for subject searching. Moreover, the wildcard “*” was used to account for occasional plural usage of subject terms. The retrieved articles were screened by keywords, and 30 articles matched the topics of interest; these have been summarized in

Table 1. Literature summary.

Material	Substrate	Condition	IR Source	Reference
DGEBA-type epoxy system	Zinc steel plates		Near-IR (NIR) panel heaters	[11]
Powder coating			Gaseous IR heaters	[12]
Unidirectional fiber composites			IR heaters	[13]
AS4/3501-6 epoxy resin prepreg	AISI 304 stainless steel		IR heaters	[14]
Glass fiber-reinforced unsaturated polyester-styrene system		85 °C/3 h	Long-wavelength IR radiation, medium-wavelength IR radiation	[7]
Polyester + TGIC powder coating/polyester-based powder coating	Steel standard test panels	255 °C/105 s	IR radiation (SIR, MIR, NIR)	[15]
Polyester-based system powder/epoxy–polyester-based system	steel panels	255 °C/105 s	IR radiation (SIR, MIR, NIR)	[16]
Polyester epoxy hybrid powder primer	SMC (sheet molding compound) panels and sheet metal panels		IR heaters	[17]
Thermosetting powders/polyester-based system	Steel standard test panels	255 °C/105 s	IR lamps (MWIR, SWIR, NIR)	[18]
Glass fiber-reinforced DGEBA-type epoxy system			IR heaters	[10]
Epoxy resin (RTM-6)			IR heaters	[19]
BADGE type epoxy resin/4-4′-aminophenylmethylaniline		28–85 °C/150 min and 28–150 °C/146 min	IR heater (3–8 μm wavelength, 2 kW capacity)	[20]
Epoxy polyester/polyurethane powders	Metal sheets	1.5 kW/30 s or 2 kW/20–30 s	IR radiation setting the power of IR lamps within the range of 1.0–2.0 kW	[9]
Decorative hydrophobic coatings		250 °C/30 min	NIR radiation	[8]
Polyestermelamine paints/highly absorbent pigments	Steel galvanized with zinc		Convective ovens, NIR heaters	[21]
Carbon fiber-reinforced epoxy matrix			IR heaters	[22]
Gold nanoparticles integrated into a maleate polyester			NIR	[23]
Solvent-blended acrylic resin (polymer matrix)/melamine as hardener	Steel sheet		NIR heating module with 12 tungsten-halogen lamps/2990 K and 4.3 kW	[24]
Composites made of epoxide thermoset resin			IR heaters	[5]
Polymer–composite rods reinforced with fibers			Ceramic IR heaters	[25]
Thermoset-automated fiber placement			LED-based heating unit	[26]
Poly-epoxide adhesive/epoxy pre-polymer		50 °C/40 min	IR heaters	[27]
One-component thermoset coatings		175 °C/15 min	NIR heaters	[28]
Catalyzed cyanate ester resin	Aluminum sheet	260 °C	Medium wavelength heaters (3–7 µm)	[29]
Fiber-reinforced polymer composites		28–85 °C/10–60 min	IR heaters	[30]
Polyepoxy adhesive/epoxy prepolymer			IR heaters	[31]
Solvent-borne epoxy primers			Gas catalytic IR heaters	[32]
Polyester-based powder coatings/triglycidyl isocyanurate (TGIC) polyester system		220 °C/3 min and 230 °C/2 min	Catalytic IR heaters	[33]

.

Table 1 and Figure 2 show that there are relatively few articles dealing with the IR curing technology in the relevant research field, both in terms of number and proportion. This is largely attributable to the complexity of the IR heat transfer and curing mechanisms, coupled with the fact that the current research on this technology tends to focus on particular aspects and lacks systematic generalization and analysis. Therefore, it cannot provide sufficient basic support for further research and promotion of this technology. This review focuses on the two fundamental processes of heat transfer and curing in the research field on thermoset curing. It provides a comprehensive summary and analysis of recent advancements in utilizing IR radiation for curing thermosetting polymers from the perspectives of equipment, models, and theoretical aspects. Furthermore, the review describes the constraints and shortcomings in the study on IR curing technology, and provides perspectives on potential directions for future research and innovation.

2. Heat Transfer Process

2.1. Classification and Selection of IR Heaters

IR heating methods are based on the conversion of electromagnetic energy to heat energy without heating the air in between, via the resonance vibration of molecules [34]. Polymers contain various couplings such as couplings of vibration modes of CH, CH₂, CH₃, and CC, which vibrate at specific frequencies. Most of the vibration frequencies of these molecules correspond to short-wavelength IR (SIR) and medium-wavelength IR (MIR) regions above 1.5 µm. Under resonance energy irradiation, the vibrations intensify and produce thermal energy [6]. Based on the energy source, IR heaters can be divided into three basic types, namely, gas-fired, gas catalytic, and electric heaters. Each type has its own unique characteristics and applications; thus, they should be selected and designed based on the practical needs [35].

2.1.1. Gas-Fired IR Heaters

Fueled by natural gas or propane, gas-fired IR heaters can produce significant amounts of heat. The IR radiation from the burning flames is dominated by medium and long wavelengths [6]. Owing to their reliance on radiation rather than convection, gas-fired IR heaters aid in the economic and efficient heating of large workpieces, especially in open or semi-open environments. Such heaters are popular for commercial and industrial heating needs and are often used in conjunction with convection ovens to achieve faster heating. Although their initial cost is higher, they offer several advantages such as independence from electricity, cost-effective operation, energy saving, and greater reliability and durability compared to electric IR emitters. Gas-fired IR heaters provide uniform heating with high thermal efficiency and rapid control; nevertheless, they require well-ventilated spaces to minimize the risk of carbon monoxide poisoning. Although they may not be suitable for extremely high heating demands, they can efficiently produce moderate heat over an extended duration [36]. Gas-fired IR emitters include direct flame IR radiators, ceramic burners, metal fiber burners, and high-intensity porous burners.

2.1.2. Gas Catalytic IR Heaters

Gas catalytic IR heaters function through the catalytic combustion of gas. The gas, which is often propane or natural gas, is passed over a catalyst, usually prepared with platinum or palladium, initiating a chemical reaction that produces heat without a visible flame [37]. This method involves a highly efficient heating process, emitting MIR radiation and far infrared (FIR) radiation (3–7 μm). Compared to traditional gas-fired or electric heaters, the heat produced is generally gentler and more evenly distributed. In oven design, gas catalytic IR heaters are commonly used in scenarios requiring consistent, low-intensity heat over extended periods. In general, diffusion catalytic combustion occurs at around 400 °C, while the temperature for the pilot-premixed catalytic combustion reaches above 500 °C. The absence of a flame during combustion allows the radiant surface to be placed closer to the object, which leads to increased efficiency. This combustion device generates low or near-zero emission concentrations of organic volatiles, such as NOx, in the flue gas, resulting in minimal pollution. Furthermore, the surface temperature of gas catalytic IR heaters is uniform, and their surface can be customized.

2.1.3. Electric IR Heaters

Electric IR heaters utilize electricity to heat an element, such as a ceramic or metal, quartz tube, or carbon element, which then emits IR radiation. Such heaters can operate at different temperatures and have quick response times, often heating up and cooling rapidly [38]. Although their operating costs may be higher than those of gas-fired heaters, they are more advantageous in applications requiring precise temperature control and rapid thermal cycling; thus, they are commonly used in small- to medium-sized IR ovens. Electric IR emitters consist of a metal filament placed inside a sealed enclosure, which is either filled with inert gas or evacuated. Radiant energy is generated by passing an electric current through a high-resistance wire, causing the element and the surrounding material to become incandescent [39]. Electric IR emitters can operate at temperatures up to 2600 K, corresponding to near-infrared (NIR) radiation of 0.7 to 1.5 μm. The wavelength spectra of these electric IR emitters and emissive powers are controlled via the power input to the system. Various electric IR radiant emitters with different specifications, e.g., reflector-type incandescent lamps, quartz tubes, metallic tubes, ceramic tubes, and non-metallic rods, are available for specific purposes. Incandescent lamps are classified as short-wave emitters, while quartz tubes and resistance elements are classified as medium- and long-wave emitters, respectively. Unlike natural gas-, diesel-, and propane-fueled emitters, electric IR heaters generate zero emissions [35].

The choice of an IR heater depends on various factors, such as specific heating requirements of the application, cost considerations, and available infrastructure. When designing an IR heating system, matching the emission spectra of the emitter with the absorption spectra of the material to be heated is crucial for the overall efficiency of the system. Moreover, the physical properties of the medium in the working chamber, the geometrical parameters describing the relative positions of the IR emitter and the irradiated object, and the spectral emissivity distribution of the IR emitter are factors that significantly affect the system’s performance.

Table 2. Classification of IR heaters and literature summary.

