Ceramic particles reinforced copper matrix composites manufactured by advanced powder metallurgy: preparation, performance, and mechanisms

For the powder metallurgy technique, the mixing of powders is the key step to obtain Cu matrix composites with good dispersity and high compactness. In the process of powder mixing, the conventional method can only obtain the uniform dispersion powders through powder mixer, and the resulting powders remain loose and are prone to agglomeration [31]. In contrast, mechanical alloying optimizes the bonding and the dispersion between the powders during the mixing process [32]. It is well known that mechanical alloying, as an atomic alloying technique, utilizes the mechanical energy generated by high-energy ball mill to make the composite powders repeatedly deformed and broken under the action of high-speed rotating grinding balls. In regard to preparing the dispersion-strengthened alloys and composites, mechanical alloying is conducive to the interatomic diffusion of each component and the enhancement of interfacial bonding strength, thereby obtaining a high strengthening effect [33–36]. As shown in figure 2(a), ductile particles (e.g. metal matrix) are deformed and broken by the collision of grinding balls and eventually flattened; by contrast, brittle particles (e.g. ceramic particles) are quickly crushed. Subsequently, a lamellar composite structure is formed by alternating the flake ductile powder and the brittle powder; that is, brittle powders are distributed at the joins of ductile layers. After further ball milling, the distance between the ductile and brittle powders becomes smaller, and eventually the composite powders are mixed and curled [37, 38].

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Figures 2(b)–(f) show the TEM images of composite powders at different milling time [39]. When the milling time is short (1 h and 5 h), the agglomerated ceramic powders can still be clearly observed. As increasing the milling time (10 h), the particle agglomeration is alleviated, as shown in figure 2(c). Furthermore, some ceramic powders have been welded with the Cu powders. Further increasing the milling time facilitates a uniform distribution of reinforced particles and dissipation of agglomerated powders. The grain size of Cu matrix decreases as increasing the milling time and reaches the minimum at a certain state [41]. Figures 2(g)–(k) show the TEM images of composite powders with different ceramic contents [40]. The sizes of particles and the agglomerated powders decrease significantly as increasing the ceramic content and the particle size reaches 45.4 nm for those nanocomposites containing 12 wt.% ceramic phase. Generally, cold-welding causes an increase in particle size, while the fracture of flakes results in the reduction in particle size [42]. The existence of hard particles leads to an increase in local deformation of Cu matrix near ceramic particles, which enhances the work hardening rate of the matrix. The increased work hardening rate is beneficial to increase the fracture of flakes. Moustafa and Taha [9] prepared the nano-sized ceramic particles reinforced Cu matrix nanocomposites with excellent comprehensive properties through mechanical alloying. The introduction of nano-sized ceramic particles triggers severe plastic deformation and grain refinement during mechanical alloying. As the content of ceramic particles in composites increases, the grain size of the Cu matrix further decreases, while both the dislocation density and microstrain of the Cu matrix increase.

In addition to powder factors and milling time, the ball-to-powder weight ratio (BPR) and the rotation speed (in rpm) also significantly affect the properties of dispersion-strengthened composites. Wang et al [43] successfully prepared TiC dispersion strengthened copper composite by a two-step ball milling process, and they systematically evaluated the effects of ball milling processes on the properties of Cu matrix composites. During this process, Ti and graphite were first ball milled and then Cu powder was added. Under the condition of high BPR together with high rotation speed, Ti and C can be completely converted to TiC, which led to higher electrical conductivity but lower strength of the composite compared with the counterparts with high BPR and low rotation speed and the ones with low BPR and high rotation speed. For the latter two cases, the dissolved Ti in the Cu matrix, caused by the incomplete reaction between Ti and C, significantly reduces the electrical conductivity of the composite but enhances its strength due to solid solution strengthening. However, the agglomeration of fine ceramic particles, especially nanometric particles, is prone to occur during ball milling process. To obtain a uniformly dispersed high-content nanocrystalline Y₂O₃/Cu composite, Huang et al [44] adopted a novel approach, namely multi-step ball milling and reduction process, to prepare Y₂O₃/Cu composites. The designed powder mixtures of CuO and Y₂O₃ particles were subjected to milling, reduction, secondary milling and annealing processes. This method can disperse the high content of Y₂O₃ uniformly in the Cu matrix and refining the crystallite size of copper. The yield strength and fracture strain of the Y₂O₃/Cu composite reach 655 MPa and 33.4%, respectively, indicating an effective combination of high strength and large ductility. Meanwhile, the electrical conductivity remains 53.8% IACS (International Annealed Copper Standard). Mechanical alloying has become an important technology to prepare ultrafine-grained and nanoparticle reinforced Cu matrix composites. Note that, in the preparation of Cu matrix composites by mechanical alloying, although long-time ball milling can refine the grains of the composites, it significantly reduces the preparation efficiency. Moreover, impurities are prone to be introduced into the matrix to affect the properties of the composites, especially the conductivity.

In conventional powder metallurgy processes, a range of thermal diffusion sintering techniques, including pressureless sintering, hot press sintering, hot isostatic sintering, etc, are often used to achieve powder consolidation [45, 46]. These thermal diffusion sintering techniques utilize a heat generator around the sample to heat samples, which inevitably prolongs the sintering time and increases energy loss due to thermal diffusion process. In comparison, spark plasma sintering (SPS), a relatively new powder metallurgy sintering technique, can prepare high-performance composite at lower sintering temperature and in shorter sintering time, compared to conventional thermal diffusion sintering methods. In the SPS process, a pulse current is directly applied between the powders for heating and sintering, as illustrated in figures 3(a) and (b). It is widely accepted that the high pulse current applied on the electrode would discharge plasma in the gap between powders, which can effectively eliminate the adsorbed gas and impurities on the surface of powders and destroy the oxide film on powder surface, thereby enhancing the thermal dissemination capability of sintered powder materials [47–50]. To reveal the SPS mechanism, Zhang et al [51] demonstrated the existence of spark discharge through direct observations and microstructural analyses. High-temperature spark is formed in the gaps instantly owing to the electrical discharge effect between powders when the switched direct current pulse is energized. Besides, the high heating rate and plastic deformation in the SPS process promote the densification of the sintered materials, thereby significantly improving the sintering efficiency and limiting grain growth.

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In general, owing to its unique heating process, SPS-produced samples always exhibit better comprehensive properties compared to the counterparts prepared by conventional sintering process. Naghikhani et al [52] compared the effects of pressureless sintering and SPS on the microstructure of WC/brass composites. As shown in figures 3(c)–(f), the composites fabricated by SPS display much more homogenous dispersion of WC particles compared with the pressureless sintered composites. Furthermore, apparent porosities can be observed in the WC-rich region of the pressureless sintered composites. Their results illustrated that the composites sintered by SPS have a density of 92%–97%, which is significantly higher than that of the pressureless sintered ones (65%–78%). As such, the SPS-produced composites show about five times higher hardness and higher wear resistance than the pressureless sintered ones. It is well known that different densification mechanisms (e.g. plasticity and creep flow) could directly affect the compactness of powder compacts in the sintering process [29, 54, 55]. During SPS, Joule heating is formed by the conduction of electric current through metals, which results in local vaporization and powder cleaning. This greatly improves the consolidation rate of the SPS process compared to the conventional sintering process. Additionally, the surface of powders can be decontaminated and activated when using pulsed direct current. The heating by the Joule effect leads to a rapid temperature rise, increased mass transfer and material transfer at the macron and micron scales. Therefore, the SPS-fabricated samples exhibit much higher compactness, hardness, strength and wear resistance than the pressureless sintered counterparts. Venkatesh and Deoghare [56] studied the effects of conventional sintering and SPS techniques on the sintering mechanism and mechanical properties of ceramic reinforced metal matrix composites. Compared with the conventional sintered composites, the SPS-fabricated composites exhibit 13.3% higher tensile strength and 11.7% higher compressive strength. Similar scenario was reported in literature, e.g. [57].

