Estimation of Effective Thermal Conductivity of Copper-Plated Carbon Fibers Reinforced Iron-Based Composites by 2D Image Analysis

Abstract

Dies with high thermal conductivity (TC) can not only speed up heat transfer but also improve the production efficiency of parts and extend the life of the dies. Taking advantage of the high axial TC of carbon fibers (C_f), thermal channels are established in the composite. To protect C_f from being destroyed, C_f was electroless plated with Cu to form copper-plated C_f (C_f-Cu). Pores impede heat conduction, and the TC of the matrix is corrected by Bruggeman’s equation. C_f-Cu has high anisotropic, and its orientation can significantly affect the TC of iron-based composites. The mathematical equation between the orientation of C_f-Cu in the 3D model, the orientation of C_f-Cu on 2D cross-section, and the aspect ratio of an ellipse were obtained by C_f-Cu intersects with cross-section was determined by establishing a model of the orientation of C_f-Cu in 3D space. The simulated TC of the composite was calculated by 2D image analysis (finite element method). The effect of the orientation of C_f-Cu on the TC of composites with different C_f-Cu contents was investigated. When the volume fraction of C_f-Cu was 20%, the measured and simulated TC reached the maximum of 68.89 W m⁻¹ K⁻¹ and 71.02 W m⁻¹ K⁻¹, respectively. Before rolling, there is a significant difference between the simulated and measured TC. After rolling on the side surface of the rolling plane of the composite, both the simulated and measured TC on the rolling plane and its side surface show the same trend with the increasing of C_f-Cu content.

1. Introduction

With the rapid development of the processing and manufacturing, the production efficiency of automobile parts needs to be further improved. The traditional cold stamping process requires a high forming pressure, which can easily deform or even crack the dies. It was replaced by the hot stamping process which promoted the rapid development of the automotive industries.^1,2) Hot stamping dies with high thermal conductivity (TC) reduce thermal stress, improve production efficiency, and extend the life of the dies. A high-strength iron (Fe) alloy is chosen as the matrix of die. The purpose of this study is to improve the efficiency of the dies for producing high-strength auto parts and prolong the service life of the dies, a hot stamping dies with high thermal conductivity (TC) need to be fabricated.

Typically, composite TC is raised by adding high TC particulate fillers. However, the heat transfer of the composite formed by the particulate filler is discontinuous, and the heat transfer efficiency is lower than that of the linear filler under the same conditions. Adding linear fillers with a high aspect ratio TC to build heat conduction channels was considered by researchers to improve the TC of the composite.³⁾ The TC of glass fiber is extremely low (0.035 W m⁻¹ K⁻¹). Carbon nanotubes are difficult to disperse, remove impurities, and store, and cause severe pollution, which limits their industrial applications. Short carbon fiber (C_f), characterized by high TC, is cheap and easy to obtain, and widely used in research on improving the TC of the composites. Therefore, this study uses short C_f for reinforcement. Li et al.⁴⁾ showed that C_f improved the tensile properties, bending properties, impact strength, and thermal deformation properties of Polyamide 6 composites better than glass fiber. The TC of the composite increases with increasing C_f content but decreases with increasing glass fiber content.

As a two-dimensional (2D) TC material, C_f is highly anisotropic in the TC,^5–8) and has excellent TC in the axial direction.^9–13) The TC of C_f-reinforced composites is also anisotropic. Moreover, because C_f possesses excellent mechanical properties, high-cost performance, and other characteristics, C_f-reinforced iron (Fe)-based composites with high TC and workability and can be used for hot stamping die materials. However, C_f gets damaged because it reacts with the Fe matrix. C_f is protected by electroless copper plating to form copper-coated carbon fibers (C_f-Cu) to avoid it coming into contact with the iron matrix and reacting.