	Gas-Fired IR Heaters	Gas Catalytic IR Heaters	Electric IR Heaters
Wavelength range (μm)	2–4.5	3–7	0.7–1.5
Temperature rating (°C)	800–1200	350–500	500–1000
Thermal efficiency (%)	80%–85%	85%–90%	70%–80%
Response time	Medium	Slow	Fast
Working lifespan (Years)	10–15	15–20	5–10
Advantages	High heat output, efficient large-area heating	Uniform heat distribution, energy-efficient	Fast response time, precise temperature control
Limitations	Low precision, high operating temperature	Slow response time, low temperature range	High operating cost, short lifespan
Literature	Deans et al., 1999 [2]	Yi et al., 2023 [6]	[16] [40] [18] [15] [29] [13] [19] [41] [42] [10] [27] [43]

presents a comparison of the key performance parameters for gas-fired, gas catalytic, and electric IR heaters and includes literature references on the use of IR curing technology. It can be observed that electric IR heaters are the most commonly used in such studies.

2.2. Monitoring Devices

The curing process is significantly affected by temperature and time, thus necessitating the use of robust, sensitive, and accurate monitoring equipment.

Table 3. Comparison of different monitoring devices.

Material Properties	Typical Instrument	Limitations	Reference
Thermal property	Thermocouple Pyrometer temperature	Low accuracy and restricted temperature range	[18] [16] [40] [15] [29] [22] [27] [43]
	IR camera	Accuracy affected by the ambient temperature, distance, and geometry	[22]
Electric property	RTD	Fragile and somewhat destructive
Heat flux	Thermopile calorimetric	High calibration complexity and high sensitivity to thermal regulation	[18] [16]

presents a comparative analysis of various temperature-monitoring devices as well as references to the relevant literature in the field of IR curing.

2.2.1. Thermal Imaging

Thermal imaging is a technique that utilizes IR cameras to capture thermal radiation emitted by the surface of an object and convert it into a visible image that depicts the temperature distribution. Thermal imaging offers a non-contact and non-invasive means of monitoring the temperature changes and the curing degree of thermosetting polymers during IR curing. Furthermore, thermal imaging can reveal spatial and temporal variations in the temperature field, which can affect the curing kinetics and mechanical properties of the final product. Thermal imaging has been extensively used to investigate the effects of various parameters, e.g., IR power, curing time, sample thickness, and IR wavelength, on the IR curing process of thermosetting polymers [44]. However, thermal imaging brings forward certain limitations, such as low spatial resolution, high cost, and sensitivity to environmental factors, including ambient temperature, humidity, and airflow [45].

2.2.2. Resistance Temperature Detectors

Resistance temperature detectors (RTDs) are sensors that measure temperature based on the change in electrical resistance of a metal wire or a thin film. RTDs can offer high accuracy, stability, and repeatability, but they also have certain disadvantages, such as slow response time, self-heating effect, and interference from external electromagnetic fields. RTDs are usually embedded in the polymer matrix or attached to the specimen surface, which may affect the heat transfer and curing processes. Although RTDs can measure the local temperature of a polymer, they cannot provide global temperature distributions or heat flux information. RTDs have been utilized to measure the temperature of thermosetting polymers during IR curing. The results of RTDs have been compared to those obtained by other methods, such as thermal imaging and thermocouples [45]. However, the use of RTDs is challenging in terms of calibration, installation, and durability, particularly for high-temperature and high-pressure applications.

2.2.3. Thermocouples

Thermocouples are sensors that measure temperature based on voltage generated at the junction of two different metals. They usually consist of two dissimilar metal wires connected at a welded junction. Their function is based on the Seebeck effect experienced by conductors with temperature gradients along their length [46]. In the context of polymer curing processes, the generation of thermoelectric voltage in thermocouples is predicated upon the temperature gradient between the sensing junction and the open ends. These sensors are capable of measuring a broad spectrum of temperatures and are valued for their rapid response times and simplistic design. However, they exhibit several limitations such as low sensitivity, inherent non-linearity, and susceptibility to calibration discrepancies. When integrated into a polymer matrix or affixed onto the surface of a specimen, thermocouples may introduce localized thermal perturbations and lead to heat dissipation issues. Although effective for recording localized temperature variations within a polymer, thermocouples do not provide comprehensive data on overall temperature distribution or heat flux across the material. This limitation is significant in applications requiring detailed thermal mapping during polymer curing. Thermocouples have been used to measure the temperature of thermosetting polymers during IR curing [5]. However, thermocouples bring forward certain disadvantages in terms of accuracy, stability, and reliability, particularly for low-temperature and low-voltage applications.

2.2.4. Heat Flux Sensors

Heat flux sensors are devices that measure the rate of heat transfer per unit area across a surface. They utilize measurement techniques with different principles, such as thermopile, calorimetric, or Gardon gauge, to perform these measurements. Heat flux sensors can provide direct and quantitative information regarding the heat transfer and curing kinetics of thermosetting polymers under IR radiation. They are usually placed on the side opposite the IR source, which may reduce the interference and disturbance to the curing process [47]. Moreover, heat flux sensors can measure the heat flux distribution and the heat balance of the system, which can help to optimize the IR curing parameters and improve energy efficiency. They have been used to measure the heat flux of thermosetting polymers during IR curing as well as to correlate the heat flux with the conversion degree and mechanical properties. However, heat flux sensors have certain drawbacks in terms of sensitivity, linearity, and durability, especially for high-heat-flux and high-temperature applications [48]. Figure 3 illustrates a novel thin-film heat flux sensor, which was developed by Xu et al. to measure heat flux in two directions [49].

2.3. Thermal Transfer Model

Modeling of heat transfer is essential to perform studies concerning heat transfer processes. However, before this can be achieved, it must be clarified whether IR heat transfer should be regarded as a surface-to-surface heat transfer phenomenon or a more complex bulk heat transfer phenomenon [50]. Chern et al. [13] considered optical depth as the determining parameter and reported that if the optical thickness was greater than 5, the radiation could be regarded as a surface phenomenon, and thus treated as a part of the boundary conditions of the energy equation. This is the case, for instance, for most carbon fiber-reinforced composites, but not for glass/epoxy composites. This section is grouped based on surface and volume transport, and both types of models are presented and analyzed with examples.

2.3.1. Surface Radiation Transport: Energy Balance and Boundary Conditions

Bombard et al. developed a mathematical model that incorporated an understanding of the fundamental mechanisms governing thermal transfers. The model was employed to predict film temperature changes and the extent of reaction when the powder coating was exposed to radiative flux. The thermal model is based on Fourier’s law of heat conduction. Figure 4 illustrates the boundary conditions imposed on the upper surface of the powder film and the lower surface of the metallic substrate [18].

The thermal equilibrium is determined by considering the temperature variation across the thickness of the powder-coated metal sample and the curing degree conversion, which ranges from 0 at the beginning to 1 upon completion. For the powder domain, the following equations apply [18]:

$$\nabla \left({\mathsf{\lambda }}_{\mathrm{c},\mathrm{p}}\nabla {\mathrm{T}}_{\mathrm{p}}\right)={\mathsf{\rho }}_{\mathrm{p}}\mathrm{C}{\mathrm{P}}_{\mathrm{p}}\frac{\partial {\mathrm{T}}_{\mathrm{p}}}{\partial \mathrm{t}}+{\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}$$

(1)

$$\nabla \left({\mathsf{\lambda }}_{\mathrm{c},\mathrm{s}}\nabla {\mathrm{T}}_{\mathrm{s}}\right)={\mathsf{\rho }}_{\mathrm{s}}\mathrm{C}{\mathrm{P}}_{\mathrm{s}}\frac{\partial {\mathrm{T}}_{\mathrm{s}}}{\partial \mathrm{t}}$$

(2)

$${\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}={\mathsf{\rho }}_{\mathrm{p}}{\mathrm{e}}_{\mathrm{p}}∆{\mathrm{H}}_0\frac{\mathrm{d}\mathrm{x}}{\mathrm{d}\mathrm{t}}$$

(3)

The kinetic model that is used to describe the polymerization of the two powder-coated systems is an autocatalytic model given by Sestak–Berggren:

$$\frac{\mathrm{d}\mathrm{x}}{\mathrm{d}\mathrm{t}}={\mathrm{k}}_0\exp (-\frac{\mathrm{E}}{\mathrm{R}\mathrm{T}}){\mathrm{k}}^{\mathrm{m}}(1-\mathrm{x}{)}^{\mathrm{n}}$$

(4)

The boundary conditions are

$${-\mathsf{\lambda }}_{\mathrm{c},\mathrm{p}}\frac{\partial {\mathrm{T}}_{\mathrm{p}}}{\partial \mathcal{Z}}={\mathsf{\alpha }}_{\mathrm{p},{\mathrm{T}}_{\mathrm{P}}}{\mathrm{\varnothing }}_{\mathrm{i}}-\mathsf{\sigma }{\mathsf{\epsilon }}_{\mathrm{S}}({\mathrm{T}}_{\mathrm{S}}^4-{\mathrm{T}}_{\mathrm{\infty }}^4)-{\mathrm{h}}_{\mathrm{s}}({\mathrm{T}}_{\mathrm{s}}-{\mathrm{T}}_{\mathrm{\infty }})$$

