Study of Microwave Healing Properties of Carbonyl-Iron-Powder-Modified Asphalt Mixture Based on Digital Image Technology

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This study is based on the use of carbonyl iron powder to replace part of a mineral powder and investigates the healing effect of a carbonyl iron powder asphalt mixture after microwave heating. The research results can provide technical references for the engineering application of microwave heating in repairing cracks of asphalt mixtures.

Abstract

To address the limitations of microwave healing and the repair capabilities of conventional asphalt mixtures, this paper employs carbonyl iron powder as a filler to replace 20% of the mineral powder in asphalt mixtures, thereby enhancing their microwave absorption and healing properties. The study uses carbonyl iron powder mixtures as the experimental group and conventional asphalt mixtures as the control group. Using digital image correlation (DIC) technology, the semi-circular bending healing test and microwave heating test were conducted to determine the optimal conditions for microwave-induced healing and to investigate the effects of multiple healing factors on the healing outcomes. The test results show that the carbonyl iron powder asphalt mixture has the advantage of heating healing, and the intermittent heating method further improves the heating uniformity. The fracture energy healing index (HI_U) and the crack initiation time healing index (HI_t) are 83.1% and 34.9% higher than the ordinary asphalt mixture (microwave heating 100 s). Among the external healing factors, the microwave heating time has the greatest influence on the healing rate, followed by the degree of damage and the standing time. The optimal healing scheme is to stand for 4 h after microwave heating for 100 s, and the curing effect is the best at the initial stage of damage (before crack initiation).

1. Introduction

Asphalt materials are temperature-sensitive and can self-heal after damage. However, in natural conditions, the self-healing process of asphalt mixtures is slow and insufficient to repair fatigue damage under static conditions. The molecular activity of asphalt is closely linked to temperature. When the temperature rises to around 40~60 °C, the glass transition temperature, the molecular thermal motion significantly increases, enhancing fluidity and facilitating the diffusion and merging of molecules at the crack interface [1], thus closing the cracks. This demonstrates that temperature plays a crucial role in the development of the self-healing behavior of asphalt materials. Therefore, adopting an appropriate heating method is essential for the healing of asphalt mixtures. At present, the ways to promote the healing of asphalt mixture include the electromagnetic induction heating method [2], the microwave heating method [3], the infrared heating method [4], and the microcapsule method [5,6]. Microwave induction technology, known for its high heating efficiency, excellent penetration, and thorough repair, has gained significant attention [7,8,9].

The traditional asphalt mixture has a weak microwave absorption capacity that cannot meet the requirements for microwave-induced heating and healing [10]. Therefore, researchers have introduced microwave-absorbing materials to enhance their microwave thermally induced performance. Examples include replacing aggregates with magnetite, steel slag, etc.; replacing mineral powder with silicon carbide powder; or incorporating carbon fibers, steel fibers, and other materials [11,12,13]. Although existing studies have achieved breakthroughs, most of them focus on replacing aggregates with large-particle-size microwave-absorbing aggregates. This solution faces challenges in engineering practice: the reconstruction of gradation increases construction complexity, and high doping amounts significantly raise maintenance costs, which restrict its promotion [14]. Thus, this paper proposes a more optimal solution of replacing fillers with microwave-absorbing materials: the microwave-absorbing materials form a mastic with asphalt (as the core bonding and filling material of the mixture, its self-healing properties directly affect the fatigue life of the pavement [15]). This mastic can be uniformly dispersed to achieve rapid crack healing, which not only simplifies the thermal conduction and heating steps of microwave-absorbing aggregates but also saves costs. Relevant studies have confirmed its effectiveness: Ren X. et al. [16] found that using carbon fiber powder (CFP) as a filler can significantly improve the microwave heating rate of asphalt mastic; Liu J. et al. [17] pointed out that the magnetic loss characteristics of Fe₃O₄(FO) filler are beneficial to the high-temperature rheological properties of the mastic and can enhance the microwave-induced heating and healing efficiency of the mixture; Yi, Z.; Bin, K.; et al. [18,19,20] found through comparison that carbonyl iron powder allows the peak load and fracture energy healing rates of the mixture to reach 67.62% and 52.05%, respectively, showing the best self-healing effect. Particularly importantly, carbonyl iron powder has excellent magnetic permeability and dielectric loss and has mature industrial production processes, and its spherical particle morphology and high specific surface area can also improve the dispersibility of asphalt.

To evaluate the healing effect of asphalt mixtures, conventional methods involve conducting fracture-healing cycle tests using beam bending fracture tests, semi-circular bending tests, and four-point bending fatigue tests and analyzing self-healing efficiency in combination with healing indicators [21,22,23,24,25]. In addition, researchers have also combined CT scanning, nanoindentation, and acoustic emission technology to improve evaluation accuracy. For example, Zhenhui, L. [12] used X-ray CT to reconstruct fatigue cracks in steel slag permeable asphalt mixtures and combined it with nanoindentation to assess the healing effect; Franesqui, M.A. et al. [26] measured the crack depth of specimens under microwave heating via ultrasonic waves and established a relationship between crack depth and heating duration to determine the optimal self-healing conditions. However, such methods have limitations: they are difficult to use for real-time monitoring of crack propagation and the crack resistance of the mixture before and after healing. Therefore, this study adopts digital image correlation (DIC) technology to evaluate self-healing performance [27]. As a non-contact, non-interfering full-field deformation optical measurement method, DIC can directly obtain the displacement field and strain field on the surface of the specimen. For instance, when Zhu, X. et al. [28] studied the healing effect of ferrites on asphalt mixtures under microwave induction, they used DIC to collect images of specimens and real-time displacement data during the semi-circular bending test, quantitatively analyzed crack propagation and changes in the strain field before and after healing, and effectively evaluated the impact of microwave heating time and healing time on self-healing performance.

The purpose of this study is to provide a theoretical basis for the application of microwave thermally induced carbonyl iron powder asphalt mixture preventive maintenance technology. To this end, micron-sized carbonyl iron powder is used to partially replace mineral powder to enhance the overall microwave absorption and healing capabilities of the asphalt mixture. Meanwhile, the optimal microwave-induced healing–heating method is determined by analyzing its microwave heating behavior, and combined with the research on the healing performance of asphalt mixtures under multiple influencing factors, the optimal maintenance scheme for microwave thermal induction is further clarified.