For composites and alloys, undesirable microstructural coarsening would decline their mechanical properties due to the high temperature and long conventional sintering time. Furthermore, due to the radial expansion rate exceeding the grain settling and rearrangement rate, cracks tend to develop at grain boundaries in the conventional sintered samples. The SPS technique can effectively solve this problem and improve the mechanical properties [58]. Refined grains could be obtained by SPS owing to the shorter sintering time and lower sintering temperature in the process, which is beneficial to improve the sintering properties and comprehensive properties of the Cu matrix composites [59–61]. Numerous studies [62–65] have confirmed that the SPS-fabricated sample display significantly smaller mean grain sizes compared with the conventional sintered samples. Moreover, the number of cracks in the samples sintered by SPS is also greatly reduced due to its special heating method.

In addition to the advantages in grain refinement and enhanced densification of Cu matrix composites manufactured by SPS, the higher heat resistance between heterogeneous particles would facilitate interfacial reactions therefore better interfacial bonding. This is also a key factor in the development of Cu matrix composites with enhanced strength-ductility synergy and superior electrical and thermal conductivity. Chmielewski et al [66] respectively prepared SiC/Cu composites by hot pressing and SPS. The composites sintered by hot pressing exhibit visible pore aggregation and structural disruption area reaching several microns at interfaces. By contrast, the composites prepared by SPS show better interfacial bonding, resulting in 10% increase in the relative density and 20% increase in the thermal conductivity compared to the composites prepared by hot pressing. As shown in figures 3(g)–(l), the 3 wt.% WC containing CuCrZr composites prepared by mechanical alloying and SPS also display good interfacial bonding [53]. The ZrC and W₂C layers are formed at the interfaces between the CuCrZr alloy and WC particles. Notably, the ZrC layer with 20 nm thick is distributed on the surface of ceramic particles and a W₂C layer is formed inside. According to the orientation relationship of each phase, the ZrC–W₂C–WC core–shell structure transforms the incoherent interface between the WC particles and the Cu matrix into a coherent/semi-coherent interface, which effectively enhances the interfacial bonding between the WC particles and the Cu matrix. For the SPS technique, severe interfacial reaction takes place between the reinforcement and the metal matrix, while such interfacial reactions are very slight and apparent sintering pores are observed in the conventional sintering process [67]. Therefore, the ceramics reinforced Cu composites fabricated by SPS are more compact, with fine grains and high interfacial bonding, resulting in significantly enhanced comprehensive properties of the composites. In short, compared with the conventional thermal diffusion sintering method, SPS has the advantages of fast heating rate, controllable microstructure, energy saving and environmental protection. The prepared composites are more compact and have finer grains and improved interfacial bonding between the ceramic phase and the matrix. However, SPS has difficulty in preparing large-sized products, which is not conducive to industrialization. The formation process of plasma during the powder consolidation and its effect on performance of composites still need to be further explored.

In order to further improve the interfacial bonding between ceramic particles and the copper substrate, the raw powders used are pretreated by many techniques, such as electroplating, chemical plating, internal oxidation, and so on [68, 69]. Among them, the internal oxidation method is widely adapted owing to its special ability to spontaneously generate oxide particles. In the internal oxidation method, oxygen is dissolved into the alloy powders and diffused in the its constituent phases, and then more active elements in the constituent phases react with oxygen to form uniformly dispersed oxide particles. In this preparation process, the alloy powders are first oxidized and the subsequent treatment is similar to that in conventional powder metallurgy method [70, 71]. Considerable endeavors have been made on the study of Al₂O₃ dispersion strengthened Cu matrix composites. This process could effectively improve the wettability of Al₂O₃–Cu interface and the strengthening ability of hard particles [72–74]. Therefore, uniformly distributed and thermally stable fine oxides are formed in the Cu matrix, and various strengthening mechanisms, such as dispersion strengthening and dislocation strengthening, could fully exert to improve the comprehensive properties of the composites, especially their high-temperature mechanical properties [75].

During the preparation of Al₂O₃/Cu composite, the Cu–Al alloy powders were first melted, then the melt were mixed with the oxidant, and internally oxidized at a certain temperature and atmosphere. Finally, the samples were prepared by the consolidation process. In general, fine Al₂O₃ particles are uniformly dispersed in the Cu matrix, while a small number of coarse particles are distributed on the grain boundaries. The strengthening mechanism at room temperature is mainly determined by the Hall–Petch relation, and the strong pinning effect of Al₂O₃ particles on grain boundaries and sub-grain boundaries is responsible for the high-temperature strengthening. On this basis, Zhao et al [76] prepared the Al₂O₃ dispersion strengthened Cu composite by a combination of internal oxidation and mechanical alloying. Their results demonstrated that this compound process could enable the aluminum to be oxidized completely in 10–20 h, which is much faster that only by mechanical alloying (exceeding 40 h). The uniform distribution of Al₂O₃ particles and the refined reinforcing particle for this compound process are conducive to obtain better comprehensive properties. However, in the process of atomized Cu-Al alloy powders and high-energy mechanical milling, the impurities in the powders could sharply reduce the properties of the Al₂O₃/Cu composites. Li et al [30] adopted a novel method to fabricate ultrafine-grained Al₂O₃/Cu bulk composites, as shown in figure 4(a). Firstly, the Al–Cu alloy powders were dealloyed to prepare nanocrystalline powders; then the dealloyed powders were heat-treated by two different methods; the powders were finally consolidated by powder compact extrusion. The locations of the Al₂O₃ nanoparticles in relation to the heat treatment route result in formation of two kinds of microstructures. The Al₂O₃ nanoparticles of the R1-treated composite are mainly distributed at grain boundaries, and the Al₂O₃ nanoparticles of the R2-treated composite are mainly distributed within grains, as illustrated in figure 4. As a result, the intragranular Al₂O₃ nanoparticles are more beneficial to realize a good strength-ductility synergy and high electrical conductivity.