(5)

at $\mathcal{Z}$ = $0$

$${-\mathsf{\lambda }}_{\mathrm{c},\mathrm{p}}\frac{\partial {\mathrm{T}}_{\mathrm{p}}}{\partial \mathcal{Z}}={-\mathsf{\lambda }}_{\mathrm{c},\mathrm{S}}\frac{\partial {\mathrm{T}}_{\mathrm{S}}}{\partial \mathcal{Z}} \mathrm{and} {\mathrm{T}}_{\mathrm{P}}={\mathrm{T}}_{\mathrm{s}}$$

(6)

at $\mathcal{Z}$ = ${\mathrm{e}}_{\mathrm{p}}$

$${-\mathsf{\lambda }}_{\mathrm{c},\mathrm{S}}\frac{\partial {\mathrm{T}}_{\mathrm{S}}}{\partial \mathcal{Z}}=\mathsf{\sigma }{\mathsf{\epsilon }}_{\mathrm{S}}({\mathrm{T}}_{\mathrm{S}}^4-{\mathrm{T}}_{\mathrm{\infty }}^4)+{\mathrm{h}}_{\mathrm{s}}({\mathrm{T}}_{\mathrm{s}}-{\mathrm{T}}_{\mathrm{\infty }})$$

(7)

at $\mathcal{Z}$ = ${\mathcal{Z}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}}={\mathrm{e}}_{\mathrm{p}}$ + ${\mathrm{e}}_{\mathrm{s}}$

The initial conditions are:

$${\mathrm{T}}_{\mathrm{P}}\left(\mathcal{Z},0\right)={\mathrm{T}}_1 \forall 0\leqq \mathcal{Z}\leqq {\mathcal{Z}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}}$$

(8)

$${\mathrm{T}}_{\mathrm{s}}\left(\mathcal{Z},0\right)={\mathrm{T}}_2 \forall {\mathcal{Z}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}}\leqq \mathcal{Z}\leqq {\mathrm{e}}_{\mathrm{p}}+{\mathrm{e}}_{\mathrm{s}}$$

(9)

$$\mathcal{X}\left(\mathcal{Z},0\right)=0^{+} \forall 0\leqq \mathcal{Z}\leqq {\mathcal{Z}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}}$$

(10)

To study the temperature and curing degree as a function of time during the curing process in the three dimensions, Igor Zhilyaev et al. [29] developed a mathematical model to predetermine the IR heater parameters required to cure composite components with complex shapes. Mathematical modeling and optimization were performed by using the finite element (FE) software COMSOL Multiphysics (https://www.comsol.com/comsol-multiphysics). The governing equations are presented in detail later in this chapter. The developed model can be described with the following general points [29]:

• The model simulates the absorption of the IR energy by the upper surface of the composite via surface-to-surface radiation equations.
• The IR energy absorbed by the upper surface of the composite is integrated into the heat transfer equations as a heat flux boundary condition.
• Heat transfer within the part occurs through conduction to the bottom of the composite.
• The curing degree is calculated based on the heating rate.
• The exothermic heat of the resin is introduced to the heat equations as the heat source.

The developed model incorporates advanced simulations to accurately represent the IR energy absorption by the upper surface of the composite. For this purpose, it utilizes surface-to-surface radiation equations and integrates the absorbed IR energy as a heat flux boundary condition into the heat transfer equations. Furthermore, conduction within the part is considered for the heat transfer to the bottom of the composite, and the curing degree is calculated based on the heating rate. Moreover, the model introduces the exothermal heat of the resin as a critical component in its comprehensive heat equations [4]:

$${\mathsf{\rho }}_{\mathrm{C}}{\mathrm{c}}_{\mathrm{p}}\frac{\partial \mathrm{T}}{\partial \mathrm{t}}=\nabla \mathrm{k}\nabla \mathrm{T}+\left(1-{\mathrm{v}}_{\mathrm{f}}\right){\mathsf{\rho }}_{\mathrm{m}}{\mathrm{H}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\frac{\partial \mathsf{\alpha }}{\partial \mathrm{t}}$$

(11)

Since only a quarter of the original geometry is considered, the symmetry boundary condition is applied to boundaries formed during the geometry division:

$$-\mathrm{n}\cdot \left(∆\mathrm{k}\right)=0$$

(12)

A heat flux boundary condition is used on the bottom boundary of the aluminum plate to simulate the heat exchange between the oven and the ambient space:

$$-\mathrm{n}\cdot \left(\mathrm{k}\nabla \mathrm{T}\right)={\mathrm{h}}_{\mathrm{b}}\left({\mathrm{T}}_{\mathrm{e}\mathrm{x}\mathrm{t}}-\mathrm{T}\right)$$

(13)

Since the air domain is not considered, the free convection boundary condition is applied on the upper surface of the composite, mount, and aluminum plate bodies:

$$-\mathrm{n}\cdot \left(\mathrm{k}\nabla \mathrm{T}\right)={\mathrm{h}}_{\mathrm{t}}\left({\mathrm{T}}_{\mathrm{a}\mathrm{m}\mathrm{b}}-\mathrm{T}\right)$$

(14)

The parameters of the curing kinetic equation for the resin were determined experimentally by isothermal and dynamic differential scanning calorimetry (DSC) trials:

$$\frac{\mathrm{d}\mathsf{\alpha }}{\mathrm{d}\mathrm{t}}=\left[{\mathrm{A}}_1\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{{\mathrm{E}}_1}{\mathrm{R}\mathrm{T}}\right)(1-\mathsf{\alpha }{)}^{{\mathrm{n}}_1}+{\mathrm{A}}_2\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{{\mathrm{E}}_2}{\mathrm{R}\mathrm{T}}\right){\mathsf{\alpha }}^{\mathrm{m}}\right](1-\mathsf{\alpha }{)}^{{\mathrm{n}}_2}$$

(15)

2.3.2. Volume Radiation Transport: Energy Balance and Boundary Conditions

The most significant difference between the volumetric absorption heat transfer model and the surface absorption heat transfer model lies in the setting of the boundary conditions. In particular, the radiant heat flow does not transfer heat to the interior of the object and the substrate in the form of heat conduction in the differential equations for heat transfer [51].

Yuan et al. [33] formulated a one-dimensional (1D) heat transfer model (see Figure 5) to investigate the heat transfer mechanism in powder coatings cured with a catalytic IR heater. Their groundbreaking study introduced an internal heat source and performed numerical simulations on the heat transfer process for polyester-based powder coatings with different substrate thickness values.

Radiative heat transfer occurred between the radiant panel and the coating surfaces. The coatings were extremely thin with low thickness compared to their area, and the radiative effect of the air on the coatings was minimal [33]. Consequently, several assumptions and simplifications were made regarding the heat transfer process [15,16,18]:

• The film was assumed to be isotropic and homogeneous. Its temperature before curing was uniform and consistent. Its thickness did not change during curing.
• The density, thermal conductivity, specific heat capacity, and other physical properties of the coating and the substrate were considered constant and not affected by the temperature changes.
• The coating thickness was denoted as ‘ep’ and heat transfer occurred only in the Z direction.
• The heat transfer in the substrate was simplified as 1D heat transfer along the Z direction, assuming a uniform heat transfer process.
• The radiative effect of the air was not considered.

The complexity of radiative heat transfer combined with the desire for stable heat transfer simulations has led to further simplifications based on the following assumptions:

• IR rays have a specific penetration capability, allowing objects to be heated within this penetration distance. Considering the thickness of the coating (100 µm) within the IR penetration zone, the IR heating rate of the coating was assumed to be higher than that of hot-air heating. Therefore, it was assumed that the temperature increased simultaneously at every point in the coating. This simplified the heat transfer process by equating the IR radiation heating of the coating with that via an internal heat source.
• Owing to the small thickness of the coating, it was assumed that no IR radiation attenuation occurred along the thickness direction. Therefore, the intensity of the equivalent internal heat source within the coating was considered equal across the entire coating.