2. Materials and Methods

2.1. Raw Materials

The raw materials used in this study include 90# base asphalt, aggregates, and filler, sourced from Ordos Lutai New Material Technology Development Co., Ltd., Ordos, China. The coarse and fine aggregates are crushed limestone gravel, and the filler is limestone powder. Technical specifications for 90# base asphalt are listed in

Table 1. Technical indexes of 90# matrix asphalt.

Technical Specifications	Penetration (25 °C, 5 s, 100 g)/0.1 mm	Ductility (10 °C)/cm	Softening Point /°C	Dynamic Viscosity (60 °C)/Pa. s	Density/g/cm3	Mass Loss (After TFOT)/%
Measured Value	90	55	46	190	1.02	0.5

, while those for the coarse and fine aggregates are detailed in

Table 2. Technical indexes of aggregates with different particle sizes.

Grain Size/mm	Apparent Relative Density	Relative Bulk Density	Water Absorption/%
10–20	3.198	3.121	1.18
5–10	3.042	2.929	1.26
0–5	2.734	2.558	—

.

Cobalt iron powder produced by Yingtai Metal Materials Co., LTD., Nangong City, China, was selected as the wave-absorbing functional filler to replace 20% of the limestone powder by volume in the asphalt mixture. The technical specifications of the filler are shown in

Table 3. Filler technical indicators.

Technical Specifications	Mineral Constituent/%		Rate of Water Content/%	Apparent Density/g/cm3	Through Sieve Percentage/%
					0.6 mm	0.15 mm	0.075 mm
Mineral Powder	CaCO3	96.5	0.2	2.745	100	97.1	83.8
	CaMg(CO3)2	3
	Others	0.5
Carbonyl Iron Powder	α-iron (body-centered cubic iron)	99.6	0.1	7.812	100	100	100
	Others	0.4

.

2.2. Asphalt Mixture Gradation Design

The AC-16-type asphalt mixture was adopted, with the design proportion of carbonyl iron powder replacing mineral powder (≤0.075 mm) set at 20%, which showed the best microwave healing ability in the preliminary research results [29]. The carbonyl iron powder asphalt mixture was used as the experimental group and the ordinary asphalt mixture as the control group. Both groups have a mineral powder content of 4%, with their optimal asphalt–aggregate ratios being 4.58% and 4.62%, respectively. The gradation curve is shown in Figure 1, and the Marshall test results are presented in

Table 4. Volume parameters of the asphalt mixture.

Carbonyl Iron Powder Replacement Ratio/%	Optimal Asphalt-Aggregate Ratio/%	Bulk Specific Gravity/g/cm3	VV/%	VMA/%	VFA/%	Stability/kN	Flow Value /mm
0	4.62	2.760	4.0	14.2	69.1	17.52	3.01
20	4.58	2.755	3.9	13.8	70.2	16.28	3.23

.

2.3. Preparation of Semi-Circular Samples

Since the Superpave gyratory compaction (SGC) method can simulate the vertical compaction and horizontal kneading effects of on-site road rollers, accurately control the degree of compaction, and avoid aggregate segregation to ensure the uniform structure of specimens—thereby allowing the performance test results of specimens to truly reflect the actual conditions of on-site pavement—this study used Superpave gyratory compaction equipment to prepare cylindrical specimens (asphalt temperature: 140 °C, aggregate temperature: 175 °C, and mixing temperature: 165 °C). Given that the test results of the semi-circular bending (SCB) test are stable and reliable [30], the cylindrical specimens were cut into SCB specimens for the microwave healing test. The compaction parameters are as follows: an internal rotation angle of 1.16° ± 0.02°, a vertical pressure of 600 kPa ± 18 kPa, and a rotation rate of 30 r/min ± 0.5 r/min. These parameters ensure that the specimens have good density uniformity. The mixing parameters for the asphalt mixture are the same as those used in Marshall compaction. The final dimensions of the specimens after rotary compaction are 150 mm in diameter and 190 ± 5 mm in height. The preparation process is illustrated in Figure 2, with the specific steps as follows:

First, pour the mixed asphalt mixture into the preheated rotary compaction mold. Use a height control method to stop the rotation when the specimen reaches 190 mm. Optimize the quality of the mixture to ensure the specimens’ volume index meets the requirements. Next, cut and process the standard cylindrical asphalt mixture specimens using an automatic cutting machine. Remove the 15 mm thick sections with higher void ratios at both ends; then, cut the remaining middle section into three 50 mm thick cylinders. Finally, divide the cylinders along their diameters to form geometrically symmetrical semi-circular specimens. To ensure that the cracks in each destructive loading test start from the center, use the SCB professional cutting machine to cut a 1.5 mm wide and 15 mm deep pre-cut seam at the center of the bottom plane of the semi-circular specimens. This completes the preparation of the specimens.

2.4. Test Method

To obtain DIC images, it is necessary to spray matte white paint on the surface of the Single Edge Notched Beam (SCB) specimen as a base coat to enhance background contrast, followed by uniform spraying of matte black paint to create speckles [27]. Before measurement, ensure that the surface of the specimen is focused with the high-speed camera (Model: MD1200TV, Resolution: 1280 pixels × 960 pixels). Adjust the angles of the two cameras (usually set to 20~35°) to ensure the specimen is fully displayed in the center of the XTDIC Ver9.7 software interface, and adjust the focal length and exposure until the image is clear and the brightness is appropriate. After completing the above settings, the center points of the two cameras should be aligned to the same position on the specimen surface. Finally, calibrate the shooting area range: use a ±0.5 μm ceramic calibration plate (attached to the surface of the mixture), capture 15~20 sets of images to inversely calculate the pixel Pitch ≈ 15.6 μm (with a standard deviation < 0.05 μm), control the residual distortion to be < 2 μm, and verify the error with a 5 mm standard block to be <±0.5 μm. For binocular calibration, capture 10 sets of images at the test temperature to ensure the reprojection error is <0.3 pixels, the coordinate error corrected by the laser displacement meter is <±2 μm, and the verification error of the 10 μm micro-displacement is <±0.5 μm.