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After internal oxidation process, partial sintering occurs between the powders due to local high temperatures caused by the exothermic internal oxidation reaction, so the quantity of fine particles is significantly reduced. Meanwhile, the Al₂O₃ particles are easily coarsened and agglomerated in the composite and cannot achieve the desired strengthening effect. In order to reveal the reasons for this phenomenon, a combining study between powder metallurgy and Rheins-pack method was conducted [77]. The experimental results suggested that the particles tend to preferentially aggregate at grain boundaries, and the increase in both diffusion distance and Al content would coarsen the particles. Even worse, coarsening and agglomeration of Al₂O₃ particles are accelerated due to the presence of water vapor during the internal oxidation process, and coarse and agglomerated particles are generated on the powder surface during water atomization. Ti doping was also found to effectively refine the size and modify the intergranular and intragranular Al₂O₃ particles [77, 78]. Similar work was also carried out on the effect of Ag addition on the morphology and size distribution of Al₂O₃/Cu composites [79]. The addition of Ag promotes the diffusion of oxygen atoms in the Cu matrix and the internal oxidation process. This is because the Ag doping provides more 'tunnels', such as grain boundaries and lattice defects, for oxygen atoms to diffuse in the Cu matrix, which allows oxygen atoms to diffuse through the dense Al₂O₃ layer to the reaction front for a continuous internal oxidation process with Al. The particle size of Al₂O₃ particles decreases from ∼63 nm to ∼37 nm as increasing the Ag content, and numerous triangular Al₂O₃ precipitates are observed in the Ag-doped Al₂O₃/Cu composites. Increasing the Ag amount can enhance the electrical conductivity and mechanical strength of the Al₂O₃/Cu–Ag composite. When the Ag/Al atomic ratio is ∼1:4, the composite exhibits the optimal electrical of 85.9% IACS and hardness of 162 HV.

Recently, different consolidation methods of internal oxide powders have also attracted extensive attention. Three consolidation methods, i.e. high-speed compaction, hot pressing and hot extrusion, were used to compare their effects on the microstructure and properties of internal oxide Al₂O₃ dispersion strengthened Cu matrix composites [74]. The composites prepared by hot pressing display the coarsest grains while the counterparts prepared by hot extrusion have the finest grains. This is attributed to the repeated stretching and pulling of the powder particles during hot extrusion, which eliminates residual pores and refines the grains. In contrast, grain growth is not restricted in the hot-pressing process. The composites prepared by high-speed compaction method exhibit the lowest relative density of 98.3% (versus 99.5% for the ones by hot pressing and 100% for the counterparts by hot extrusion) owing to the small amount of air entrained in the composites during the rapid compaction process. This leads to the minimum electrical conductivity of 81% IACS (versus 86% IACS for the ones by hot pressing and 87% IACS for the counterparts by hot extrusion). However, the higher strength could be obtained by the composites prepared by high-speed compaction owing to severe plastic deformation and dislocation formation. Furthermore, the composites prepared by high-speed compaction demonstrate higher softening temperature and high-temperature serviceability.

In addition to the manipulation of the particles in the composites, good interfacial bonding between ceramic particles and Cu matrix is also required for obtaining a composite with excellent properties. The fully coherent interface between internal oxidized Al₂O₃ and Cu matrix is conducive to accumulating high-density dislocations in the interior of grains and hindering dislocation motion, thereby significantly enhancing the strength-ductility synergy of Cu matrix composites. Oxidation-induced nano-Al₂O₃ particles and interface-optimized carbon nanotubes (CNTs) could significantly enhance the strength of Cu matrix composites and preserve their plasticity. Based on this strategy, Long et al [80] developed an internal oxidation method for preparing high-performance Al₂O₃/Cu matrix composites doping with CNTs. As shown in figures 5(a)–(g), coherent Al₂O₃ nanoparticles are formed in CNTs and amorphous copper oxide (Cu_x O_y ) is formed between CNTs and Cu, due to the diffusion of oxygen atoms and in-situ reactions resulting from the thermodynamic driving forces during internal oxidation process. The combined strengthening role of Al₂O₃ nanoparticles and interface-optimized CNTs enables the composite to obtain high mechanical properties (tensile strength of 510 MPa and plasticity of 20.2%). The Al₂O₃ nanoparticles and CNTs render the composite high strength because of Orowan strengthening and high-efficiency load transfer strengthening. Meanwhile, the synergistic effect of the internal dislocation stacking of Al₂O₃ nanoparticles and the enhanced crack resistance by optimized CNTs interfacial bonding collectively contributes to the tensile ductility.

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The CNTs/Al₂O₃/Cu composites can also be produced by in-situ chemical vapor deposition (CVD) [81]. The Al₂O₃/Cu powders were obtained by the internal oxidation method and the CNTs were compounded in-situ on the surface of powders by CVD, as illustrated in figures 5(h)–(n). The CNTs are distributed individually in the matrix and they do not agglomerate on the powder surface. Besides, the wall surfaces of CNTs are clean with no amorphous carbon, and the diameter of the CNTs tubes is uniform over the whole length at about 20 nm. The presence of Al₂O₃ on the CNTs surface promotes to form Cu nanoparticles, thereby facilitating the growth of CNTs. The CNTs with high surface cleanness and high degree of graphitization are evenly distributed on the surface of composite powders and are well bound with the matrix. Subsequently, the SPS technique was employed to sinter CNTs/Al₂O₃/Cu bulk composites [82]. In bulk composites, the CNTs that are well bound with the Cu matrix and Al₂O₃ particles play a synergistic role in enhancing the mechanical and electrical properties. Since Al₂O₃ and CNTs are distributed at grain boundaries, the Zener pinning effect is responsible for the inhibition of grain growth in the Cu matrix.

In brief, the internal oxidation method can be used to prepare uniformly distributed and thermally stable fine oxides in Cu matrix composites to obtain excellent comprehensive properties, especially high-temperature mechanical properties. Besides, doping CNTs in the composite by internal oxidation can further improve the interfacial bonding and play a synergistic role in enhancing the mechanical and electrical properties. Nevertheless, in additional to its complicated process and high cost, the control of oxygen content is the challenge in preparing Cu matrix composites by this method. This is also a key problem to realize large-scale and industrialized production of Cu matrix composites.

The in-situ synthesis method is a novel preparation technique developed in recent years for fabricating Cu matrix composites in which a series of thermo-mechanical treatments or chemical reactions take place under certain conditions to form one or more reinforcing phases inside the matrix with aim to improve the performance of composites [83–86]. However, most of the reinforcements are prone to aggregate and coalesce at the grain boundaries of the Cu matrix and to form semi-coherent or incoherent interfaces with the Cu matrix because they have radically different physical and chemical properties from the Cu matrix [87]. On this basis, in-situ synthesis method could perfectly solve the disadvantages that are demonstrated in the composites fabricated by ex-situ preparation methods (addition of existing ceramic phases), such as poor interfacial wettability and weak interfacial bonding between the reinforcing phases and the Cu matrix. As such, the in-situ Cu matrix composites generally demonstrate good thermodynamic stability with refined and homogeneously distributed reinforcements in Cu matrix [88–91].

In the in-situ prepared Cu matrix composites, ceramic or intermetallics including oxides, carbides, borides, etc, are in-situ formed in the Cu matrix. Among the in-situ generated reinforcements, some rare earth oxides with superior thermodynamic stability are attractive as dispersions in composites. Furthermore, these rare earth elements with larger atomic radii exhibit low solubility and diffusivity in the Cu matrix, which would improve the microstructure stability and prevent grain coarsening [92, 93]. However, this also limits their ability to prepare Cu matrix composites by internal oxidation methods. To obtain uniformly distributed oxides in the Cu matrix, Zhou et al [94] used Cu–Y alloy to prepare Y₂O₃/Cu composites by in-situ synthesis method at the liquidus temperature. Microstructure transformation takes place during the solidification of the molten Cu–Y alloy, accompanied by an in-situ formation of Y₂O₃ particles. On the one hand, yttrium reacts with oxygen (which is diffused into the solution) to form Y₂O₃ particles. Meanwhile, the yttrium content in the regions around the particles is locally reduced and a supercooled zone is formed around the Y₂O₃ particles. On the other hand, Y₂O₃ particles can act as a nucleation agent to further promote solidification. This promotes the isothermal solidification of the Cu–Y melt, which results in the formation of an equiaxed microstructure. As a result, the nano-sized rare earth oxides with an average grain size of 5 nm and interspacing of 20 nm are evenly distributed in the matrix and are coherent with the Cu matrix. Under the joint strengthening effect of Orowan and shearing mechanism, the prepared Y₂O₃/Cu composite exhibits significantly higher ultimate tensile strength than the pure Cu.