The heat released by the curing chemical reaction was negligible compared to the other heat flux values. Thus, it was ignored in the calculation. The heat balance equation for the powder coating and the metal substrate system was simplified as Equation [33]:

$$\frac{\mathrm{d}\mathrm{T}}{\mathrm{d}\mathrm{t}}({\mathrm{C}}_{\mathrm{P},\mathrm{P}}{\mathsf{\rho }}_{\mathrm{P}}{\mathrm{e}}_{\mathrm{p}}+{\mathrm{C}}_{\mathrm{P},\mathrm{s}}{\mathsf{\rho }}_{\mathrm{s}}{\mathrm{e}}_{\mathrm{s}})={\overline{\mathrm{Q}}}_{\mathrm{a}\mathrm{b}\mathrm{s}}-\mathsf{\sigma }\left[{\mathsf{\epsilon }}_{\mathrm{S}}({\mathrm{T}}_{\mathrm{S}}^4-{\mathrm{T}}_{\mathrm{\infty }}^4)+{\mathsf{\epsilon }}_{\mathrm{p}}({\mathrm{T}}_{\mathrm{p}}^4-{\mathrm{T}}_{\mathrm{\infty }}^4)\right]-\left[{\mathrm{h}}_{\mathrm{s}}({\mathrm{T}}_{\mathrm{s}}-{\mathrm{T}}_{\mathrm{\infty }})+{\mathrm{h}}_{\mathrm{p}}({\mathrm{T}}_{\mathrm{p}}-{\mathrm{T}}_{\mathrm{\infty }})\right]$$

(16)

The boundary conditions are as follows:

• The ambient temperature remains within 5% of its value during experimental testing, reflecting actual fluctuations.
• The area surrounding the coating and the substrate is treated as an insulated boundary, allowing heat exchange only with the surrounding air and not affecting the surface temperature.

Véchot et al. [15] assumed that when the film thickness was small enough and the metal substrate was a fairly good conductor of heat, then the temperature could be assumed to be constant in all the substrate + paint systems. This assumption was experimentally verified by measuring the temperature with two thermocouples (type K, 3% accuracy): one fixed underneath the metal plate and the other attached on the cured paint.

Subsequently, they used the following mathematical expression to solve the thermal balance [15]:

$$\begin{array}{c}\frac{\mathrm{d}\mathrm{T}}{\mathrm{d}\mathrm{t}}\left(\mathrm{C}{\mathrm{p}}_{\mathrm{p}}{\mathsf{\rho }}_{\mathrm{p}}{\mathrm{e}}_{\mathrm{p}}+\mathrm{C}{\mathrm{p}}_{\mathrm{s}\mathrm{u}\mathrm{p}}{\mathsf{\rho }}_{\mathrm{s}\mathrm{u}\mathrm{p}}{\mathrm{e}}_{\mathrm{s}\mathrm{u}\mathrm{p}}\right)={\mathrm{Q}}_{\mathrm{a}\mathrm{b}\mathrm{s}}-{\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}-{\mathrm{Q}}_{\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{t}\mathrm{t}\mathrm{e}\mathrm{d}}-{\mathrm{Q}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}\end{array}$$

(17)

Assuming that the substrate absorbs all the energy, the thermal equilibrium can be established as follows:

$${\mathrm{Q}}_{\mathrm{a}\mathrm{b}\mathrm{s}}={\mathrm{Q}}_0\left(1-{\mathsf{\rho }}_{\mathrm{P}}^{\mathrm{*}}\right)-{\mathrm{Q}}_0{\mathsf{\tau }}_{\mathrm{P}}^2\left(1-{\mathsf{\alpha }}_{\mathrm{s}\mathrm{u}\mathrm{p}}\right)={\mathrm{Q}}_0-{\mathrm{Q}}_1-{\mathrm{Q}}_3={\mathrm{Q}}_2+{\mathrm{Q}}_4+{\mathrm{Q}}_5$$

(18)

where ${\mathrm{Q}}_0$ is the incident radiative flux, ${\mathrm{Q}}_2$ and ${\mathrm{Q}}_4$ are the energy absorbed by the paint film, ${\mathrm{Q}}_5$ is energy absorbed by the metallic substrate, and ${\mathrm{Q}}_3$ denotes energy transmitted by the paint and reflected by the substrate; this term (order two) was considered negligible for this paint. Furthermore, ${\mathrm{Q}}_{\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{t}\mathrm{t}\mathrm{e}\mathrm{d}}$ represents the energy lost by radiative emission from the two faces of the system and is defined as follows:

$${\mathrm{Q}}_{\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{t}\mathrm{t}\mathrm{e}\mathrm{d}}=\mathsf{\sigma }{\mathsf{\epsilon }}_{\mathrm{s}\mathrm{u}\mathrm{p}}\left({\mathrm{T}}^4-{\mathrm{T}}_1^4\right)+\mathsf{\sigma }{\mathsf{\epsilon }}_{\mathrm{p}}\left({\mathrm{T}}^4-{\mathrm{T}}_2^4\right)$$

(19)

${\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}$ represents the heat released by the exothermic chemical reaction.

$${\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}={\mathsf{\rho }}_{\mathrm{p}}{\mathrm{e}}_{\mathrm{p}}\frac{\mathrm{d}\mathrm{x}}{\mathrm{d}\mathrm{t}}\mathsf{\Delta }{\mathrm{H}}_0$$

(20)

${\mathrm{Q}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}$ represents the thermal losses due to natural convection from the upper and lower surfaces of the system.

$${\mathrm{Q}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}={\mathrm{h}}_{\mathrm{a}\mathrm{i}}\left(\mathrm{T}-{\mathrm{T}}_1\right)+{\mathrm{h}}_{\mathrm{a}\mathrm{s}}(\mathrm{T}-{\mathrm{T}}_2)$$

(21)

The numerical simulations of the heat balance were performed using the Matlab software, and the results revealed that despite its simplicity, the thermal model was able to satisfactorily predict the experimental heating rate.

Genty et al. [31] developed a kinetic model for IR-cured poly-epoxide adhesive based on volume absorption, but no published study has focused on heat transfer modeling.

Over the last three decades, several researchers have devoted significant research efforts to develop heat transfer models for the IR curing process. These heat transfer models are classified and compared in

Table 4. Thermal transfer model classification.

Model	Heat Transfer Method		Geometric Model		Controller	Software	Reference
	Radiation	Radiation and Convection	3D/2D Model	1D Model
Surface absorption		√		√	PID	Matlab	[16]
		√		√	MPC	-	[18]
		√		√	PID & MPC	-	[40]
	√		√		PID	COMSOL	[29]
		√		√	-	-	[13]
		√		√	-	COMSOL	[19]
		√		√	-	COMSOL	[41]
	√		√		SQP	Matlab & COMSOL	[42]
	√		√		-	COMSOL	[22]
	√			√	-	-	[12]
		√	√		-	FLUENT	[43]
Volume absorption		√		√		Matlab	[15]
		√		√		ANSYS	[33]
		√		√	-	-	[13]
	√			√	-	-	[27]

.

2.4. Numerical Simulation Methods

IR radiative transfer problems encountered in various engineering fields are usually very complex. This is attributed to factors such as nonlinearity of the governing equations, transparent or opaque radiation interfaces in complex geometrical systems, and radiation characteristics that vary with wavelength and direction. In this section, six commonly used numerical simulation methods for radiative heat transfer are introduced, and their applicability is compared and evaluated based on six different requirements [52].

2.4.1. Zone Method

The zone method treats each zone (a discrete volume in the computational domain) as a separate radiating surface. The radiation exchange between different zones is computed based on view factors, which quantify the geometric relationship between zones. This method is suitable for problems that involve complex geometries, where the view factor calculations are manageable [53].

2.4.2. Monte Carlo Method

The Monte Carlo method (MCM) is based on probabilistic principles and involves tracking numerous photon ‘packets’ or ‘particles’ within the computational domain. At each interaction point (due to scattering or absorption), a random process determines the new direction of the photon ‘packet’ and the energy it carries forward. Monte Carlo method (MCM) is one of the sampling-based approaches which can handle the issue of high dimensionality in the probabilistic Uncertainty quantification (UQ) framework. MCM has many advantages, such as non-intrusive, robust, flexible, and simple for implementation [54]. However, due to the cumbersome computational work of large amount of ray tracings, the computational speed of this method is very slow which is not suitable to conducting coupled analysis with other process in thermal fluid problems [55].

2.4.3. Ray-Tracing Method

The ray-tracing method (RTM) is a widely used numerical simulation approach in the field of radiative heat transfer. RTM involves tracing the path of energy-carrying rays as they move through a medium and interact with surfaces, enabling the calculation of radiant heat transfer within complex systems. By considering the emission, absorption, and scattering phenomena encountered by the rays, this method provides a comprehensive analysis of radiative energy transfer. RTM provides a systematic approach to model and predict thermal radiation behavior, facilitating the design and optimization of high-performance thermal systems [56].

2.4.4. Discrete Ordinates Method

The discrete ordinates method (DOM) is used to solve the radiative transfer problem. The solution of radiative transfer equation (RTE) requires discretization of both angular and spatial domains. The idea of DOM is to represent the angular space by a discretized set of directions, and only radiative intensity at these discrete directions is solved. Each direction is associated with a quadrature weight. Both the directions and the weight are chosen carefully to ensure accuracy of angular integration, which is important for discretizing the in-scattering term and calculating the radiative heat flux. After the angular discretization is finished, the original integral-differential form of RTE becomes a set of coupled partial differential equations, which can then be discretized and solved by traditional techniques for solving partial differential equations [57].