At the start of the test, the Universal Testing Machine (UTM) hydraulic servo system and the image acquisition system must be started synchronously. The high-speed cameras continuously capture the position changes of the tracking points on the specimen surface, with an image capture time interval of 0.01 s. After these images are imported into the analysis software, the system automatically tracks the movement trajectory of the speckles, compares the image differences before and after deformation, calculates the displacement and strain distribution on the specimen surface, and finally generates full-field deformation data. The measurement process is shown in Figure 3.

2.4.1. Semi-Circular Bending Healing Test

Our study of the healing performance of carbonyl iron powder asphalt mixtures was conducted using a semi-circular bending test. The experimental group consisted of carbonyl iron powder asphalt mixtures, while the control group comprised ordinary asphalt mixtures. The UTM-100 hydraulic servo system was used for the tests. Under a constant temperature of 15 °C, specimens preheated for 4 h were placed on two supports spaced 120 mm apart. The first loading [31] was applied at a rate of 50 mm/min. Data was collected using load sensors and displacement meters, and the load–displacement curve was automatically plotted. When the applied load decreased to 50% of the peak load (setting the damage level to 50%), the test was automatically terminated [32]. After the specimen failed, it was secured with rubber bands and then heated in a microwave heating box to heal the damaged specimen. As shown in Figure 4, when the specimen reached the set heating time, the heating was stopped, and the specimen was removed and left to rest at room temperature. After the resting period, the specimen was placed back into an environment chamber at 15 °C for 4 h of insulation, followed by a second loading, completing the test [33].

Combined with the relevant literature research [34,35,36], three main influencing factors of microwave heating time, standing time, and damage degree were selected to explore the influence of different factors on the healing ability of carbonyl iron powder asphalt mixture. The heating times were 20 s, 40 s, 60 s, 80 s, 100 s, and 120 s. The standing times were 2 h, 4 h, and 6 h, and the damage degrees were 30%, 50%, and 70%. In order to improve the reliability of the test results, three parallel tests were carried out on each group of asphalt mixture samples [37].

2.4.2. Microwave-Induced Heating Test

The microwave heating equipment used in the experiment is a custom-made instrument, as shown in Figure 5. The multi-port direct feeding method allows the mixture to directly receive electromagnetic field energy, resulting in more uniform heating of the asphalt mixture. Semi-circular specimens of ordinary asphalt mixture and carbonyl iron powder asphalt mixture were prepared for microwave heating tests, with each set of specimens undergoing three parallel tests. Continuous heating was employed, with an output power of 800 W, a microwave frequency of 2.45 GHz, and a total microwave heating time of 120 s. An infrared imaging device was used to measure the surface temperature of the specimens every 20 s. Additionally, the heating characteristics of the carbonyl iron powder asphalt mixture under various heating methods were studied to determine the optimal microwave heating method.

2.5. Metric

2.5.1. Time of Crack Initiation

Digital image correlation (DIC) was used to collect image data during the semi-circular specimen healing test, and the whole-field displacement of the specimen surface was obtained through quantitative calculation. Eight characteristic points (P₁–P₈) were selected symmetrically on both sides of the pre-cut section of the specimen. As shown in Figure 6, the horizontal displacement information of the feature points was calculated by Formula (1) to characterize the change of the crack width of the specimen, as shown in Figure 7. At first, the growth of $\Delta \mathrm{U}$ was slow, and the amplitude was small. With the increase in loading time, it suddenly increased, and there was an obvious inflection point. The time point of the first sudden expansion of the crack is defined as the crack initiation time. Combined with the cloud diagram of the incision position before and after the inflection point in the figure, it can be seen that the incision is not cracked before the inflection point, and it is in the crack initiation period. After the inflection point, the crack propagation at the incision suddenly occurs, a macroscopic crack appears, and the front and rear comparisons are obvious. Therefore, the time information of the inflection point position can be defined as the crack initiation time, which is the evaluation basis. Taking the ratio of the crack initiation time after healing to the crack initiation time before healing as the healing rate index, HI_t, the healing characteristics of the carbonyl iron powder asphalt mixture under multiple influencing factors were studied.

The displacements of the feature points on both sides of the incision are positive to the right and negative to the left. The sum of the horizontal displacement of characteristic points P₈, P₇, P₆, and P₅ on the right side of the pre-incision is subtracted from the sum of the horizontal displacement of characteristic points P₁, P₂, P₃, and P₄ on the left side of the pre-incision, and the average value is taken to characterize the deformation of the specimen and the change in crack width. The specific formula is as follows:

$$\mathsf{\Delta }U = {\displaystyle \frac{\left({P_8 +{ P}_7 + P}_6 +{ P}_5\right) - \left(P_1 + P_2 + P_3 + P_4\right)}{4}}$$

(1)

2.5.2. Fracture Energy

The load–displacement curve of the semi-circular bending healing test is shown in Figure 8. The load change in the asphalt mixture in the loading process is divided into two stages: the first stage is the elastic deformation stage, where, with the increase in load, the deformation gradually increases, the load of the specimen gradually accumulates during the loading process, and deformation occurs, but not yet obvious cracking; the second stage is the plastic failure stage. When the load reaches the peak value, the crack resistance of the specimen reaches the limit, and obvious cracking occurs, resulting in a significant reduction in the bearing capacity of the mixture. Fracture energy refers to the energy consumed per unit length of crack propagation per unit area. A larger fracture energy indicates the stronger crack resistance of asphalt concrete. The calculation formula for fracture energy is shown in Equation (2), and the calculation formula for fracture work is shown in Equation (3) [38].