Powder metallurgy is an important technology for preparing the metal and metal matrix composites. The main processes involved in composite powder metallurgy are spark plasma sintering (SPS) and hot pressing. During SPS, high pressure can reduce Fe spacing, the energy barrier required for Fe movement, and sintering time. Spark plasma can reduce the energy barrier required for the reaction and movement of Fe and reduce the sintering temperature of the material. Compared to the traditional sintering process, SPS can quickly sinter powders at low temperatures to make them dense. Low temperatures reduce the energy loss and temperature requirements of sintering equipment, extend the life of the equipment, and inhibit the growth of crystal grains to yield a high-performance composite. Therefore, the SPS technology is extremely suitable for preparing C_f-Cu-reinforced Fe-based composites.

Since the TC characteristics of C_f are anisotropic, the orientation of the anisotropic reinforcement in the matrix must be controlled.¹⁴⁾ So far, the methods that have been studied to control the orientation of C_f are the pressure impregnation¹⁵⁾ and pre-plating spraying methods.^16,17) However, the production efficiency of the two methods is extremely low, the bonding force between the C_f and matrix is small, and the direction of the C_f is difficult to control. Matsuura et al.^18,19) used hot extrusion to change the orientation of C_f in Composites through mechanical extrusion to improve the TC of the composite. Considering the cost and convenience of the experiment, this experiment adopted the method of hot rolling to control the distribution of C_f in the composite. After sintering, the composite was only heated to 1273 K and then rolled.

The C_f-reinforced composite is a typical high-anisotropy material, and the axial TC of carbon fibers exceeds the radial TC.^20–22) Therefore, the orientation and volume fraction of C_f significantly affect the TC of C_f-reinforced composites.²³⁾ Classical theoretical models have been proposed to predict the TCs of composites. However, in these theoretical analyses, the interaction between adjacent microstructure components is usually simplified. In this paper, the simulations using the finite element model provide an effective method for studying the influence of microstructure on the heat conduction of composites. However, in this experiment, Cu did not react with Fe, and there are many voids in the composite, which significantly hindered heat conduction.²³⁾ Existing theoretical models cannot adequately deal with the effects of pores, which leads to inaccurate predictions of the TC of a composite. Many studies have been conducted on the thermal conductivity prediction of void-containing composites, however, this problem has not been satisfactorily solved.^24–26) In this study, under the condition of uniform mixing, assuming uniformly distributed the voids are in the composite and regarding the voids and the matrix, the TC of the whole under different C_f-Cu contents was corrected, and the finite element was used to simulate the TC of the composite.

In this study, powder metallurgy was used to produce C_f-Cu-reinforced Fe-based composites. The distribution of various elements in the composite was analyzed, and the TC of the matrix was corrected. The actual TC of the composite before and after rolling can also be measured by the steady-state measurement method. The TC of the matrix is between the axial and radial TC of C_f, to take advantage of the high TC of C_f and maximize the TC of C_f-enhanced iron-based metal dies, it is crucial to study the effect of the anisotropic TC of C_f. In this study, the mathematical relationship between the orientation of C_f-Cu in the 3D model and the orientation of the 2D section is obtained by establishing a 3D model containing C_f-Cu for the first time. A novel 2D image analysis method^14,27,28) was employed to calculate the simulated TC of C_f-Cu/Fe. The deviation between the measured TC and the simulated TC is very small, and this simulation method provides an effective way to predict the TC of C_f-reinforced metal composites.

2. Materials and Methods

2.1 Materials

Fe powder (FEE14PB, 99% in purity, Kojundo Chemical Laboratory Co., Ltd., Japan) with a particle size of 5–10 µm was used as starting material for the matrix. The filling material was a commercial pitch-based C_f (mean diameter: 8.6 µm, density: 2.18 Mg m⁻³, K13C6U, Mitsubishi Chemical Co., Ltd., Japan) cut to an mean length of 5 mm.