2.4.5. Discrete Transfer Method

The discrete transfer method (DTM) is one of the widely used methods in radiative transfer. It has been extensively used to solve pure radiation and combined radiation, conduction and/or convection mode problems [58]. In this method, the energy emitted is divided into the hemisphere along finite number of rays, the radiation leaving the surface element in a certain range of solid angles can be approximated by the single ray [59]. In recent times, DTM has attracted the attention of various researchers as the method offers an advantage in terms of its applicability for complex geometries as compared to DOM. Coelho [60] has compared the accuracy of results obtained using DTM and DOM for radiative heat transfer in non-grey gases. It was reported that for such applications, the DTM predicts more accurate results and fares better in comparison with DOM. In addition, Nirgudkar et al. [61] proposed a simplified method for solving transient forms of RTE in two-dimensional participating media using DTM.

2.4.6. Finite Volume Method

The finite volume method (FVM) is a method for obtaining numerical solutions to differential equations, such as the radiative transfer equation. In FVM, the computational domain is divided into a finite number of small ‘control volumes’ and the governing equations are integrated over each control volume. The net flux of radiation across the control volume boundaries is used to update the radiation energy density within each control volume. FVM is particularly good at conserving energy, a key requirement for precise radiative transfer simulations [57].

There are benefits and drawbacks to each of the aforementioned strategies. The adaptability of the geometry, compatibility with flow, burns, chemical reactions, and other heat transfer modes, adaptability to anisotropic scattering and inhomogeneous media, feasibility of multiscale analyses and simulations (microscopic, mesoscopic, and macroscopic), ease of handling semi-transparent interfaces and probing directions, and efficient and accurate calculations are all necessary for a successful simulation method. To yet, there isn’t a flawless computational technique that can meet all of the aforementioned criteria at once. Based on the aforesaid description, the advantages and disadvantages of several numerical simulation methods for radiation heat transfer are listed in

Table 5. Comparison of different numerical simulation methods and available studies.

Calculation Method	Complex Shapes	Anisotropic Scattering	Inhomogeneous Media and Variable Parameters	Semi-Transparent Interfaces	Calculation Accuracy	Reference
Zone Method	−	−	+/−	−	Good
MCM	+	+	+/−	++	Good	[12]
RTM	−−	++	+/−	++	Very good	[41]
DTM	−	−−	+/−	+/−	Good
DOM	+	+	+	+/−	Moderate
FVM	+	+	+	+	Good

(++) Easy, (+) Feasible, (+/−) Moderate, (−) Difficult, (−−) Very difficult.

; the “Literature” column includes relevant studies on the subject of IR curing.

3. Curing Process

3.1. Monitoring Techniques and Models

Numerous types of curing reactions can occur in thermosetting polymers. The curing process is intricate, involving the cross-linking of linear polymer chains or the polymerization of low polymers. here is general agreement that nearly all ultimate properties of thermoset systems are dependent on the state of crosslinking or curing situation when a resin reacts with a curing agent in such sysetms [62]. The properties of cured products depend highly on the structural composition of the material system and the curing reaction conditions [63]. Moreover, even products of the same brand but from different batches may exhibit different curing characteristics due to discrepancies in the material production process. Therefore, it is crucial to accurately monitor, evaluate, and study the curing process and its related parameters.

The complexity of the curing process and the actual curing system poses challenges in establishing an absolute measurement standard, leading to the absence of a unified standard measurement method at present. Typically, a measurable physical or chemical quantity related to the curing degree is selected as the basis for measurement. Careful observation of the changes and change rate of this value enables the determination of the curing degree and reaction rate, as well as essential process parameters such as the gelation time and complete curing event [64].

Different physical meanings are assigned to measurement methods according to the quantities that need to be measured. While some techniques work well in laboratories, others are more appropriate for online production line monitoring.

Table 6. Comparison of different monitoring techniques and models.

Method Classification	Representative Measurement Methods	Measured Physical Quantity	Reference
Chemical reactions	Chemical titration	Chemical group concentration
	IR, Raman, and other spectroscopic methods	Spectral signal intensity of chemical bonds
Thermal properties	Differential thermal analysis (DSC, DTA)	Heat fusion changes during curing	[19] [41] [42] [22] [18] [16] [40] [15] [42] [27] [43]
Electrical properties	Dielectric analysis (DEA)	Dielectric loss and ionic conductivity, and resistance	[29]
Mechanical properties	Dynamic spring method, dynamic thermo-mechanical analysis, dynamic torsion vibration method	Correlation of mechanical modulus and mechanical loss
Fiber optic-based measurements	Fiber optic monitoring	Change in refractive index or absorption of signal waves
Ultrasound measurements	Ultrasonic monitoring	Longitudinal ultrasonic velocity and attenuation
Other methods	Viscosity method, hardness method, swelling method	Corresponding physical properties

summarizes the commonly used research methods for curing processes.

3.1.1. Spectrum Analysis

IR spectroscopy aids in direct determination of molecular structure information related to a measured system, which is mainly manifested by the position and intensity of absorption peaks [65]. The type of chemical bond (functional group) corresponding to an absorption peak can be assessed from the position of the absorption peak, as well as the effect of its chemical environment, e.g., solvation and adjacent groups. The intensity of the absorption peak reflects the concentration of corresponding groups within the material. By analyzing this information, the curing reaction mechanism during the curing reaction and the microstructure of the cured product can be inferred. Moreover, relevant curing kinetic parameters, such as gelation time, complete curing time, and curing rate, can be quantitatively calculated [66].

The concentration changes of the molecular groups involved in the curing reaction and the curing degree in the system can be calculated according to Equations (22) and (23), respectively [67].

$$\mathrm{C}\left(\mathrm{t}\right)=\frac{\mathrm{A}\left(\mathrm{t}\right)/{\mathrm{A}\left(\mathrm{t}\right)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d}}}{\mathrm{A}\left(0\right)/{\mathrm{A}\left(0\right)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d}}}$$

(22)

$$\mathsf{\alpha }=1-\mathrm{C}\left(\mathrm{t}\right)=\frac{\mathrm{A}\left(0\right)/{\mathrm{A}\left(0\right)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d}}-\mathrm{A}\left(\mathrm{T}\mathrm{t}\right)/{\mathrm{A}\left(\mathrm{t}\right)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d}}}{\mathrm{A}\left(0\right)/{\mathrm{A}\left(0\right)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d}}}$$

(23)

where A(t) and A(t)_standard are the absorption peak areas of the group to be analyzed and the internal standard group at time (t), respectively. Similarly, A(0) and A(0)_standard are the absorption peak areas of the group to be analyzed and the internal standard group at the beginning of the reaction, respectively.

3.1.2. Electrical Property Analysis

The electrical properties of thermosetting resins can sensitively reflect changes in the internal structure of the material and the state of molecular motion. DEA is the most widely used method for monitoring the curing process of thermosetting resins [68]. It involves the investigation of the changes in the dielectric properties of the resin during curing, enabling the monitoring of the liquid and solid states. DEA is flexible and suitable for real-time monitoring and process simulation on the production line and can be applied to various systems such as composite materials, adhesives, and coating sols. The basic principle of DEA involves the orientation response of polar groups and ions in an electric field, with the orientation degree being affected by factors such as temperature, frequency, polymerization, and viscosity. Changes to dielectric properties during curing are effected by factors including polymerization degree, temperature, and viscosity [69]. The phase change and amplitude attenuation of the inductive signal during dielectric testing can provide information regarding the resin viscosity, reaction rate, and curing degree.

The dielectric coefficient of a thermosetting resin can be expressed in complex form as [70]:

$${\mathsf{\epsilon }}^{\mathrm{*}}={\mathsf{\epsilon }}^{\prime }-\mathrm{i}{\mathsf{\epsilon }}^{\prime \prime }$$

(24)

$$\tan \mathsf{\delta }={\mathsf{\epsilon }}^{\prime \prime }/{\mathsf{\epsilon }}^{\prime }$$

(25)

where ${\mathsf{\epsilon }}^{\mathrm{*}}$ is the complex dielectric coefficient, ${\mathsf{\epsilon }}^{\prime }$ is the dielectric coefficient that indicates the storage capacity of the resin, ${\mathsf{\epsilon }}^{\prime \prime }$ denotes the dielectric loss or loss factor that indicates the energy dissipation part of the resin, and $\tan \mathsf{\delta }$ is the tangent of the loss angle.