According to the above method, the test results of the same mixture specimen before and after healing are calculated, and the fracture energy ratio is used as the healing evaluation index to carry out quantitative analysis on the healing performance of the asphalt mixture. The larger the healing index, HI_U, the better the healing effect. The calculation is shown in Equation (4).

$$\mathrm{U}={\displaystyle \frac{{\mathrm{W}}_{\mathrm{m}}}{\mathrm{A}}}$$

(2)

$$\mathrm{W}={\int }_0^{{\mathrm{u}}_{\mathrm{m}}}{\mathrm{P}}_{\left(\mathrm{u}\right)}\mathrm{d}\mathrm{u}$$

(3)

$$H{I}_U={\displaystyle \frac{U_1}{U_0}}\times 100\%$$

(4)

In the formula, U is fracture energy; W_m is the fracture work, that is, the area surrounded by the load–displacement curve; A is the fracture area; A = (h − a) * b, where h is the height of the semi-circular specimen, a is the length of the pre-notch, and b is the thickness of the specimen; P(u) is the load; u is the displacement; and um is the displacement corresponding to the end of the loading of the specimen. HI_U—healing index of the specimen; U₀—the fracture energy of the first loading test (J); U₁—fracture energy of the second loading test (J).

3. Results and Discussion

3.1. Microwave Heating Characteristics

3.1.1. Heating Behavior of Asphalt Mixture Filled with Carbonyl Iron Powder

The three figures on the left of Figure 9a,b are 2D surface temperature distribution diagrams of semi-circular specimens of an ordinary asphalt mixture and a carbonyl iron powder asphalt mixture after being heated for 40 s, 80 s, and 120 s. The figure on the far right is the 3D surface temperature distribution diagram of the specimens heated for 120 s. The average surface temperatures under different microwave heating durations were selected, and the average value of three parallel tests was taken as the test result. Thus, the curve of the average surface temperature of the specimens changing with microwave heating time was obtained, as shown in Figure 10.

It can be seen from Figure 9a that during the heating process, the surface temperature distribution of the semi-circular specimen of the ordinary asphalt mixture is uneven, and the high temperature is mostly concentrated on several points, showing a speckled distribution. It can be seen from Figure 9b that after adding carbonyl iron powder, the high temperature is mostly concentrated in several areas, and the area is larger. Then, it transits to the whole surface of the specimen, and the temperature distribution is relatively uniform. This feature can be seen more intuitively from the three-dimensional temperature field diagram. The incorporation of carbonyl iron powder improves the microwave heating performance of the asphalt mixture, and the heating is more uniform. When the heating rate of the carbonyl iron powder asphalt mixture is faster, the temperature difference (57.4 °C) is not significantly different from that of the matrix asphalt mixture (58.6 °C). The reason is that carbonyl iron powder asphalt mortar can achieve uniform heating after absorbing the wave and then transfer heat to the asphalt mortar and aggregate. At the same time, aggregate absorbs the wave as another heat source to transfer heat together [39,40] so that the overall temperature of the asphalt mixture increases uniformly. The heat of the ordinary asphalt mixture is mainly transferred to the asphalt through heat conduction after the aggregate is heated; the aggregate itself has a difference in microwave absorption efficiency under the action of the microwave, and a temperature concentration phenomenon occurs, which causes uneven heating in the whole specimen [41].

As shown by the linear fitting results in Figure 10, after the same duration of microwave heating, the average surface temperature of ordinary asphalt mixtures is lower than that of carbonyl iron powder asphalt mixtures. The heating rates for these two types of mixtures are 0.384 °C/s and 0.446 °C/s, respectively, with the heating rate of carbonyl iron powder increasing by approximately 16.1%. The correlation coefficients for both fitting results are greater than 0.98, indicating a strong linear relationship between the surface temperature increase and microwave duration for both types of asphalt mixtures. This controllable heating characteristic provides a fundamental basis for research on temperature healing.

3.1.2. Study on the Heating Characteristics of Carbonyl Iron Powder Asphalt Mixture Under Different Heating Methods

In order to further explore the influence of different microwave heating methods on the heating characteristics of the asphalt mixture and determine the best heating method, carbonyl iron powder asphalt mixture was selected as the test object. The total microwave heating time was 120 s, and the surface temperature of the sample was collected by an infrared imager every 20 s. Three different heating methods were set up to carry out the microwave heating indoor test: the upper graphs in Figure 11a–c represent the 2D distribution maps of the surface temperature of the test piece heated for 120 s, while the corresponding lower graphs represent the 3D distribution maps of the surface temperature of the test piece. In Figure 11a, the heating method is continuous heating; the heating mode of Figure 11b is 60 s of heating–4 min of interruption–60 s of heating; the heating mode in Figure 11c is 40 s of heating–2 min of interruption–40 s of heating–2 min of interruption–40 s of heating. Three parallel tests were carried out in each group; the average value was used to draw the temperature rise curve under different heating methods, as shown in Figure 12; and the standard deviation index was used to evaluate the uniformity of temperature rise.

As shown in Figure 11, after being heated for 120 s using different methods, the average temperatures of the three groups of mixed material specimens were similar at 68.8 °C, 65.0 °C, and 71.0 °C. This indicates that setting an intermittent time does not cause heat loss due to heat exchange between the specimen surface and the air. The temperature differences among the three groups of mixed material specimens varied significantly, with Group a having the highest temperature difference, followed by Group b, and then Group c. Different heating methods have a certain impact on the temperature difference in the mixed materials. Setting an intermittent time helps regulate the uniformity of temperature rise during microwave induction heating. The more intermittent the times set, the better the uniformity of temperature rise. Under the same total heating time, setting two 2 min intervals results in better temperature uniformity compared to one 4 min interval. This phenomenon can be more intuitively observed from the three-dimensional surface temperature distribution diagram.

As can be seen from the heating curve in Figure 12, the average surface temperature of the mixture increases with the increase in heating time under different heating methods, and the heating trend is consistent. The temperature values are similar under the same heating time, indicating that different heating methods will not have a great impact on the average temperature of the mixture.

As can be seen from the temperature standard deviation bar chart in Figure 12, the standard deviation in Group a increases with the increase in heating time under continuous heating, indicating that the local temperature difference becomes larger and larger with the increase in temperature.