Compared to the oxide enhancements, in-situ synthesized carbides and borides are easier to generate in Cu melts and to avoid the oxidation of the Cu matrix. Furthermore, most carbides and borides, such as TiC, NbC, TiB₂, ZrB₂, and so on, demonstrate better interfacial bonding and comprehensive properties. Generally, these in-situ enhancements are formed by the chemical reaction of Mc (=Zr, Ti) and Nm (=C, B, BN, B₄C) in the Cu–Mc–Nm systems. For instance, in-situ TiB₂/Cu composites were generated through exothermic dispersion synthesis in the Cu–Ti–B system [95]. As shown in figure 6, intermediate phase Cu₄Ti is first formed by the reaction of Cu and Ti, and then Cu₄Ti reacts with B to form uniformly distributed ultrafine-grained TiB₂ particles as the reinforcement. The reaction process in this system can be described as: Cu + Ti + B → Cu₄Ti + B → Cu + TiB₂. Meanwhile, the ultrafine TiB₂ particles are uniformly distributed in the Cu matrix, which greatly enhances the mechanical performance of the composites. On this basis, the Cu matrix can be a catalyst for in-situ reaction. The Cu matrix first reacts with the reactant Mc (=Zr, Ti) to form the intermetallic compound and then reacts with the reactant Nm (=C, B, BN, B₄C) to form the ceramic phase. This process can lower the temperature threshold of the reaction and allow the in-situ reactions below the liquidus of Cu matrix, which facilitates grain refinement and enhances the dispersion of ceramic particles.

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However, during the preparation process, not all the added reactants could be fully reacted. The added Nm (=C, B, BN, B₄C) reactants tend to react incompletely with the solute Mc (=Zr, Ti) reactants to form ceramic phase owing to their poor wettability and limited solubility in Cu melts. The residual reactants would dissolve into the Cu matrix and induce deformation of the surrounding lattice, thus scattering electrons and significantly affecting the conductivity of the composite. Ding et al [96] found that only around 70% of graphite has reacted with soluble Ti to form TiC. Thus, element B was added into the composite to dissipate the remaining Ti by forming TiB₂. Their results showed that the introduction of B improves the distribution homogeneity of the reinforcing particles, thereby enhancing the hardness and electrical conductivity of the Cu matrix composites. Guo et al [97] prepared the molybdenum carbide coated graphene (GNP) nanosheets (Mo₂C@GNPs) through a combination of impregnation reduction and in-situ reaction. As shown in figures 7(a)–(g), Mo₂C is uniformly dispersed both at the interfaces between GNPs and the Cu matrix and in the Cu matrix adjacent to GNPs. This demonstrates that Mo₂C not only modifies the interface between the reinforcements and the matrix but also acts as a reinforcement phase dispersed around the GNPs. As a result, the Mo₂C@GNPs reinforced Cu matrix composite demonstrates yield strength reaching 303 MPa, which is 72% and 23% higher than the corresponding ones for pure Cu (176 MPa) and GNPs/Cu composite (247 MPa), respectively, and electrical conductivity exceeding 90% IACS.

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In the process of in-situ synthesis, the type, physicochemical properties and adaptability of reactants directly determine the reinforcing effect of the products. Zhang et al [98] fabricated in-situ TiC/Cu composites by combustion synthesis and hot pressing in the Cu–Ti–CNTs system. By controlling the mixing mode of CNTs, TiC particles with different sizes and morphologies were formed in the composites and exhibited different reinforcing effects. In addition to the pretreatment of the reactants, using different sources of reactants could also greatly affect the in-situ synthesis. Previous work [99] intensively investigated the effect of carbon sources (graphite, CNT and graphene) on the phases formation and comprehensive performance of in-situ TiC–C/Cu composites in the Cu–Ti–C system. Among the carbon sources, CNTs and graphene can promote to form fine TiC nanoparticles, which greatly enhances the tribological properties of the Cu matrix composites. The previous work from the current team [100] prepared high-volume-fraction TiB₂/Cu and (TiC + TiB₂)/Cu composites in the Cu–Ti–B and Cu–Ti–B₄C systems by the in-situ method. As shown in figure 8(a), the reactions are sufficient, and only diffraction peaks of TiB₂, TiC and Cu are detected. The ceramic particles in the Cu matrix are evenly distributed without evident pores and aggregation of particles (figures 8(b) and (c)). Computational simulation results suggested that the nearly spherical ceramic particles could modify the thermal transfer routes and stress–strain response and reduce stress concentration, which further enhances its properties (figures 8(d)–(f)). From the above results, in-situ synthesis has become a promising technique for the preparation of Cu matrix composites. This process could effectively solve the challenges of poor interfacial wettability and reduce the pretreatment process of the reinforcing phase, further simplifying the preparation process. However, this method has high requirements on reactants and it can only prepare reinforcements with good reactivity and matrix compatibility. Furthermore, further in-depth understanding is need on precisely controlling of the content and morphology of the enhanced phase and the in-situ reaction process to improve the comprehensive performance of Cu matrix composites.

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In conclusion, the Cu matrix composites fabricated by various techniques tend to possess different comprehensive properties [61, 101]. The Cu matrix composites by these advanced preparation processes, including mechanical alloying, spark plasma sintering, internal oxidation and in-situ processing, demonstrate better comprehensive properties compared with the counterparts prepared by conventional powder metallurgy process. Table 1 summarizes the advantages and disadvantages of various advanced techniques. Among them, the dispersion of ceramic particles in the Cu matrix and the interfacial bonding between ceramic particles and the Cu matrix are greatly enhanced in the Cu matrix composites prepared by these advanced techniques. Meanwhile, the combination of these processes can further enhance the comprehensive properties of Cu matrix composites.

Figure 9 summarizes the comprehensive performance of Cu matrix composites prepared by various processes reported in the literature. The representative performance of ceramic reinforced Cu matrix composites prepared by various processes are summarized in table 2. It can be found that the Cu matrix composites prepared by combining multiple advanced techniques tend to exhibit better synergistic strengthening effects in strength-ductility and strength-conductivity. For instance, 1.1Al₂O₃/Cu composites fabricated by internal oxidation followed by hot extrusion demonstrate excellent synergetic enhancement in strength-ductility and in electrical conductivity [73]. Their yield strength and fracture strain are 533 MPa and 25% respectively, and their electrical conductivity is still maintained at 85% IACS. Generally, the Cu matrix composites prepared by combining advanced processing techniques would further increase the relative density (i.e. compactness), refine the grains, and optimize the dislocation distribution of ceramic reinforced Cu matrix composites. This is beneficial for repairing the defects of the specimens during the process of powder metallurgy, thereby enhancing their comprehensive performance. Therefore, further combining the advanced preparation processes along with appropriate processing techniques is the focus of future work.