3.1.3. Thermal Property Analysis

The thermodynamic parameters and physical properties of substances often exhibit correlations that are sensitive to temperature changes. Thermal analysis (TA), a method based on this principle, is widely employed in examining polymer structures and properties. The curing process of thermosetting resins is typically accompanied by noticeable thermal effects; therefore, it can be analyzed using TA methods. Commonly used TA techniques for resin curing analysis include enthalpy analysis and thermo-mechanical analysis (TMA), among others. Enthalpy analysis includes differential thermal analysis (DTA) and DSC [71]. In particular, the DSC method directly measures enthalpy data during the curing process, offering ease of operation, high resolution, and convenience for quantitative analysis; thus, it is more commonly used in resin curing research [72]. Currently, DSC is the most commonly used method for studying the IR curing kinetics of thermosetting resins (Table 6). According to Table 4, the DSC technology mainly focuses on the surface absorption mode. The use of DSC by Genty et al. [26] may be controversial considering the mechanism-based differences exhibited by thermal and IR curing, particularly the different kinetic parameters of curing [30]. Mafi et al. [73] investigated the thermal behavior of hybrid epoxy/polyester and pure polyester powder coatings by DSC. The effect of curing temperature on the coating glass transition temperature (Tg) was also assessed via dynamic TMA (DTMA). The non-isothermal DSC spectra of the hybrid and pure polyester coatings obtained under a scanning rate of 10 °C·min⁻¹ are presented in Figure 6.

It is generally assumed that the heat released during fusion is a result of the curing reaction. Therefore, the area under the exothermic curve is directly related to the curing degree (α), which can be calculated by determining the curing rate. This rate can be obtained as follows [74]:

$$\mathsf{\alpha }=\frac{{∆\mathrm{H}}_{\mathrm{t}}}{{∆\mathrm{H}}_{\mathrm{R}}}$$

(26)

$$\frac{\mathrm{d}\mathsf{\alpha }}{\mathrm{d}\mathrm{t}}=\frac{1}{{∆\mathrm{H}}_{\mathrm{R}}}\frac{{\mathrm{d}\mathrm{H}}_{\mathrm{t}}}{\mathrm{d}\mathrm{t}}$$

(27)

where ${∆\mathrm{H}}_{\mathrm{R}}$ is the reaction heat of the entire curing process, which is constant for a particular resin curing system, and ${∆\mathrm{H}}_{\mathrm{t}}$ denotes the reaction heat of the curing reaction at time t.

3.1.4. Optical Fiber Measurement Analysis

Besides DSC, optical fiber measurement analysis can also be utilized to monitor and measure the temperature of the curing process [75]. Optical fiber sensors are advanced sensors that are based on optical measurement technology. They are characterized by high sensitivity and strong anti-electromagnetic interference. Simultaneously, optical fibers offer unique advantages such as small diameter, flexibility, high temperature resistance, and good compatibility with composite materials. Such sensors can be used to monitor the refractive index changes of the curing system or the absorption of the measured signal wave by the resin, thereby reflecting the curing process characteristics of the system. The advantages of fiber optic sensors include their small size, high sensitivity, and little effect on the mechanical properties of the material [76]. The need for implantation into the material, which can interfere with its curing reaction, high production costs, and lack of reusability are some of their disadvantages. Cusano et al. [76] designed and experimentally assessed an optoelectronic fiber optic sensor (FOS) capable of monitoring the polymerization reactions of thermoset polymer–matrix composites. As shown in Figure 7, the FOS output was recorded during isothermal scans at temperatures of 50, 60, and 70 °C.

3.1.5. Ultrasonic Analysis

The ultrasonic echo pulse technique is commonly used in ultrasonic thickness gauges to measure coating thickness on non-metallic matrix materials such as plastic and wood [77]. By analyzing the echo waveform digitally, the thickness of the coating can be accurately determined. Recent studies have reported the online monitoring of resin curing via ultrasonic methods. The propagation of high-frequency elastic waves in the ultrasonic state is associated with the dynamic mechanical deformation of the object being measured, reflecting changes in its internal structure and cohesive state [78]. The ultrasonic properties of resins are highly sensitive to the gelation and complete curing processes, providing valuable information regarding the changes in mechanical property. Ultrasonic measurement is essentially a dynamic mechanical analysis at high frequency, offering insights into the viscoelastic properties of the resin at different states of physical structure. Ultrasonic monitoring of resin curing offers several advantages such as non-destructive material assessment, high detection sensitivity, and simple operation [79]. Currently, ultrasound technology is primarily used for monitoring the resin curing process. The instantaneous curing of a resin can be determined by measuring its modulus E_m, which is directly correlated with the cross-linking degree [80]:

$$\mathsf{\alpha }\left(\mathrm{t}\right)=\frac{{\mathrm{E}}_{\mathrm{m}}\left(\mathrm{t}\right)-{\mathrm{E}}_{\mathrm{m}}^0}{{\mathrm{E}}_{\mathrm{m}}^{\mathrm{\infty }}-{\mathrm{E}}_{\mathrm{m}}^0}$$

(28)

where ${\mathrm{E}}_{\mathrm{m}}^0$ and ${\mathrm{E}}_{\mathrm{m}}^{\mathrm{\infty }}$ are the initial and fully cured moduli of the resin system, respectively, and E_m(t) denotes the modulus at time t.

3.1.6. Mechanical Property Analysis

The curing process of thermosetting resins involves the formation of cross-links between linear polymers or the polycondensation of functional monomers. The curing degree can be assessed by monitoring the consumption of functional groups [72]. Nevertheless, this measurement becomes less significant in the final stage of curing despite its effect on the mechanical properties of the resin. This final stage plays a critical role in determining the optimal properties of the cured resin. Consequently, relying solely on chemical methods to evaluate the resin curing behavior is inadequate. On the other hand, mechanical methods involve the measurement of relevant mechanical moduli such as the shear modulus, flexural modulus, and torsional modulus [81]. Tests are performed at different frequencies to determine the mechanical moduli and mechanical loss of the resin. Commonly used mechanical testing methods include the torsional pendulum method [82], twisted braid method [83], rheological method [84], DMTA [85], dynamic torsion vibration method [86], and others. Torsional braid analysis is derived from the torsional pendulum approach and is a free decay vibration method. DMTA measures and determines the dynamic mechanical properties of the specimen under cyclic alternating stress, and varying temperature, time, and frequency parameters. Commercial DMTA can accommodate a wide range of deformation modes. Resin samples are typically treated as those in torsion braid analysis, where the samples are fixed to an inert material for analysis. During resin curing, the viscosity increases with increasing curing degree, particularly near the gelation point. This increase approaches infinity when the resin is fully cured, enabling the assessment of the resin curing process by measuring the viscosity changes. A plate rheometer can measure the complex shear modulus or the complex shear viscosity of the resin. Based on the need to control the mechanical properties of engineering materials, Ramis et al. [72] conducted a study on the curing process of a thermosetting powder coating. This coating was prepared using carboxyl-terminated polyester and TGIC, and its curing was analyzed using DMTA, TMA, and DSC. Figure 8 depicts the isothermal curing of the coating determined via DMTA.

Different measurement modes can be utilized to obtain the time, frequency, and temperature spectra of modulus and loss [87].

$${\mathsf{\alpha }}_{\mathrm{m}}=\frac{{\mathrm{E}}_{\mathrm{t}}^{\prime }-{\mathrm{E}}_0^{\prime }}{{\mathrm{E}}_{\mathrm{\infty }}^{\prime }-{\mathrm{E}}_0^{\prime }}$$

(29)

$${\mathsf{\alpha }}_{\tan \mathsf{\delta }}=\frac{∆\tan {\mathsf{\delta }}_{\mathrm{t}}}{∆\tan {\mathsf{\delta }}_{\mathrm{\infty }}}$$

(30)

where ${\mathrm{E}}_{\mathrm{t}}^{\prime }$, ${\mathrm{E}}_0^{\prime }$, and ${\mathrm{E}}_{\mathrm{\infty }}^{\prime }$ are the shear energy storage modulus at time t, at the beginning of curing, and at the end of curing, respectively, and $∆\tan {\mathsf{\delta }}_{\mathrm{t}}$ and $∆\tan {\mathsf{\delta }}_{\mathrm{\infty }}$ are the areas below the loss peak at time t and full curing, respectively.

3.2. Curing Theory

Numerous methods have been developed to characterize the curing reaction of thermosetting polymers. Consequently, various curing models have been established, which are mainly categorized as mechanism-based and phenomenological models. The mechanism-based models focus on analyzing the specific curing reaction mechanism, studying the kinetic relationships of the curing process, and theoretically considering all elementary reactions during the entire process. Conversely, phenomenological models do not consider individual elementary reactions but use a virtual apparent reaction to represent the entire curing process and study the main kinetic characteristics from a macroscopic perspective. Owing to the complexity of the curing process, particularly in its later stages where diffusion factors become dominant, it is challenging to identify each specific elementary chemical reaction. In such cases, a phenomenological model is a better option to describe the curing reaction.

3.2.1. Flory–Stockmeyer Theory

The Flory–Stockmayer theory describes the cross-linking and gelation processes of step-growth polymers. This theory was first proposed in 1941 by Paul Flory and was further developed in 1944 by Walter Stockmayer, who included crosslinks of any initial size distribution. Initially, Flory made the following three assumptions:

All functional groups on the branch unit have the same reactivity.

All reactions occur between functional groups A and B.

There are no intramolecular reactions.