Under the intermittent heating method of Group b, the standard deviation increased with heating time within 60 s. However, in the 60–80 s interval (with a 4 min break), the standard deviation significantly decreased from 5.0 to 4.7, while the surface average temperature continued to rise from 40.6 °C to 50.9 °C. This is because the carbonyl iron powder, asphalt emulsion, and the wave-absorbing aggregate absorb heat during heating, and the high-temperature areas spread to the surroundings through thermal conduction during the break, thereby improving the overall temperature uniformity of the asphalt mixture. This indirectly demonstrates that microwave heating can achieve comprehensive heating from the inside out, so a reasonable break time will not result in temperature loss for the mixture. Subsequently, in the 80–120 s interval, the standard deviation gradually increased again, but at 120 s, the standard deviation was smaller than that of Group a, decreasing from 10.2 to 7.6, a reduction of 25.5%.

Under the intermittent heating method of Group c, the standard deviation initially increases with the heating time, then significantly decreases during the intermittent phase (40 s to 60 s; 80 s to 100 s), and rises again after the intermittent phase. Notably, after two 2 min intervals, the standard deviation at 120 s is only 6.5, representing reductions of 36.3% and 14.5% compared to Groups a and b, respectively.

Based on the above analysis, the heating method with two 2 min intervals in Group c shows better temperature uniformity compared to the other two methods. It also maintains the original temperature after the interval, indicating that intermittent heating can more effectively convert microwave energy into thermal energy for the asphalt mixture of carbonyl iron powder, ensuring uniform healing of the mixture. Therefore, the subsequent research on microwave-induced asphalt mixture healing will use the heating method with two 2 min intervals within 120 s.

3.2. Horizontal Strain

3.2.1. Feature Cloud Map

During the loading process of the semi-circular bending (SCB) test based on digital image correlation technology (DIC), the displacement and strain changes on the surface of the specimen were collected at a frequency of 25 Hz, and the healing of the carbonyl iron powder asphalt mixture was analyzed from a microscopic perspective. As illustrated in Figure 13, which shows the relationship between the crack development pattern and the load–displacement curve, the loading failure of the semi-circular specimen can be divided into four stages: the load accumulation stage (0~1/3 Fmax), where the load continues to increase without visible cracks, primarily characterized by elastic deformation; then, as the load increases, the specimen enters the stress concentration stage (1/3~2/3 Fmax), where the stress concentration at the notch significantly increases, but no cracks appear; when the load reaches the critical failure stage (2/3~Fmax), the load reaches its peak, and the notch reaches the ultimate failure stress limit, indicating that cracks begin to form at the peak load; subsequently, as the load is unloaded (Fmax~2/3 Fmax), macroscopic cracks start to appear on the specimen surface [42].

It is evident that the stress at the cut before the peak load continuously concentrates, reaching the ultimate failure stress limit during the peak load, which initiates crack initiation. After the peak load, due to the continuous application of the load, macrocracks rapidly grow, significantly reducing the crack resistance. Therefore, strain cloud diagrams of the three key nodes, P₂, P₃, and P₄, are selected to analyze the difference in horizontal strain before and after healing.

3.2.2. Analysis of Horizontal Strain Field Variation Before and After Healing

The horizontal strain field of the specimen was calculated by the XTDIC Ver9.7 software, and the horizontal strain cloud diagram was derived to analyze the change in the horizontal strain on the surface of the specimen during the loading process. Figure 14a,b represent the horizontal strain cloud map of the crack area of carbonyl iron powder asphalt mixture after the first loading and healing, and Figure 14c,d represent the horizontal strain cloud map of the crack area of ordinary asphalt mixture after the first loading and healing. As shown in Figure 14, in the horizontal strain cloud diagram, the range from dark blue to dark red represents the change in strain value, from low to high, and the right digital ruler shows the maximum and minimum strain values in this area. The horizontal strain field nephograms of the ordinary asphalt mixture and carbonyl iron powder asphalt mixture with a microwave heating–healing time of 100 s, a standing time of 4 h, and a damage degree of 50% before and after healing are compared in the figure.

It can be seen from Figure 14a that the maximum horizontal strain increases with the continuous action of the load. When the load increases from P₂ to P₃, the strain growth rate is 225%. When the load increases from P₃ to P₄, the strain growth rate is 5.73%. The horizontal strain increases faster before the peak load than after the peak load. Figure 14b–d all show this result. This is because the deformation before cracking is mainly elastic deformation. Although there may be microcrack initiation in the material, it does not form a penetrating macrocrack. There will be no sudden dissipation of energy caused by crack propagation, so the strain energy can be efficiently converted into strain growth. The appearance of the crack leads to the re-adjustment of the internal stress distribution of the specimen, and the stress is concentrated at the crack tip, while the material force on both sides of the crack is obviously weakened. The original uniform strain field is broken, the strain growth no longer increases linearly with the external force, and the growth rate decreases. From the comparison of the horizontal strain field before and after healing, it can be seen that the maximum horizontal strain value of the carbonyl iron powder asphalt mixture after healing is higher than the value of the first loading, and the ordinary asphalt mixture is also the same. It can be seen that the strain concentration value of the crack area during reloading is larger. This is because after the asphalt mixture heals, the elastic recovery of the binder at the crack is incomplete, and the stiffness decreases. This “low stiffness healing layer” will make the crack area more prone to deformation at the initial stage of loading, resulting in more accumulation of overall strain before reaching the critical value of cracking. The macroscopic cracks appear earlier when the specimen is loaded after healing, and the reason can be explained by the micro- and macro-levels. At the micro-level, there may be pores, bubbles, or areas with weak intermolecular binding force at the healing interface, forming a “mechanical weak zone”; at the macro-level, after the crack healing, the original crack path may still be used as a potential stress concentration point, and its crack resistance is much lower than that of the undamaged substrate. This “imperfect healing” makes the stress easily re-concentrate in the original crack healing area when the healed specimen is loaded again, resulting in earlier initiation of macroscopic cracks. All in all, the larger the strain value at the same load position, the earlier the macroscopic crack initiation of the mixture specimen, and the worse the crack resistance.

Through the comparison of the carbonyl iron powder asphalt mixture and the ordinary asphalt mixture, it is found that the maximum horizontal strain value of both is at the same level when the first loading is applied. When the healing is applied again, the horizontal strain value of both shows a difference, the strain of the carbonyl iron powder asphalt mixture is significantly smaller, and the most significant difference is in P₂. The maximum strain values for the two cases were 2.55 (1.91 at the first loading) and 7.75 (0.98 at the first loading), indicating that macrocracks in the carbonyl iron powder asphalt mixture develop later after healing. These results suggest that the carbonyl iron powder asphalt mixture shows better healing effects under microwave-assisted heating, and its crack resistance is significantly improved when loaded again after healing.