After cutting, peeling, acidification, sensitization, and activation C_f-Cu with a copper layer was obtained in the electroless copper plating solution (OPC-750 electroless copper MA, OPC-750 electroless copper MB, and OPC-750 electroless copper MC), at temperatures ranging from 293 to 303 K and pH = 12. In this study, (5/10/15/20/25) vol% C_f-Cu were mixed with Fe powder. The mixture was rotated through Al₂O₃ balls in a V-shaped mixer 50 times per min and mixed for 2 h in ethanol. The C_f-Cu and Fe were mixed with five times the weight of Al₂O₃ milling balls. The volume ratio of Φ5 mm and Φ8 mm in the Al₂O₃ grinding ball is 2:3, and the mixed powder was dried at 303 K in air. Approximately 7 g of the C_f-Cu and Fe mixture was placed into a graphite mold for SPS. The mixed powder was sintered with a pulse spark for 0.9 ks at a current was about 300 A, the frequency of the pulse current was 5 Hz, and the pressure in the axial direction was 50 MPa. These experimental parameters were set with reference to the parameters commonly used in the actual manufacturing process of sintering metals by SPS. The sample was heated to 1100 K under pressure and sintered into a cylindrical Fe-based composite with dimensions of Φ10 × 5 mm³. The composite was placed in rolling equipment (100GML 400, TEST NO. 99805444.) at 1000 K, the diameter of the roll was 5 cm, and the rolling speed was 15–18 r/min, no lubrication, the total thickness of the sample is reduced to 50% of the original sample, and each pass reduces the thickness of the original sample by 1%.

The phase compositions of the composite were analyzed by using XRD. The Archimedes method was used to measure the porosities of the composite. The Bruggeman equation was used to correct the TC of the matrix. According to the cross-sectional OM image, the distribution of various elements in the composite and the influence of the content and distribution of C_f-Cu on its TC were analyzed. The TC of the composites was simulated using the finite element method. The TC of values of composites with different C_f-Cu contents were measured using the steady-state method.

2.2 Method

2.2.1 Calculation of radial thermal conductivity of C_f-Cu

The C_f-Cu obtained by electroless copper plating of C_f had a constant TC of 580 W m⁻¹ K⁻¹ in the axial direction. The radial TC can be obtained from eq. (1) for the coating TC.   

\begin{equation} K^{*} = \frac{KK_{0}h}{K\delta + K_{0}(h - \delta)} \end{equation} (1)

Where K^* is the radial TC of C_f-Cu, K is the radial TC of C_f (5 W m⁻¹ K⁻¹), K₀ is the TC of Cu, is 398 W m⁻¹ K⁻¹; h is the diameter of C_f-Cu, and δ is the sum of the upper and lower coating thicknesses.

2.2.2 Calculation of thermal conductivity of matrix of composites

Heat conduction occurs because of the thermal movement of molecules and electrons from neighboring atoms. Fe contains many electrons, and the interatomic distance is small (10⁻¹⁰ m). The energy generated by thermal motion is small and the TC is high (54 W m⁻¹ K⁻¹). Since the molecular distance in the air is larger (10⁻⁹ m), the collision between molecules consumes more energy, and the TC is lower (0.03 W m⁻¹ K⁻¹). Therefore, the voids in the composite significantly influence the TC, and therefore, the TC of the matrix must be corrected. The effective TC of the matrix changed with the porosity. The Bruggeman, eq. (2) can be used to calculate the effective TC of a porous composite.²⁹⁾   

\begin{align} K_{m} &= \frac{1}{4}[K_{p}(3V_{p} - 1) + K_{\textit{Fe}}(3V_{\textit{Fe}} - 1) \\ &\quad + \{ [K_{p}(3V_{p} - 1) + K_{\textit{Fe}}(3V_{\textit{Fe}} - 1)]^{2} \\ &\quad + 8K_{p}K_{\textit{Fe}} \}^{1/2}] \end{align} (2)

K_Fe and K_p denote the TCs of the Fe matrix (54 W m⁻¹ K⁻¹) and air (0.03 W m⁻¹ K⁻¹), respectively. V_Fe and V_P represent the volume fraction of the matrix and the porosity of the composite, respectively.