Owing to these assumptions, a slightly higher conversion rate than that predicted by the Flory–Stockmayer theory is required to form a polymer gel. Gels are formed at slightly higher conversion rates due to steric hindrance, which prevents each functional group from having the same reactivity. Moreover, intramolecular reactions occur during this process [88].

The Flory–Stockmayer equation can be expressed as follows [89]:

$$\mathsf{\alpha }=\frac{1}{{\left[\mathrm{r}+\mathrm{r}\mathsf{\rho }\left(\mathrm{f}-2\right)\right]}^{\frac{1}{2}}}$$

(31)

where $\mathsf{\alpha },\mathrm{r}$, and $\mathsf{\rho }$ denote the curing degree at the gelation point, the ratio of the A and B functional groups at the beginning of the reaction, and the functionalization unit concentration, respectively.

3.2.2. Non-Equilibrium Thermodynamic Fluctuation Theory

The curing process of thermosetting polymers, which transitions from a liquid to a solid state, is inherently a non-equilibrium process. This process is best understood through the non-equilibrium thermodynamic fluctuation theory, a branch of thermodynamics that addresses systems not in thermodynamic equilibrium [90]. In such systems, macroscopic quantities are used to extrapolate variables typically applied to systems in equilibrium, making this theory particularly useful for investigating these curing processes.

In the context of applications, Hsich utilized this theory to study the curing process of carbon black-filled natural rubber systems. The curing process of the rubber was monitored via a Monsanto rheometer. The measured quantity was the torque $\mathrm{G}\left(\mathrm{t}\right)$ generated during the curing process, which is related to a certain modulus of the resin, e.g., the shear modulus. The magnitude of the torque reflects the curing degree. Based on the non-equilibrium thermodynamic fluctuation theory, the dynamic relationship of its curing process can be expressed as follows [91]:

$$\frac{{\mathrm{G}}_{\mathrm{\infty }}-\mathrm{G}\left(\mathrm{t}\right)}{{\mathrm{G}}_{\mathrm{\infty }}-{\mathrm{G}}_0}=\mathrm{e}\mathrm{x}\mathrm{p}\left[-{\left(\frac{\mathrm{t}}{\mathsf{\tau }}\right)}^{\mathsf{\beta }}\right]$$

(32)

where ${\mathrm{G}}_0$ and ${\mathrm{G}}_{\mathrm{\infty }}$ denote the minimum and maximum torque values on the experimental curing curve, respectively, and $\mathsf{\tau }$ is the relaxation time.

3.2.3. Avrami Theory

The Avrami theory, proposed by Kolomon Avrami, has been widely used to describe the phase transformation kinetics, including the curing of thermosetting polymers. This theory quantitatively relates the extent of the reaction to the transformation of the polymer structure over time [92]. By analyzing the nucleation and growth of polymer domains, the Avrami theory offers a systematic means to understand the curing process and predict the properties of the final thermoset materials.

The Avrami theory has been applied to interpret the kinetics of the curing of powder coatings, particularly polymer crystallization [93]. During the formation of an infinite network, several high-molecular-weight particles or molecular microgels due to cross-linking can be observed. Polymer crystallization that occurs during the curing of powder coatings is thought to be a physical form of crosslinking. Thus, the Avrami equation can be applied to predict the curing process of powder coatings. The relative curing degree at time t can be expressed by using the following equation [91]:

$$\mathsf{\alpha }=\frac{\mathrm{G}\left(\mathrm{t}\right)}{{\mathrm{G}}_{\mathrm{\infty }}}$$

(33)

where ${\mathrm{G}}_{\mathrm{\infty }}$ and G(t) denote the final elastic modulus and the elastic modulus at time t, respectively. Noteworthy, G can also denote other physical and mechanical quantities, e.g., the torque modulus.

After the gelation point, a modified Avrami equation can be used to explain the iso-thermal curing process [90]:

$$\mathsf{\alpha }=1-\exp \left(-\mathrm{k}{\left(\mathrm{t}-{\mathrm{t}}_{\mathrm{g}}\right)}^{\mathrm{n}}\right)$$

(34)

where ${\mathrm{t}}_{\mathrm{g}}$ is the gelation time, which is indicated on the isothermal curing curve, and $\mathrm{k}$ represents the constant of the curing reaction rate after the gelation point. At lower curing temperatures (<90 °C), n = 3; as the reaction temperature increases, ‘n’ gradually decreases.

3.2.4. DSC Kinetic Model

The DSC kinetic model provides a quantitative analysis of the curing kinetics of thermosetting polymers [94]. By employing TA techniques, this model can determine the reaction rate, activation energy, and curing degree during the curing process. The DSC kinetic model has proven to be valuable in characterizing the curing behavior of thermosetting polymers, enabling the precise control of both the curing conditions and the resultant material properties. The kinetic relationship is expressed by the following equation [95]:

$$\frac{\mathrm{d}\mathsf{\alpha }}{\mathrm{d}\mathrm{t}}=\mathrm{k}{\left(1-\mathsf{\alpha }\right)}^{\mathrm{n}}$$

(35)

Autocatalytic reactions have certain characteristics. For example, they exhibit an induction period where the reaction rate is initially low, and only after a certain period, the reaction rate reaches its maximum value. The autocatalytic model applied to the curing process of thermosetting resins was first proposed by Smith [96]:

$$\frac{\mathrm{d}\mathsf{\alpha }}{\mathrm{d}\mathrm{t}}=\mathrm{k}{\mathsf{\alpha }}^{\mathrm{m}}{\left(1-\mathsf{\alpha }\right)}^{\mathrm{n}}$$

(36)

Kamal and Horie further improved it into the following composite form:

$$\frac{\mathrm{d}\mathsf{\alpha }}{\mathrm{d}\mathrm{t}}=\left({\mathrm{k}}_1+{\mathrm{k}}_2{\mathsf{\alpha }}^{\mathrm{m}}\right){\left(1-\mathsf{\alpha }\right)}^{\mathrm{n}}$$

(37)

where the terms $\mathrm{d}\mathsf{\alpha }$/$\mathrm{d}\mathrm{t}$ represent the reaction rate, α represents the curing degree, $\mathrm{m}$ and $\mathrm{n}$ are variables that determine the reaction order, and k, ${\mathrm{k}}_1$, and ${\mathrm{k}}_2$ are apparent rate coefficients that correspond to the reaction rate intrinsic to the system and that catalyzed by protons generated during the curing process. These kinetic parameters can be determined by analyzing experimental data or mathematical fitting.

All the above-mentioned theoretical models start from a certain chemical or physical mechanism of the thermosetting material system, which is closely related to the curing process and thus aids in deducing its relevant kinetic relationship. The physical meanings of the obtained relationships differ, and so do their respective applications.

Table 7. Comparison of different curing theories.

Theory	Main Feature	Reference
Gelation theory	The critical conditions of gelation are derived theoretically; the chemical conversion at the gelation point depends only on the curing components in the system and is not related to the reaction temperature and experimental conditions.	[27]
DSC kinetic model	The reaction details in the curing process are ignored, and the entire curing process is considered a virtual macroscopic reaction. The kinetic characteristics of the virtual reaction (e.g., reaction order, activation energy, etc.) are investigated from a macroscopic perspective.	[18] [16] [40] [15] [29] [19] [41] [42] [22] [43]
Avrami theory	The solidification process is compared with the crystallization process of polymers. The micro-mechanism of the solidification process is analyzed using the crystallization kinetics equation.
Non-equilibrium thermodynamic fluctuation theory	This theory connects the curing degree with the physical and mechanical properties of the resin and can predict their change during curing.

summarizes common theoretical models that have been used to describe the curing process of thermosetting polymers.

3.3. Non-Thermal Effect and Properties of Cured Products

Epoxy resins and unsaturated polyester resins, as well as vinyl resins, are the most used and widely applied varieties of general-purpose thermosetting resins. The materials used in the IR curing research (Table 1) mainly concern these three categories. The absorption peaks of the IR spectra of the main reactive groups are concentrated in the MIR and FIR regions. This strong IR absorption property, which is different from the conventional ‘thermal effect’ and is called the ‘non-thermal’ effect, facilitates the acceleration of the curing process and affects the mechanical properties of the curing product [27]. By analyzing the contents presented in Table 5, Table 6 and Table 7, it can be concluded that the current kinetic research on IR curing technology is mainly focused on the ‘thermal effect’, while the research focusing on the ‘non-thermal effect’ is scarce (

Table 8. Comparison of absorption models.

Absorption Model	Monitoring Device	Curing Theory	Reference
Surface absorption	DSC	DSC kinetic model	[19] [41] [42] [22] [18] [16] [40] [15] [42] [43]
	DEA	DSC kinetic model	[29]
Volume absorption	DSC	Gelation theory	[27]

). Moreover, research on the kinetic mechanisms and supporting monitoring tools are still lacking.