Then, the difference in the horizontal strain field of the carbonyl iron powder asphalt mixture under different healing factors was studied in order to understand the influence of external factors on healing more comprehensively. For the visibility of the image data, only the horizontal strain field at the peak load (P₃) was analyzed. A heating time of 100 s, a standing time of 4 h, and a damage degree of 50% were selected as the benchmark healing conditions to study the effect of single influencing factor changes on the healing effect. The effects of multiple factors, such as heating time, standing time, and damage degree, on the horizontal strain after healing were discussed. Figure 15a is a horizontal strain field cloud map of the carbonyl iron powder asphalt mixture after healing under the conditions of microwave heating; healing times of 20 s, 60 s, and 100 s; a standing time of 4 h; and a damage degree of 50%. Figure 15b shows a horizontal strain field cloud diagram of the carbonyl iron powder asphalt mixture after healing under the conditions of microwave heating, a healing time of 100 s; standing times of 2 h, 4 h, and 6 h; and a damage degree of 50%. Figure 15c is a horizontal strain field cloud map of carbonyl iron powder asphalt mixture after healing under the conditions of microwave heating, a healing time of 100 s; a standing time of 4 h; and damage degrees of 30%, 50%, and 70%. It can be seen from Figure 15a–c that the maximum horizontal strain value of reloading after healing is higher than that of the first loading in Figure 14, indicating that the macroscopic crack initiation is advanced and the crack resistance is weakened after healing. Through analysis, it can be seen that the conclusion of heating time and standing time is consistent with the negative correlation with the maximum strain value, indicating that with the extension of heating–healing time and standing time, the macroscopic cracks appear later when reloading after healing, and the crack resistance is better. Prolonging the heating–healing time and standing time is beneficial to healing and repair efficiency. Conversely, the maximum strain value is positively correlated with the damage degree, which indicates that the more serious the damage of the specimen is, the earlier the macroscopic crack appears, and the worse the crack resistance is.

3.3. Self-Healing Characteristics

3.3.1. Influence of Carbonyl Iron Powder on Self-Healing Index

The semi-circular bending healing test was carried out under the same heating time (100 s), standing time (4 h), and damage degree (50%) test conditions. The healing performance differences between the ordinary asphalt mixture and the carbonyl iron powder asphalt mixture were compared. The healing rate indexes, HI_U and HI_t, of the two groups of specimens were used to evaluate the enhancement effect of carbonyl iron powder incorporation on the microwave-induced self-healing ability of the asphalt mixture. The final results are shown in Figure 16.

The results show that the healing rate of the carbonyl iron powder asphalt mixture is significantly higher than that of the ordinary asphalt mixture. The crack initiation time healing index, HI_t, is more sensitive to the evaluation of the healing effect, and the fracture energy healing index, HI_U, is more sensitive to the difference in the healing effect. The addition of carbonyl iron powder can increase the healing rate, HI_U, from 33.1% to 55.1% and the healing rate, HI_t, from 59.1% to 79.7%. The healing ability of the mixture was significantly improved, which was increased by 83.1% and 34.9%, respectively. This indicates that the addition of carbonyl iron powder significantly enhances the crack repair capability of microwave-induced asphalt mixtures, primarily due to two factors: first, the high microwave absorption properties of carbonyl iron powder rapidly convert microwave energy into thermal energy, enhancing the mobility of asphalt molecules and accelerating crack repair. After 100 s of microwave heating, the average temperatures were 60 °C and 50.8 °C, respectively, indicating a significant temperature increase in the carbonyl iron powder asphalt mixture. Second, the modified asphalt mortar with carbonyl iron powder exhibits superior flowability and an earlier healing onset temperature during the crack repair process. The results show that carbonyl iron powder significantly improves the self-healing ability of the mixture through better energy conversion efficiency and better flow performance in the modified asphalt mortar.

3.3.2. Influence of Healing Factors on Self-Healing Index

In order to more systematically evaluate the healing characteristics of carbonyl iron powder asphalt mixture, the healing rate under the condition of multiple healing influencing factors was analyzed. The healing conditions were a heating time of 100 s, a standing time of 4 h, and a damage degree of 50%. The effect of a single factor on the healing effect was studied. The changes in healing rate under different heating times, standing times, and damage degrees were explored. Figure 17 shows the effect of different microwave heating times on the healing rate of the carbonyl iron powder asphalt mixture. Figure 18 shows the effect of different standing times on the healing rate of the carbonyl iron powder asphalt mixture. Figure 19 shows the effect of different damage degrees on the healing rate of the carbonyl iron powder asphalt mixture.

From Figure 17, Figure 18 and Figure 19, it can be seen that the evaluation results of the two healing indexes, HI_U and HI_t, are consistent under different healing influencing factors. The microwave healing performance of the carbonyl iron powder asphalt mixture is significantly affected by three factors: heating time, standing time, and damage degree. The healing ability is positively correlated with the heating time and standing time. In a range of 0–100 s for the microwave heating time, prolonging the microwave heating time can significantly improve the healing rate, and the healing indexes, HI_U and HI_t, increase from about 30% to 55.1% and 79.7%, respectively. This is because the carbonyl iron powder absorbs microwave energy and converts it into heat energy, which promotes the flow and recombination of asphalt molecules. As the microwave heating time increases, the temperature continues to increase, thereby increasing the healing efficiency of asphalt fluidity [43]. However, when the microwave heating time reaches 120 s, the average temperature of the carbonyl iron powder asphalt mixture, as shown in 3.1, reaches 68.8 °C. The high temperature causes the asphalt paste to become too fluid, leading to its flow into surrounding voids. This reduces the adhesion at crack sites, decreases the healing strength, and makes the asphalt mixture prone to loosening, resulting in a sharp decline in the healing rate. Regarding the duration of static placement, 4 h is the optimal duration. After stopping the microwave heating, the carbonyl iron powder filler continues to release heat through wave absorption, warming the entire mixture and accelerating crack healing. Additionally, the static placement provides time for molecular movement, promoting further diffusion and reintegration at microcrack interfaces, thus increasing the healing rate. When the static placement time is extended from 2 h to 4 h, the growth rates of HI_U and HI_t are 16.7% and 16.5%, respectively. However, as the static placement time increases, the continuous heat exchange between the mixture and air during this period leads to a gradual decrease in overall temperature. When the standing time is extended from 2 h to 4 h, the healing growth rates are 16.7% and 16.5%. With the extension of the standing time, the overall temperature gradually decreases due to the continuous heat exchange between the mixture and the air during the standing period. When the standing time exceeds 4 h, the internal temperature is not enough to support the diffusion and melting of asphalt molecules, and the crack repair capacity is close to the limit, resulting in a decrease in the growth rate. When it is further extended to 6 h, the growth rates are only 4.2% and 2.6%.