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Table 2. Summary of comprehensive properties of ceramics reinforced Cu matrix composites prepared by various processes. σ_0.2: yield strength; σ_FS: fracture strength; : fracture strain; CS: compressive strength; TS: tensile strength. MA: mechanical alloying; SPS: spark plasma sintering; IO: internal oxidation.

Composites (wt.%)	Preparation technique	σ0.2 (MPa)	σFS (MPa)	(%)	CTE (10−6 K−1)	Electrical conductivity (% IACS)	Thermal conductivity (W mK−1)	References
3ZrO2/Cu	MA	61 (CS)	310	44	—	73.45	—	[40]
6ZrO2/Cu	MA	69 (CS)	346	43	—	14.17	—
9ZrO2/Cu	MA	72 (CS)	368	39	—	5.79	—
12ZrO2/Cu	MA	79 (CS)	385	35	—	1.65	—
5.9Y2O3/Cu	MA + SPS	655 (CS)	932	33	—	53.8	—	[44]
1SiC/Cu	MA	48 (CS)	268	33	14.8	47.4	—	[9]
2SiC/Cu	MA	51 (CS)	283	32	14.1	42.9	—
4SiC/Cu	MA	60 (CS)	312	27	12.9	37.9	—
8SiC/Cu	MA	75 (CS)	340	21	11.2	16.7	—
0.42Y2O3/Cu	MA + SPS	272 (TS)	296	12	—	—	—	[33]
3TiC/Cu	MA + SPS	572 (TS)	602	8	—	71.5	—	[43]
2.1WC/Cu	Pressureless sintering	244 (TS)	270	8	—	—	—	[102]
2.1WC/Cu	SPS	285 (TS)	310	11	—	—	—
2.1WC/Cu	SPS + rolled	312 (TS)	361	12	—	—	—
10SiC/Cu	SPS	110 (TS)	140	9	—	—	338	[103]
20SiC/Cu	SPS	68 (TS)	75	2.3	—	—	282
10SiC/Cu	SPS + high-pressure torsion	395 (TS)	440	2.9	—	—	385
20SiC/Cu	SPS + high-pressure torsion	385 (TS)	420	1.9	—	—	362
2Al2O3/Cu	SPS (10 min) + hot extrusion	428 (TS)	510	14.7	—	87.1	—	[60]
2Al2O3/Cu	SPS (20 min) + hot extrusion	430 (TS)	497	11.5	—	83.2	—
1Ti2AlC/Cu	In-situ	118 (TS)	—	—	—	84.3	—	[104]
2Ti2AlC/Cu	In-situ	132 (TS)	—	—	—	74.8	—
3Ti2AlC/Cu	In-situ	198 (TS)	—	—	—	50.5	—
5Ti2AlC/Cu	In-situ	241 (TS)	—	—	—	33.6	—
1.1Al2O3/Cu	IO + hot-extruded	533 (TS)	570	25	—	85	—	[73]
1.8La2O3/Cu	IO + SPS	239 (TS)	349	37.6	—	93.1	—	[71]
0.34Al2O3/Cu	IO + high-velocity compaction	396 (CS)	443	—	—	81	—	[74]
0.34Al2O3/Cu	IO + hot pressing	281 (CS)	386	—	—	86	—
0.34Al2O3/Cu	IO + hot extrusion	312 (CS)	378	—	—	87	—
0.3 Y2O3/0.3Al2O3/0.3La2O3/Cu	IO	—	545 (TS)	—	—	93.5	—	[105]
2Al2O3/Cu	MA + extrusion + hot rolling	610 (TS)	648	6.2	—		—	[70]
1.6 Al2O3/Cu (R1)	IO + heat treatment	335 (TS)	387	6.6	—	95	—	[30]
1.6 Al2O3/Cu (R2)	IO + heat treatment	461 (TS)	522	8.2	—	90	—
1.5 Al2O3/Cu	IO + hot extruded	330 (TS)	358	17.1	—	—	—	[80]
1.1 Al2O3/Cu	IO	502 (TS)	563	—	—	—	—	[75]
0.2 Al2O3/Cu	IO	420 (TS)	458	—	—	—	—	[106]
0.12 Al2O3/Cu	IO	163 (TS)	220	11.8	—	89	—	[82]
0.6 Al2O3/Cu		261 (TS)	312	5.1	—	77	—
12.1TiC/Cu	In-situ	183 (CS)	549	25.9	—	65.5	—	[98]
12.1TiC/Cu	In-situ	132 (CS)	526	35.7	—	55.6	—
12.1TiC/Cu	In-situ	121 (CS)	417	34.9	—	40.3	—
1TiC/Cu	In-situ	281 (CS)	584	35.8	—	77	—	[84]
11.2TiB2/Cu	In-situ	168 (TS)	318	4.4	—	—	—	[95]
25.6 TiC + TiB2/Cu	In-situ	949 (CS)	1239	7.1	—	—	—	[107]
34.1 TiC + TiB2/Cu	In-situ	1003 (CS)	1252	5.8	—	—	—
43.7 TiC + TiB2/Cu	In-situ	1156 (CS)	1346	4.9	—	—	—

As known, ceramic particles can greatly enhance the strength and wear resistance of metal matrix composites. The ceramic particles with high specific elastic modulus effectively increase the Young's modulus and yield strength of the Cu matrix composites. In theory, the Young's modulus of ceramic particles reinforced Cu matrix composites is predicted by the classical Hashin–Shtrikman elasticity theory [130]:

$$\begin{align}{E_{{\text{HS - Upper}}}} = \frac{{{E_{\text{p}}}\left[ {{E_{\text{p}}}{V_{\text{p}}} + {E_{\text{m}}}\left( {2 - {V_{\text{p}}}} \right)} \right]}}{{{E_{\text{m}}}{V_{\text{p}}} + {E_{\text{p}}}\left( {2 - {V_{\text{p}}}} \right)}}\end{align} \tag{ 1 }$$

$$\begin{align}{E_{{\text{HS - Lower}}}} = \frac{{{E_{\text{m}}}\left[ {{E_{\text{m}}}(1 - {V_{\text{p}}}} \right) + {E_{\text{p}}}\left( {1 + {V_{\text{p}}}} \right)}}{{{E_{\text{m}}}\left( {1 + {V_{\text{p}}}} \right) + {E_{\text{p}}}\left( {1 - {V_{\text{p}}}} \right)}}\end{align} \tag{ 2 }$$

$$\begin{align}{E_{{\text{HS}}}} = \left( {{E_{{\text{HS - Upper}}}} + {E_{{\text{HS - Lower}}}}} \right)/2\end{align} \tag{ 3 }$$

where V is the volume fraction and E is the Young's modulus. The subscripts c, m, and p denote the composite, matrix, and particle, respectively. ${E_{{\text{HS - Upper}}}}$ and ${E_{{\text{HS - Lower}}}}$ are the upper limit and the lower limit of Hashin–Shtrikman theory, respectively, and ${E_{{\text{HS}}}}$ is the Young's modulus of the composite predicted by Hashin–Shtrikman theory.