3.3.1. Non-Thermal Effect

Kumar et al. [10] investigated the use of IR radiation curing as an alternative to conventional thermal curing. They concluded that IR curing could effectively reduce the process cycle time for polymer composites without compromising their strength. In another study, Kumar et al. [20] found that the IR technique achieves comparable properties with only 25% of the time required for conventional thermal curing, significantly reducing power consumption to between 33% and 41%. Genty et al. [27] referred to this rapid curing phenomenon as the ‘non-thermal effect’.

The ‘non-thermal effect’ concept in IR curing was introduced by Genty et al. [27], who highlighted the significant reduction in the gelation point time and glass transition time of IR curing at temperatures below 60 °C. This phenomenon, which is closely related to the IR heat flux, demonstrates evident selectivity for the molecular groups and the steps involved in the reactions. Moreover, during the entire curing process, the activation energy is lower than that under thermal curing. The thermal and ‘non-thermal’ effects are not correlated but competitive. Yuan et al. [33] developed a integrated catalytic IR radiation curing system. Their study demonstrated that catalytic IR radiation effectively cures polyester-based coatings, ensuring they meet engineering quality standards. By optimizing curing parameters, the curing efficiency can be increased four to nine times compared to conventional hot-air curing within the same production timeframe. Knischka et al. [97] demonstrated that the ‘non-thermal effect’ due to volume absorption could significantly reduce the curing time.

3.3.2. Properties of Cured Products

Several studies have explored the efficacy of infrared (IR) and near-infrared (NIR) radiation for curing coatings and their impact on mechanical and chemical properties. Genty et al. [31] focused on IR curing, finding that while it did not affect adherence or moduli, it notably increased tensile and flexural strength in polymer composites. Yuan et al. [33] investigated catalytic IR curing systems and observed that higher temperatures and longer curing times improved mechanical strength but reduced gloss and darkened coating color at excessive temperatures. Choi et al. [24] highlighted challenges with NIR heating alone, emphasizing the importance of uniform temperature distribution to prevent defects like cracking and delamination during curing. Stojanović et al. [32] compared catalytic IR-cured primers with conventionally dried coatings, revealing enhanced cohesion and corrosion resistance in catalytic IR-cured primers, validated through DSC and FTIR analyses, indicating superior curing efficacy.

4. Discussion

The heat transfer mechanism of IR radiation involves the conversion of the electromagnetic energy into heat energy through the resonance of electromagnetic waves with molecules. Polymers contain many couplings such as vibrational couplings of CH, CH₂, CH₃, and CC, and these molecules’ vibrations correspond to IR regions above 1.5 µm. The wavelength of IR radiation is concentrated between 0.7 and 7 μm. The spectra of electric IR heaters can also be tailored according to the characteristics of the cured material. The volumetric absorption mode of IR radiation leads to a ‘non-thermal effect’, which reduces curing time and improves energy efficiency, leading to a reduction in overall costs. In particular, catalytic IR heaters, which are advantageous in the SIR and MIR regions, are rather attractive for heating polymers.

From the perspectives of heat transfer and curing process research, the numerical model can be better supported by experimental data, and it is especially good for matching complex 3D structures. However, the study of curing kinetics is still centered on the ‘cured material’ and lacks research on the kinetic model in line with the characteristics of IR curing technology. Correspondingly, the current monitoring techniques for heat transfer and curing processes tend to be more traditional, with a lack of applications such as radiant heat flux sensors and FTIR analysis, which are more suited to the characteristics of IR technology.

There has been controversy as to whether IR curing is a surface absorption phenomenon or a volume absorption phenomenon. It depends mainly on the physical properties of the material as well as on the spectral properties of the IR radiation. Combined analysis of the data presented in Table 1 and Table 4 indicates that materials such as carbon fibers and glass/natural fibers usually absorb IR radiation at the surface. Moreover, attention should also be paid to the phenomenon of strong surface absorption consuming excessive electromagnetic energy, leading to a decrease in penetration depth.

In recent years, with the development of science and technology and the exploration of engineering practice, the curing technology of thermosetting polymers has also been developing. For instance, Dilmurat et al. [6] assessed the curing mechanism, current application status, and primary pros and cons of different curing processes for advanced polymer composites. Hay et al. [98] described the pros and cons of the main radiation curing routes compared to the thermal curing process. To analyze the IR curing technology more comprehensively, this section presents the systematic probe into the advantages and disadvantages of IR curing technology in four ways, using ultraviolet (UV) curing technology and traditional heat convection curing technology as reference objects, as presented in

Table 9. Comparison of three different curing technologies.

Curing Method	Material	Penetration	Applicability	Cost	Reference
Infrared	No special requirements for polymers, good applicability, universality, and potential	Highly affected by physical properties, low penetration into carbon fiber and glass/natural fiber polymer	Potential for fast curing, good at handling flexible workpieces, high controllability	Lower investment, running, and maintenance costs	[99] [100] [101] [102] [103]
Ultraviolet	Need to add photoinitiators to polymers, can be used for curing energetic materials	Can be hindered by fillers, very limited penetration in semi- and non-transparent polymers	Fast-curing, good at handling flexible workpieces, high controllability	High cost of photoinitiators and acrylic toxicity	[104] [105] [106] [107] [108]
Convection	No special requirements for polymers, good applicability, universality, and potential	Faces the issue of ‘surface heating’ mechanism	High controllability but limited by curing time	Lower investment, running, and maintenance costs	[109] [110] [111] [112] [113] [114]

.

Comparative analysis reveals that compared with the traditional curing technology, IR curing technology offers advantages in the universality of curing materials, penetration, applicability, and economy, but in terms of curing speed, UV curing technology has a greater advantage.

Furthermore, UV-curable resins such as epoxides, vinyl ethers, and acrylates are also important monomers that offer effective media for energetic materials [115]. The integration of UV curable resin into energetic materials has been a new direction in the field of explosive inks with high curing speed and high solid loading. Guo et al. prepared CL-20-based UV-curable explosive composites by UV-curable and direct ink writing techniques. The rate of curing, micro-scale structure, morphology, crystal type, impact sensitivity, and detonation ability of the specimen were characterized and analyzed. The results showed that the curing process of CL-20-based UV-cured explosive ink could be completed within 7 min after UV-curing for 3 min, revealing rapid curing speed [116]. The integration of UV-curing resins into energetic materials has shown good results, and the potential of applying IR curing to energetic materials can be explored in the future.

5. Conclusions

This article provides a comprehensive review of IR curing technology. The relevant literature on IR curing is summarized, analyzed, and compared, with specific emphasis on IR heaters, heat transfer models, numerical simulation methods, heat transfer and curing monitoring devices, and curing theory. The main conclusions are as follows:

Based on the summary and analysis of IR heaters, three common types emerged: electric IR heaters, gas-fired IR heaters, and gas catalytic heaters. Among them, electric heaters are widely used; nonetheless, they have higher operating costs and shorter lifespans. The feasibility of gas catalytic IR technology in powder coating curing has been proven to be effective. In particular, combined with the ‘non-thermal effect’, gas catalytic IR heaters offer broader application prospects in the field of low-temperature rapid curing. Based on the careful review on the heat transfer models, two main types of models emerged: surface and volume absorption models. Owing to the complexity of heat transfer radiation and the limited research on relevant mechanisms, heat transfer models are often simplified into one-dimensional surface-to-surface heat transfer models when simple geometric shapes are involved. Moreover, there is limited research on volume absorption heat transfer models for complex geometric shapes. The most commonly used numerical simulation method is FVM, which is implemented by using commercial simulation software (COMSOL). DSC is commonly used for the parameter monitoring of surface absorption curing processes, while curing monitoring techniques for volumetric absorption modes have rarely been reported to date. The curing theory based on the DSC kinetics model is the most commonly used. Theoretically, IR volume absorption models should consider the decrease in the activation energy. Thus, the applicability of the DSC curing monitoring technique needs to be further investigated. Compared to conventional curing techniques, the IR technology, especially with respect to the volume absorption model, exhibits advantages in terms of curing time, mechanical properties, and corrosion resistance performance of the cured products. The improvement in these curing processes and the mechanical properties of the cured products are directly related to the decrease in the activation energy and the increase in the curing degree. However, the low penetration of IR radiation into some materials largely limits the application of this technology.

Based on the systematic analysis of the literature reviewed, several future research directions are suggested:

• From the perspectives of energy consumption and wavelength matching, catalytic IR curing technology deserves further research and new application directions.
• For broadening the range of applications, particularly for curing materials (such as energetic materials) and substrates, the potential of IR curing technology for rapid curing at low temperatures needs to be further systematically explored.
• Undeniably, a lot more systematic explorations are further demanded to carry out research on curing monitoring techniques that match IR curing technology (volume absorption).
• Modeling of curing kinetics matching the characteristics of IR curing technology (volume absorption) should be pursued in the future.
• Quantification of the benefits of IR curing is still a complex task, and establishing a simple yet effective evaluation index would aid the research on IR curing technologies and engineering applications.