The healing ability was significantly negatively correlated with the degree of injury. When the degree of injury was less than or equal to 50%, the healing rate of HI_U could reach more than 55%, and HI_t could reach more than 75%. When the degree of injury increased to 70%, the healing rates were 25.2% and 55.1%, respectively, and the healing rate was significantly reduced. The reason for this result may be that high damage (70% and above) leads to the growth of cracks, the difficulty of asphalt flow repair increases, and the uneven temperature distribution caused by excessive cracks makes it difficult to provide good healing conditions. Given this, the preventive maintenance of pavement should intervene in the early stages of microcrack or damage development. To sum up, optimizing the heating time is the key to balancing the energy utilization and healing effect of microwave healing technology, that is, to maximize the healing effect of microwave heating while avoiding the reduction in healing rate caused by excessive temperature. This is limited to improving the repair ability of the asphalt mixture by prolonging the standing time. It is suggested that the standing time should be 4 h to balance the healing efficiency and time cost. Considering the sharp decline of pavement healing efficiency after high damage, it is suggested that microwave healing repair projects should be completed as soon as possible.

3.3.3. Correlation Analysis of Self-Healing Index

In this study, two evaluation indexes were selected to evaluate the healing effect of the asphalt mixture. The fracture energy index, HI_U, based on the SCB test before and after healing, was used to evaluate the macroscopic healing. This evaluation method has the advantages of short, discrete results and simple testing operations, but there are also limitations in the lack of microscopic-scale healing evaluation. Therefore, the cracking time healing index, HI_t, obtained by DIC digital image technology, is used to evaluate the healing performance of the mixture. This method can observe the changes in crack displacement during the loading process and evaluate the healing on the microscopic scale. In summary, the combination of macro- and micro-methods can evaluate the healing of asphalt mixture more comprehensively, but whether the two healing indexes of the carbonyl iron powder asphalt mixture are correlated needs further study.

Pearson correlation analysis method is used to calculate the correlation coefficient (Pearson) of macroscopic index HI_U and microscopic index HI_t under the same influencing factors, so as to obtain the healing rate and correlation coefficient of the asphalt mixture under the conditions of heating time, standing time, and damage degree. The calculation results are shown in

Table 5. Correlation analysis of macro- and micro-healing indexes.

Influencing Factor	Variate Value	Micro-Index: HIt/%	Macro-Index: HIU/%	Healing Indicators: Pearson Correlation
Heating Time/s	20	35.7	31.9	0.932
	40	42.2	41.5
	60	50.4	47.5
	80	69.4	52.7
	100	79.7	55.1
	120	50.1	42.6
Standing Time/h	2	68.4	47.2	0.998
	4	79.7	55.1
	6	81.8	57.4
Damage Degree/%	30	83.7	65.2	0.991
	50	79.7	55.1
	70	51.2	25.2

.

It can be seen from the correlation coefficient in the table that the two healing indexes are highly positively correlated, both higher than 0.93, indicating that the macro- and micro-evaluation methods are consistent. The reason is analyzed. The microscopic index is based on the displacement changes in the crack. The change process of the crack is closely related to the load during loading, and the macroscopic fracture energy healing index is calculated based on the area enclosed by the load–displacement curve and the fracture area, which is also closely related to the load. This shows that the application of digital image correlation technology to the SCB test to evaluate the healing performance of asphalt mixture has good reliability, and the use of macro–meso-multi-scale evaluation of asphalt mixture healing performance can make the conclusion more reliable.

3.3.4. Significance Level Analysis of Healing Influencing Factors

Through gray correlation analysis, the correlation coefficient between the influencing factors and the healing rate index, HI_U, was analyzed, and the significance level of the influencing factors of healing was determined. The healing parameters under multiple influencing factors are shown in

Table 6. Influencing parameters and the healing rate of carbonyl iron powder asphalt mixture.

Grade	1	2	3	4	5	6	7
Heating Time/s	20	60	100	100	100	100	100
Standing Time/h	4	4	4	4	4	2	6
Damage Degree/%	50	50	30	50	70	50	50
HIU/%	31.9	47.5	65.2	55.1	25.2	47.2	57.4

. After the calculation, the average value of the gray correlation coefficient of each factor was taken as the correlation degree. The closer the correlation degree was to 1, the more significant the influence of this factor on the healing effect was. The dimensionless step adopts the mean value method, and the resolution coefficient, ρ, is 0.5. The calculated gray correlation coefficient is shown in Figure 20, and the average value of the gray correlation coefficient is recorded. Finally, the correlation degree of each influencing factor is shown in

Table 7. Results of the gray correlation degree of healing influencing factors.

Evaluation Items	Correlation	Ranking
Heating Time/s	0.686	1
Damage Degree/%	0.663	2
Standing Time/h	0.625	3

.