2.2.3 Calculation of the orientation of C_f-Cu in the 3D matrix

The 2D cross-sectional can be regarded as a part extracted from the three-dimensional (3D) structure. Figure 1(a) shows that a three-dimension (3D) model with a three-dimensional coordinate system, X-Y-Z is established. Figure 1(b) can be obtained by simplifying Fig. 1(a), where C_f-Cu passes through the origin O (0,0,0), heat flow along the X-axis, and θ_3D, which is the angle between C_f-Cu and heat flow, characterizes the orientation of C_f-Cu in the 3D matrix. The angle between the projection of C_f-Cu and heat flow is α, and the angle between the projection of C_f-Cu and C_f-Cu is β.

Fig. 1

C_f-Cu in the 3D model. Simplify (a) to get (b), heat flow is X-axis, θ_3D is the angle between C_f-Cu and heat flow, α is the angle between the projection of C_f-Cu and heat flow, β is the angle between C_f-Cu and projection of C_f-Cu. (c) when C_f-Cu is not parallel to X-O-Z plane, rotating (a) counterclockwise by 90° produces cross-section line. (d) when C_f-Cu is parallel to X-O-Z plane, rotating (a) counterclockwise by 90°, produces a rectangle cross-section.

When C_f-Cu is not parallel to the X-O-Z plane, Fig. 1(c) can be obtained by rotating Fig. 1(a) counterclockwise by 90°. The cross-section line of C_f-Cu in the X-O-Z planes is an ellipse. The ellipse and aspect ratio (R) in eq. (3) can be expressed as follows.   

\begin{align} &\sin^{2}\theta_{3D}x^{2} - \cos\theta_{3D}\sqrt{\cos^{2}\beta - \cos^{2}\theta_{3D}}\\ &z^{2} = r^{2}\quad R = \frac{b}{a} = \sin\beta \end{align} (3)

The θ_3D in the 3D model is closely related to the α and R of C_f-Cu. Their relationship is given by eq. (4).   

\begin{align} &\cos\theta_{3D} = \cos\alpha * \cos\beta = \cos\alpha * \sqrt{1 - \frac{1}{R^{2}}}\\ & 0^{\circ} \ll \alpha, \beta, \theta_{3D} \ll 90^{\circ} \end{align} (4)

When C_f-Cu is parallel to the X-O-Z plane, the cross-section of C_f-Cu in X-O-Z planes is a rectangle. In Fig. 1(d), α = 0, and substituting α into eq. (4), θ_3D = β. θ_3D can be obtained using eq. (3) and (4) by measuring and counting the value of α, β, and R.

2.2.4 Calculation of the effective thermal conductivity of C_f-Cu

C_f is a highly anisotropic material with respect the thermal conductivity in two dimensions. If the heat flux is through the X-axis, the effective TC of a C_f-Cu on the X-axis (K_i) and Y-axis (K_j) can be expected as following equations.^14,28)   

\begin{align} K_{i} &= K_{x}\left[1 - \left(1 - \frac{K_{y}}{K_{x}} \right)\sin^{2}{\theta_{3D}} \right]\\ K_{j}& = K_{x}\left[1 - \left(1 - \frac{K_{y}}{K_{x}} \right) \cos^{2} \theta_{3D} \right] \end{align} (5)

K_x and K_y are the TCs in the directions parallel and perpendicular to C_f-Cu, respectively. While K_i and K_j are the TCs of C_f-Cu in the directions parallel and perpendicular to the heat flow, respectively. The temperature distribution on the 2D section can be obtained by considering the K_i and K_j of each C_f-Cu.

2.2.5 Simulation of composites

Figure 2 shows that the finite element method is used to simulate the temperature distribution in the composite in the equilibrium state of heat exchange. During the simulation, the temperature of the left edge element and the initial temperature of other elements are 301 K and 300 K, respectively. The composite is sandwiched between the upper and lower heat sources, while the left and right edges were the adiabatic edges. The temperatures on the left and right are kept constant. Using the temperature distribution in the 2D section, the temperature of the remaining elements was updated iteratively until the average change in the temperature was less than 10⁻¹³, and the temperature distribution attained a steady state. The TC of the composite was estimated using steady-state eq. (6) of the temperature distribution.²⁸⁾   

\begin{equation} K = \frac{K_{m}\Delta T_{12}N_{x}}{\Delta T_{LR} + N_{L}\Delta T_{12} - N_{x}\Delta T_{12}} \end{equation} (6)

Fig. 2

Simulation model using the finite element method.