For Hashin–Shtrikman elasticity theory, only the Young's modulus and content of the matrix and ceramic phases are considered. While the Tsai–Halpin equation takes into account the aspect ratio of ceramic particles, and it is expressed as [131]:

$$\begin{align}{E_{\text{c}}} = \frac{{{E_{\text{m}}}\left( {1 + 2s\tau {V_{\text{p}}}} \right)}}{{1 - \tau {V_{\text{p}}}}}\end{align} \tag{ 4 }$$

$$\begin{align}\tau = \frac{{{E_{\text{p}}}/{E_{\text{m}}} - 1}}{{{E_{\text{p}}}/{E_{\text{m}}} + 2s}}\quad \end{align} \tag{ 5 }$$

where s is the aspect ratio of particles and the parameter τ is calculated by the equation (5). Both models are effective in estimating the Young's modulus of Cu matrix composites.

For the yield strength of Cu matrix composite, the modified shear-lag model can make good theoretical predictions [132, 133]:

$$\begin{align}{\sigma _{\text{c}}} = {\sigma _{\text{m}}}\left[ {1/2{V_{\text{P}}}\left( {S + 2} \right) + {V_{\text{m}}}} \right].\end{align} \tag{ 6 }$$

This model assumes that the presence of the ceramic particles does not impact the stress–strain response of the matrix, which allows the properties of the matrix to be incorporated into the model. Besides, the effect of particle sizes is not considered in this model. Recently, a micromechanics method has been widely used to predict the yield strength of composites, which is ascribed to several strengthening mechanisms including grain refinement strengthening, dislocation strengthening caused by CTE mismatch, load transfer strengthening and Orowan strengthening [134, 135]. This model can not only accurately predict the yield strength of composites but also provide a deep insight into the strengthening mechanism of ceramic particles reinforced metal matrix composites. The final yield strength of the metal matrix composites is computed as the sum of the single strengthening contributions Δσ_i :

$$\begin{align}{\sigma _{\text{c}}} = {\sigma _{\text{m}}} + {\mathop \sum \nolimits }_i\Delta {\sigma _i}.\end{align} \tag{ 7 }$$

Generally, the particles uniformly dispersed in matrix effectively impede dislocation motions, and fine-grained particles provide strong barriers to grain boundary migration via the Zener pinning mechanism [136],

$$\begin{align}{d_{\text{m}}} = \frac{{4\alpha {D_{\text{p}}}}}{{3{V_{\text{p}}}}}\end{align} \tag{ 8 }$$

where d_m is the grain size of matrix, α is the proportionality constant, and D_p is the dimensions of particles. The resulting grain refinement reduces the formation of defects and improve crack propagation resistance. The contribution of grain refinement strengthening could be formulated using the classical Hall–Petch theory:

$$\begin{align}\Delta {\sigma _{{\text{HP}}}} = \frac{k}{{\sqrt d }}\end{align} \tag{ 9 }$$

where k is a constant and d is the mean grain size.

In addition, owing to the discrepancy in the physicochemical properties of the ceramic particles and the Cu matrix, the ceramic second phase would induce dislocation pinning and accumulation at the interface, which results in dislocation strengthening. The effect caused by dislocation is expressed as [137]:

$$\begin{align}\Delta {\sigma _{{\text{CTE}}}} = \alpha Gb{\left( {\frac{{12\Delta T\Delta C{V_{\text{p}}}}}{{b{d_{\text{p}}}}}} \right)^{1/2}}\end{align} \tag{ 10 }$$

where ΔT is the difference in temperature and ΔC is the difference in CTE between the matrix and the ceramic particles; G refers to the shear modulus of the matrix and b is Burger's vector; d_p represent the mean diameter of reinforcing particles. When the particles size is relatively fine (<100 nm), the Orowan strengthening mechanism is also prominent [138]. The Orowan strengthening effect is modeled as [139, 140]:

$$\begin{align}\Delta {\sigma _{{\text{Orowan}}}} = M\frac{{0.4Gb}}{{\pi {{\left( {1 - v} \right)}^{1/2}}}}\frac{{\ln \left( {D/b} \right)}}{\lambda }\end{align} \tag{ 11 }$$

where M is orientation factor on average, v is Poisson's ratio, λ is the nanoparticle spacing, and D is the nanoparticle average grain size.

The resulting bending of dislocations would increase the lattice distortion energy in the area affected by the dislocation, increasing the resistance to the movement of the dislocation line and the resistance to slippage. From the TEM images illustrated in figures 10(a)–(d) [126], the Y₂O₃ particles remain stable in the Cu matrix during the sintering process, and the Y₂O₃ particles do not react with the Cu matrix. Besides, the good interfacial bonding between Y₂O₃ particles and the Cu matrix significantly enhances the mechanical performance of the composites and minimizes the impact on their thermal and electrical conductivity. The electron backscatter diffraction (EBSD) results of the Cu matrix composite are illustrated in figures 10(e)–(h) [59]. For the composite samples, the microstructure consists of equiaxed grains with uniform dimensions, which are the result of grain growth and static recrystallization in the sintering process. The grain orientations of the two samples can be considered random. Nanoparticles penetrate the Cu grain boundaries and pin the Cu grains, thereby preventing grain growth based on the Zener mechanism. Besides, the high strain generated by the reinforcements in the Cu matrix promotes the recrystallization process at high temperature therefore delays the strain release, which is the driving force for grain growth at high temperature. Therefore, the composites have significantly smaller grain size than the pure Cu.

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In addition to the grain refinement strengthening, dislocation strengthening and Orowan strengthening, the load transfer strengthening mechanism between the softer matrix (Cu matrix) and the harder nanoparticles (ceramic phase) also comes into play when external loading is applied [141]. Nardone and Prewo [142] presented a modified model to describe the strengthening effect of load transfer:

$$\begin{align}\Delta {\sigma _{{\text{LT}}}} = {V_{\text{p}}}{\sigma _0}\left[ {\frac{{\left( {l + t} \right)A}}{{4l}}} \right]\end{align} \tag{ 12 }$$

where σ₀ is the yield strength of the matrix, l and t are the dimensions of the particles in the direction parallel and perpendicular to the load, respectively. Generally, for the composite with high content of ceramic particles, the force transfer process would be the main strengthening mechanism. As shown in figure 8(f), the finite element modeling (FEM) based on the three-dimensional representative volume element (RVE) of real microstructure was employed to investigate the stress distribution inside the composite under loading [100]. The results clearly show that the average stress on particles is several times higher than that of the matrix, which demonstrates that the ceramic particles carry most loadings. The uniformly dispersed ceramic particles greatly enhance the mechanical properties of the composite. However, a large stress concentration occurs at the tip of the particle. Thus, fracture occurs at that location and then initiates cracks in the matrix, resulting in failure of the composite. As such, the morphology of ceramic particles greatly affect the performance of the composite. This will be further discussed in the next section.

For the CTE of ceramic reinforced Cu matrix composite, the inherent performance of the matrix material and the reinforcement phase and their interaction directly determine the CTE of the composite. So far, a series of work has been conducted on the thermal expansion behavior of metal matrix composites through experimental investigations and theoretical calculations, which results in several reasonable calculation models to more accurately predict the CTE of different composites [125, 143–145].

• (1)  
  ROM model

The ROM model is a simplest mixed rule, which is expressed as:

$$\begin{align}{\alpha _{\text{c}}} = {\alpha _{\text{m}}}{V_{\text{m}}} + {\alpha _{\text{p}}}{V_{\text{p}}}\end{align} \tag{ 13 }$$

where α is the CTE. This model is suitable for composites with similar modulus differences of components, which is the result given by ignoring the elastic interaction between components.