It can be seen from Table 7 that the correlation degree of each influencing factor is greater than 0.6, which indicates that these three influencing factors have a significant impact on the healing rate of carbonyl iron powder asphalt mixture. By sorting the correlation degree, it can be seen that the heating time > the damage degree > the standing time. The heating time has the most significant effect on the healing effect of the mixture, and the correlation degree is 0.686, followed by the damage degree and the standing time. Because of this, microwave-heat-induced asphalt mixture maintenance technology should balance the two key factors of heating time and standing time to ensure that the asphalt pavement achieves the best healing effect. At the same time, it is suggested that preventive maintenance should be carried out at the initial stage of cracking to avoid the degradation of the asphalt’s healing ability after serious damage. According to the above research, it is found that the carbonyl iron powder asphalt mixture has the best effect with a heating time of 100 s, a standing time of 4 h, and healing at the initial stage of damage (30% damage).

3.4. Theoretical Analysis

It can be seen from this article that the carbonyl iron powder modified asphalt mortar has good microwave heating characteristics. After the mixture is prepared, the overall temperature is also improved, and a higher self-healing efficiency can be obtained by replacing the incorporation with a smaller proportion. Based on the law of conservation of energy, the temperature rise in the filler absorbent and large-particle-size aggregate in the mixture system is calculated, and the temperature rise characteristics of the two are compared and analyzed by a theoretical model and formula derivation [13].

Microwave Energy Absorption and Thermal Conversion: According to the law of conservation of energy, the microwave power absorbed by the absorbing material can be converted into heat energy, in which the heat energy is mainly generated by the electric Joule heating effect and electromagnetic energy dissipation. Its expression is

$$P^{\prime }=\eta P=q_v=2\pi f{\epsilon }_0{\epsilon }_r^{″}{E}^2+2\pi f{\mu }_0{\mu }_r^{″}{H}^2$$

(5)

where P is the microwave power, W; $\eta$ is the microwave absorption coefficient of the material; $f$ is the microwave frequency, Hz; ${\epsilon }_0$ is the vacuum dielectric constant; ${\mu }_0$ is the free space permeability; E is the electric field intensity, V/m; H is the magnetic field strength, T; ${\epsilon }_r^{″}$ and ${\mu }_r^{″}$ are the effective dielectric loss factor and magnetic loss factor of the material, respectively. Since the magnetic loss is usually small, Formula (5) can be simplified to

$$q_v \approx 2\pi f{\epsilon }_0{\epsilon }_r^{″}{E}^2$$

(6)

Integral Equation of Material Temperature Rise: The heat energy absorbed by the material leads to an increase in temperature, according to the energy conservation equation, $m{C}_{P}dT ={ q}_{v}dt$, integral:

$$T=T_0+{\int }_0^t{\displaystyle \frac{2\pi f{\epsilon }_0{\epsilon }_r^{″}{E}^2}{m{C}_P}}dt$$

(7)

where $T$ is the final temperature, °C; $T_0$ is the starting temperature, °C; $m$ is mass, kg; $C_P$ is the specific heat capacity of the material, J/(kg·°C); t is time, s. Assuming that the dielectric loss factor, ${\epsilon }_r^{″}$, and the specific heat capacity, $C_P$, are constants, the integral can be simplified as

$$T={ T}_0+{\displaystyle \frac{2\pi f{\epsilon }_0{\epsilon }_r^{″}{E}^2}{m{C}_P}}\cdot t$$

(8)

Influence of Mass Ratio on Temperature rise: From Formula (6), it can be seen that the temperature rise performance of fillers and aggregates in the same microwave field is mainly related to $m$, ${\epsilon }_r^{″}$, and $C_P$. Assuming that the effective dielectric loss factor, ${\epsilon }_r^{″}$, and the specific heat capacity, $C_P$, of the two are the same, the temperature rise in the material can be simplified as

$$\mathit{\Delta }T\propto {\displaystyle \frac{1}{m}}$$

(9)

Formula (9) shows that the temperature rise value ($\mathit{\Delta }T$) of the material is inversely proportional to its mass (m) during the microwave-induced heating process, which indicates that the final temperature of the absorbing material depends on the mass. In the asphalt mixture system, the mass proportion of the filler is generally 4~10%, while the proportion of the aggregate is generally 85~95% [44]. According to the above theoretical analysis, under the same microwave power and heating time, the smaller the mass of the absorbing agent, the greater the heating amplitude. Therefore, when the carbonyl iron powder is added to the asphalt mixture in the form of a filler absorbing agent, the energy absorbed per unit mass is higher, and the temperature rise is greater. It is revealed that during the microwave heating process, the filler absorbent can more efficiently increase the temperature of the asphalt mortar, thereby improving the self-healing efficiency of the asphalt mixture.

4. Conclusions

(1)

The carbonyl iron powder asphalt mixture exhibits excellent heat uniformity and linear temperature rise characteristics. Its heating rate is increased by 16.1% with more uniform heating; the average temperature reaches 68.8 °C after 120 s of heating, which can meet the healing temperature requirement of the asphalt mixture.

(2)

The heating temperatures of the carbonyl iron powder asphalt mixture under continuous and intermittent heating are basically the same. Intermittent heating has no heat loss and better heating uniformity, and the optimal microwave heating method is a 3-cycle process of “heating for 40 s–resting for 2 min”.

(3)

When the wave absorber is mixed into the asphalt mixture as a filler, it can improve the microwave heating efficiency, thereby enhancing the self-healing performance of the mixture.

(4)

The macroscopic fracture energy healing index, HI_U, is highly correlated with the mesoscopic crack initiation time healing index, HI_t, and multi-scale evaluation can improve the reliability of conclusions. Carbonyl iron powder significantly improves the healing effect of the mixture, and the optimal healing effect is achieved under the best condition of microwave heating for 100 s (at a temperature of 60 °C).

(5)

External factors have a significant impact on the healing effect of the carbonyl iron powder asphalt mixture, with the order of influence being microwave heating time > damage degree > standing time. The optimal healing scheme is as follows: heating for 100 s, standing for 4 h, and performing healing at the initial stage of damage (before crack initiation).

(6)

The dosage of carbonyl iron powder needs to balance high-temperature performance, low-temperature performance, microwave heating temperature sensitivity, and healing performance. Relevant studies have been conducted in previous research on the self-healing behavior and rheological properties of carbonyl-iron-powder-modified asphalt mortar based on microwave induction. However, no corresponding research has been carried out on asphalt mixtures. The current research has certain limitations, which can serve as a direction for future studies.