K_m, ΔT_LR, and ΔT₁₂ represent the TC of the matrix with different C_f-Cu content, the temperature difference between the left and right sides, and the average temperature difference between the first and second columns. N_L and N_R are the numbers of elements on the left and right heat sources, respectively. N_x is the number of composite elements. The size of the heat sources was 5 × 600 elements for each sample (N_L = N_R = 5 elements). The size of the composite part (N_x × N_y) was 450 × 600 elements, where the size of each element was 1.34 × 10⁻⁶ m. The TCs of the C_f-Cu was set to 880 W m⁻¹ K⁻¹ and 5.3 W m⁻¹ K⁻¹ along the axial and radial directions, respectively.

3. Results and Discussion

3.1 Radial thermal conductivity of C_f-Cu

Figure 3 shows that the diameter of C_f-Cu, the thickness of the Cu coating, and δ after electroless copper plating are 9.42 µm, 0.27 µm, and 0.54 µm, respectively. Substituting this value into eq. (1), the radial TC of C_f-Cu was 5.3 W m⁻¹ K⁻¹.

Fig. 3

Diameter change of C_f by Cu plating and element distribution of C_f-Cu cross section.

3.2 Phase of composites and Cu distribution

Figure 4(a) shows the XRD patterns of composites at different temperatures. At sintering temperatures higher than 1100 K, cementite and ferrite combine to form a small amount of martensite. The carbon in cementite and ferrite originates from C_f, which indicates the destruction of C_f. Figure 4(b) shows the XRD patterns of the composite with different volume fractions of C_f-Cu. C_f-Cu does not react with the Fe matrix. In Fig. 5, owing to the lower sintering temperature and sintering time, Cu distributed near C_f tightly, C_f, and Cu, which can still be regarded as a whole in the composite.

Fig. 4

XRD of composites (a) different sintering temperatures and (b) different volume fractions of C_f-Cu.

Fig. 5

SEM image of 10 vol% C_f-Cu/Fe composite.

3.3 Porosity of composites and thermal conductivity of the matrix

The theoretical density of composite is obtained through the calculation of the rule of mixture, and the actual density is obtained by the Archimedes method. The relative density is the ratio of the actual density to the theoretical density, and the sum of the relative density and porosity is 1. The porosity of the C_f-Cu/Fe composite and the matrix TC correction results are listed in Table 1. The porosity of the composite and TC of the matrix both increase with the increasing of the C_f-Cu content. When the volume fraction of C_f-Cu is lower than 20%, the porosity does not exceed 2.5%, and there are very few voids in the composite. These voids have little effect on the TC of the matrix. When the volume fraction of C_f-Cu exceeds 20%, the porosity increases to 6.8%, and there are many voids in the composite. The effect of air on its internal heat conduction hindering effect increases significantly and the TC of the matrix decreases to 48.5 W m⁻¹ K⁻¹.

Table 1 Volume fraction of voids in the C_f-Cu/Fe composite and the corresponding TC of the matrix, V_p and K_m denote the Volume fraction of voids and TC of matrix, respectively.

3.4 Orientation of C_f-Cu in 3D matrix

In the composites, a frequency histogram was obtained by counting the occurrence frequencies of α, β, and R of C_f-Cu in each direction. The statistical results α and R corresponding to the case When C_f-Cu is not parallel to the X-O-Z plane are shown in Fig. 6, and θ_3D can be obtained using eq. (4). The statistical results of β, corresponding to the case when C_f-Cu is parallel to the X-O-Z plane, are shown in Fig. 7, and θ_3D = β, where β = 0. This indicates that hot rolling promoted the arrangement of C_f-Cu along the heat flow, which is consistent with the result shown in Fig. 9(a).