• (2)  
  Turner model

The Turner model takes into account the effect of hydrostatic stress on adjoining phases, which is expressed as:

$$\begin{align}{\alpha _{\text{c}}} = \frac{{{\alpha _{\text{m}}}{V_{\text{m}}}{K_{\text{m}}} + {\alpha _{\text{p}}}{V_{\text{p}}}{K_{\text{p}}}}}{{{V_{\text{m}}}{K_{\text{m}}} + {V_{\text{p}}}{K_{\text{p}}}}}\end{align} \tag{ 14 }$$

where K is the bulk modulus and $K = \frac{E}{{3\left( {3 - E/G} \right)}}$; E is the elasticity modulus. Compared to the ROM model, the Turner model assumes that no internal stress exists in the composite and that the deformation degree of each component of the composite is the same.

• (3)  
  Kerner model

The Kerner model is currently the most used theoretical formula to calculate the CTE of metal matrix composites with particle reinforcement, which includes the shear strain in particulate composites,

$$\begin{align}{\alpha _{\text{c}}} & = {\alpha _{\text{p}}}{V_{\text{p}}} + {\alpha _{\text{m}}}{V_{\text{m}}} + ({\alpha _{\text{p}}} - {\alpha _{\text{m}}}){V_{\text{p}}}{V_{\text{m}}}\nonumber\\ & \quad \times \frac{{{K_{\text{p}}} - {K_{\text{m}}}}}{{{V_{\text{p}}}{K_{\text{p}}} - {V_{\text{m}}}{K_{\text{m}}} + 3{K_{\text{p}}}{K_{\text{m}}}/\left( {4{G_{\text{m}}}} \right)}}\end{align} \tag{ 15 }$$

where G is the shear modulus. This model utilizes a classical self-consistent method to predict the CTE of composites. It assumes that the intermediate reinforcement particles of the composite material are spherical and the outer layer is uniform matrix, and there exist both shear force and isostatic pressure in each phase of the composite.

• (4)  
  Eshelby model

The Eshelby model, also known as the equivalent inclusion model, is also a classical method for calculating the CTE of composite.

$$\begin{align}{\alpha _{\text{c}}} & = {\alpha _{\text{m}}} - {V_{\text{m}}}{\left\{ {\left( {{C_{\text{m}}} - {C_{\text{P}}}} \right)\left[ {S - {V_{\text{m}}}\left( {S - N} \right)} \right] - {C_{\text{m}}}} \right\}^{ - 1}} \nonumber\\ & \quad \times {C_{\text{p}}}\left( {{\alpha _{\text{p}}} - {\alpha _{\text{m}}}} \right)\end{align} \tag{ 16 }$$

where S is the Eshelby tensor, C is the stiffness and N is the matrix tensor corresponding to the reinforcement. The model assumes that both the matrix and the ceramic phase are isotropic in expansion and the model can more accurately estimate the CTE of the composites.

The above theoretical models have been widely applied to the design and preparation of composites. Moreover, all these models clearly reflect that the content of ceramic phase directly affects the CTE of the composites. The CTE tends to decrease with increasing the ceramic content. However, the initial assumptions of each model have certain defects and cannot fully objectively reflect the actual internal conditions of metal matrix composites. These models show different prediction accuracy for different types of metal matrix composites. Therefore, the predicted CTE values of metal matrix composites are often different from the actual results because the effects of non-uniform stress distribution, thermal residual stress, matrix plastic deformation, etc on the thermal expansion behavior of composites are not considered. Fei et al [146] pointed out that the CTE of composites is closely associated with the rate of change of thermal residual stress and dislocation density of the matrix. Due to the large CTE differences between the ceramic phase and the metal matrix, all the metal matrix contains thermal residual stress. When different heat treatment processes are applied to the composites, both the dislocation density and thermal stress of the composites prepared by slow cooling are lower than the corresponding ones of the composites prepared in fast cooling (water quenching) condition. The composites after quenching demonstrates much different thermal expansion behavior compared with the counterparts by slow cooling (figures 11(a)–(d)). The CTE curve as a function of temperature of quenched composite shows a minimum peak and a maximum peak, while there is no maximum peak for composite prepared under slow cooling. This can be ascribed to the thermal elastic relaxation and plastic relaxation of the matrix during the CTE test, and the rate of change of thermal residual stress directly determines the CTE of the composite. Therefore, the microstructure and thermal stress in the matrix have significant influences on the thermal expansion behavior of the metal matrix composite. In fact, the size and morphology of the particles, as well as the complex stress–strain state inside the matrix, also have a great impact on the CTE of the composites. Non-uniform stress distribution would lead to non-uniform thermal expansion behavior of the composite, which is difficult to predict by theoretical calculations. The microstructure defects such as pores, reaction products, interface debonding, and agglomeration of ceramic particles would also inevitably affect their thermal expansion behavior. Therefore, novel micromechanical models are needed to reflect the CTE of composites.

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On this basis, FEM is an effective strategy to perform deep analyses on the experimental results of the composite microstructure with respect to particle characteristics, thermal residual stress, interfaces, holes, etc to study the complex thermal expansion behavior [148–151]. The detailed stress and strain distribution and deformation can be visualized in the RVE model, which provides a more accurate prediction of the CTE for metal matrix composites. Sharma et al [147] constructed the RVE models according to the actual microstructure of composite to evaluate the effect of thermal residual stress on CTE, as illustrated in figures 11(e)–(h). By studying the temperature-dependent linear elastic and elastoplastic matrix material behavior, they found that the presence of thermal residual stress affects the effective CTE in the heating process. The contact status of the reinforcing particles greatly impact the thermal expansion behavior of the composite. The predicted CTE using RVE with overlapping microstructure is in accordance with the measured CTE. For RVE with separated or contact particles, the predicted CTE is higher than the experimental one. The presence of voids reduces the effective CTE of the metal matrix composite. Compared to the theoretical calculations, FEM provides a more intuitive prediction from a microscopic perspective [152, 153]. The effects of non-uniform stress distribution, thermal residual stress, matrix plastic deformation and microstructure defects in the composite are comprehensively considered through reasonable modeling methods [154]. Therefore, the FEM tends to show more accurate predictions.

While effectively improving the strength and CTE of the Cu matrix, it is also important to maintain good conductivity. For metal matrix composites, the thermal and electrical conduction process is determined by the matrix and the reinforcing phase. In metals, electron conduction is the main heat transfer mechanism; while for ceramics, the conduction mechanism is mainly phonon conduction. In comparison, the conductivity of ceramics in metal matrix composites is negligible and the presence of ceramics largely hinders the electronic conductivity in the metal matrix. The conductivity of composite is affected by microstructural features such as the type and volume fraction of the ceramic phase, particle size, and interfacial barrier. In fact, the matrix of the composite is the main conduction path and metal conduction mainly relies on current carrier electron transmission. Lattice defects, impurities and lattice vibrations in the matrix would scatter free electrons, which is similar to the process of electronic heat transfer. As a result, the electrical conductivity of metal is approximately proportional to the thermal conductivity. The metal electronic thermal conductivity (γ_e) and electrical conductivity (η) can be related by:

$$\begin{align}{L_0} = \frac{{{\lambda _{\text{e}}}}}{{{\eta _{\text{T}}}}} = \frac{{{\pi ^2}}}{3}\frac{{{\lambda _{\text{B}}}}}{{{e^2}}}\end{align} \tag{ 17 }$$

where λ_B is the Boltzmann constant, and L₀ is a constant, known as the Lorentz constant. In order to more directly reflect the effect of reinforcement particles on the conductivity of the metal matrix, the following theoretical models are commonly employed to predict the thermal conductivity of metal matrix composites [125, 155]. Herein, the electrical conductivity of composite is proportional to its thermal conductivity, so it will not be described here.