Fig. 6

Frequency of α in the 3D matrix and R in the 2D cross-section of C_f-Cu/Fe composites with different C_f-Cu content. α is the angle between projection of C_f-Cu and heat flow.

Fig. 7

Frequency of β in the 2D cross-section of C_f-Cu/Fe composites with different C_f-Cu content. β is the angle between C_f-Cu and its projection.

3.5 Effect of the orientation of C_f-Cu on the effective thermal conductivity

We all know that the TC of C_f-Cu in the axial and radial directions are 580 W m⁻¹ K⁻¹ and 5.3 W m⁻¹ K⁻¹, respectively. Substituting this result into eq. (5), obtain the influence of θ_3D on the TC of C_f-Cu in the direction of heat flow, as shown in Fig. 8. Obviously, the effective thermal conductivity (ETC) gradually decreases as θ_3D increases. Regardless of the effect of voids on the TC of the matrix, K_m = 54 W m⁻¹ K⁻¹, when θ_3D is 73.08°, K_Fe and K_i has the same value. When θ_3D was less than 73.08°, K_i is greater than K_Fe, and the TC of C_f-Cu in the direction of heat flow was higher than that of the pure Fe, C_f-Cu can improve the TC of composite, and vice versa. The same principle, considering the effect of voids on the TC of the matrix, K_m ≠ 54 W m⁻¹ K⁻¹, The corrected results of K_m for C_f-Cu/Fe with different volume fractions are listed in Table 1. C_f-Cu/Fe with different volume fractions has different θ_3D. (x vol%C_f-Cu/Fe, x = 5, θ_3D = 73.14. x = 10, θ_3D = 73.26. x = 15, θ_3D = 73.32. x = 20, θ_3D = 73.44. x = 25, θ_3D = 74.09.) Figure 7 shows that most of C_f-Cu have an angle less than 73° with the direction of heat flow, which indicates that most of the C_f-Cu can be used as a heat conduction channel to effectively improve the TC of the composite.

Fig. 8

Relationship between θ_3D and the effective TC of C_f in the direction of heat flow.

3.6 Effect of hot rolling on the TC of composites

Figure 9(a) shows that the frequency distribution of β of 25 vol%C_f-Cu/Fe has been counted and plotted. There are still a few C_f-Cu perpendiculars to the heat flow after hot rolling, β = 90°, because of the cross-connect and folding of C_f-Cu during sintering and rolling. Figure 9(b) shows that during the rolling process, C_f-Cu folds, and cross-links. Figure 9(c) shows the real state of C_f-Cu in the composite after rolling. This causes part of the C_f-Cu to bend, while some C_f-Cu intersect and obstruct each other. This accounts for the large θ_3D value in the composites after rolling. The rolling process promoted the arrangement of C_f-Cu along the direction of heat flow, which effectively increases the TC of the composite. This was also observed in the study of Yang.¹⁴⁾ During SPS and hot rolling, the composite gradually became dense, the height, β, and θ_3D decrease, and TC increase. After hot rolling, the TC of the composite increases from 47.18 W m⁻¹ K⁻¹ to 68.89 W m⁻¹ K⁻¹.

Fig. 9

(a) Orientation of C_f-Cu in the 20 vol%C_f-Cu/Fe composite before and after rolling. (b) Large values of θ_3D which exist because the C_f-Cu fold over and cross each other. (c) Folding of C_f-Cu in the rolled composite.

3.7 Temperature distribution of A/B plane (rolling plane and its side surface) of composites

The ETC in the direction of the heat flow of each element (C_f-Cu and Fe matrix) was calculated and an effective TC map of the elements on the 2D section was obtained in the steady state. Figure 10 shows the map of the ETC of elements on the 2D section of composites with different volume fractions on the A/B plane. On the A plane, most of the C_f-Cu is parallel to the heat flow, C_f-Cu exhibits a high TC, and β is primarily distributed at a smaller angle, which is consistent with the result shown in Fig. 9(a). In the 2D cross-section simulation diagram, assuming that the right direction is the direction of heat flow, the matrix of the composite is blue, C_f-Cu exhibited high TC, and the C_f-Cu is marked in red, θ_3D = 0°. As θ_3D increases, the color of C_f-Cu gradually changes from red to blue, indicating a decreasing in TC. C_f-Cu is evenly distributed in the Fe matrix. On the B plane, C_f-Cu is uniformly distributed in the composite because it was not rolled on the A plane.

Fig. 10

Effective TC diagrams of the elements (C_f-Cu and Fe matrix) on the 2D cross-section of composites with different volume fractions of C_f-Cu.

3.8 Measured and simulated thermal conductivities

Figure 11 shows the results for the measurements of TC on the α plane before and after rolling and the simulated TC on the A/B plane of composites with different volume fractions of C_f-Cu. On the A plane, after rolling, the simulated value is larger than the measured value owing to experimental error, and displays the same trend as the measured value, with a small deviation of 3% to 4%. When the volume fraction of C_f-Cu is lower than 20%, the simulated and measured values increase with increasing C_f-Cu content. When the volume fraction of C_f-Cu exceeds 20%, both decrease with the increasing of C_f-Cu content; in addition, the porosity increases sharply (shown in Table 1) and the TC decreases. Its hindering effect on TC was greater than the effect of increasing C_f-Cu content on the improvement of TC. When the volume fraction of C_f-Cu is 20%, the simulated and measured values attain their maximum values simultaneously, which are 71.02 W m⁻¹ K⁻¹ and 68.89 W m⁻¹ K⁻¹, respectively. Before rolling, the measured TC increases with the C_f-Cu content. C_f-Cu acted as a heat conduction channel to increase the TC of the composites. Because β ≠ 0 (the angle between C_f-Cu and the projection of C_f-Cu), the measured TC before and after rolling had large deviations (40%–60%).

Fig. 11

Simulated and measured TC of C_f-Cu/Fe composites with different volume fractions of C_f-Cu on the A/B plane.

4. Conclusion

In this study, 5 (10, 15, 20, 25) vol% C_f-Cu/Fe composites were fabricated by SPS. The porosity and TC of the composites were measured, and the TC of the matrix was calculated. The TCs of the composites were also simulated. Our conclusions are listed below.

1. (1)    The C_f surface was covered with a 0.27 µm-thick copper layer via electroless Cu plating. The radial TC of C_f-Cu was 5.3 W m⁻¹ K⁻¹.
2. (2)    When the sintering temperature of the composite was 1100 K, C_f-Cu did not react with the Fe matrix, and Cu was distributed near C_f-Cu.
3. (3)    The TC of the matrix decreases with the increasing C_f-Cu content. When the volume fraction of C_f-Cu exceeds 20%, the porosity was higher than 2.5%, and the TC dropped to 48.5 W m⁻¹ K⁻¹.
4. (4)    The ETC of each element (C_f-Cu and Fe matrix) in the 2D section can be obtained by counting the distribution and frequency of α, β, and R on the 2D section.
5. (5)    Rolling treatment can effectively control the orientation of C_f-Cu, and almost all the axial directions of C_f-Cu are oriented along the direction of heat flow. When θ < 73°, C_f-Cu can increase the TC of the composite.
6. (6)    On the A plane, the simulated value is consistent with the measured value, with deviations between 3%–4%. When the volume fraction of C_f-Cu was 20%, the simulated and measured values attained their maximum value of 68.89 W m⁻¹ K⁻¹ and 71.02 W m⁻¹ K⁻¹, respectively. Owing to the rolling treatment, the measured TCs before and after rolling exhibit a large deviation of 40% to 60%.

Acknowledgments

Funding: This study was supported by the JSPS KAKENHI [Grant Number, 18k63840 and 17k06819].

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