• (1)  
  Maxwell model

The Maxwell model is the most classic theoretical model for predicting the thermal conductivity of composites, which is expressed as:

$$\begin{align}{{{\gamma }}_{\text{c}}} = {{{\gamma }}_{\text{m}}}\frac{{2\left( {1 - {V_{\text{p}}}} \right) + \left( {{{{\gamma }}_{\text{p}}}/{{{\gamma }}_{\text{m}}}} \right)\left( {1 + 2{V_{\text{p}}}} \right){\text{ }}}}{{\left( {2 + {V_{\text{p}}}} \right) + \left( {{{{\gamma }}_{\text{p}}}/{{{\gamma }}_{\text{m}}}} \right)\left( {1 - {V_{\text{p}}}} \right){\text{ }}}}\end{align} \tag{ 18 }$$

where γ is the thermal conductivity. This model assumes that the reinforcement particles are spherical, and it ignores the effect of interfacial thermal resistance on the thermal conductivity of the composite. This model takes into account the thermal conductivity of both the matrix and the reinforcing phase in the composite and the effect of the reinforcing phase content on the thermal conductivity of the composite material.

• (2)  
  Hasselman–Johnson model

The Hasselman–Johnson model, also known as effective medium approximation, is expressed as:

$$\begin{align}{\gamma _{\text{c}}} = {\gamma _{\text{m}}}\left[ {\frac{{2\left( {1 - {V_{\text{p}}}} \right) + \left( {{\gamma _{\text{p}}}/{\gamma _{\text{m}}}} \right)\left( {1 + 2{V_{\text{p}}}} \right) + 4\left( {{\gamma _{\text{p}}}/Dh} \right)\left( {1 - {V_{\text{p}}}} \right)}}{{\left( {2 + {V_{\text{p}}}} \right) + \left( {{\gamma _{\text{p}}}/{\gamma _{\text{m}}}} \right)\left( {1 - {V_{\text{p}}}} \right) + 2\left( {{\gamma _{\text{p}}}/Dh} \right)\left( {2 + {V_{\text{p}}}} \right)}}} \right]\end{align} \tag{ 19 }$$

where D is the diameter of the reinforcement, h is the thermal boundary conductance. This model takes into account the influence of interfacial thermal resistance and particle dimensions on thermal conductivity. Interfacial thermal resistance is caused by physical differences between phases, defective mechanical or chemical adhesion at the interface, and mismatches in the CTE.

If D → ∞, equation (19) is the equation of Maxwell model, which is equivalent to ignoring the interface thermal barrier.

Setting D → 0, equation (19) becomes:

$$\begin{align}{\gamma _{\text{c}}} = {\gamma _{\text{m}}}\frac{{1 - {V_{\text{p}}}}}{{1 + 0.5{V_{\text{p}}}}}\end{align} \tag{ 20 }$$

where V_p equals the porosity. This is equivalent to the situation where the particles in the metal matrix are pores.

The above theoretical models have been well applied in a large number of studies [125, 156]. The prediction results by theoretical models can well reflect the heat transfer capacity of the metal matrix composite and explore the effect of various factors on the thermal conductivity. Moreover, like the prediction model for CTE, ceramic content is also the most important influencing factor, and the conductivity decreases as increasing the ceramic content. In addition, the theoretical values of the metal matrix composite calculated by the models often differ from the experimental results. The initial assumptions of each model still have certain defects, and the actual internal conditions of metal matrix composites cannot be fully and objectively reflected by theoretical models. Therefore, the thermal conductivity of Cu matrix composites is usually far below the theoretical expectations [157]. The work of Molina et al [158] and Chu et al [159] pointed out that the actual thermal conductivity of Cu decreases from 389 W (m·K)⁻¹ to about 70 W (m·K)⁻¹ due to the scattering of electrons by the crystal defects, sub-grains and lattice distortion induced by dissolved solute element in matrix. The selected area electron diffraction (SAED) patterns shown in figure 12 also demonstrate that the Si element is solidly soluble in the Cu–Si layer and Cu matrix. Although considering the low thermal conductivity of the matrix, the theoretical results are still higher than the actual results, as shown in figure 12(a). There are still other factors that govern the thermal conductivity of composites. As shown in figures 12(b) and (c), interfacial reactions have occurred and an evident graphite layer and Cu–Si layer appear between the Cu matrix and SiC phase. This induces high interfacial thermal resistance and leads to low thermal conductivity of SiC/Cu composites.

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In conclusion, there are many factors that affect the conductivity of composites. The refined grain size increases the area of grain boundary and phase boundary in the composite, which would intensify the interfacial scattering to electrons and hence decrease the conductivity of composite. Besides, the residual stress and plastic strain in the composite caused by the difference of CTE between the ceramic particles and metal matrix also negatively affect its conductivity. On this basis, research and development of the more applicable and comprehensive theoretical models is also one of the future research directions. Notably, the MAX phase as an advanced ceramic material is a competitive reinforcement in Cu matrix composites [160, 161]. These ternary carbides or nitrides (e.g. Ti₃AlC₂, Ti₃SiC₂, etc) combine the properties of ceramics and metals, exhibiting high conductivity, mechanical properties, good thermal shock resistance, excellent oxidation resistance and corrosion resistance owing to their unique atomic bonding and crystalline structure [162–165]. Recently, extensive work has been done to explore the preparation process and the conduction and mechanical properties of Cu-MAX composites. The results show that the MAX phases are efficient to strengthen the mechanical properties of Cu matrix composites, without a drastic reduction of their conductivity [166–168]. Nevertheless, the research of Cu-MAX composites is still in its infancy, and more in-depth research and exploration are urgently needed.

It was reported [19, 169] that the content of ceramic phase directly determines the comprehensive properties and the potential application fields of Cu matrix composites. As shown in figure 13, as the ceramic content increases, the strength of the composites tends to increase to a certain degree, by sacrificing the ductility. The FEM results [170] also demonstrated that both the elastic modulus and yield strength of the TiB₂/Cu composites increase with increase in the particle content while the elongation decreases, as illustrated in figure 14(a). Figures 14(b) and (c) show the total stress and average stress on the ceramic particles with different particle contents. The total stress on particles increases with the increase in the particle content, while the average stress on particles is maintained approximately the same. Therefore, the ceramic particles with higher content can sustain the load more effectively and enhance the strength of the composite. However, as the ceramic particle content increases, the spacing between ceramic particles gradually decreases and a large amount of aggregation takes place. As shown in figures 14(d) and (e), large areas of interfacial damage occur in the RVEs, and the damage area of the Cu matrix increases with the increase of particle content. This results in more pronounced stress concentration in the Cu matrix and the composites with high particle content are more prone to microcracking and rapid propagation into the main cracks. Therefore, the load is not effectively transferred from the matrix to the ceramic particles, which reduces the ductility of the composite.

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With regard to the CTE and conductivity, the content of ceramic particles performs a crucial role in determining the CTE and conductivity of ceramic particle reinforced Cu matrix composites. As described in sections 3.2 and 3.3, both the CTE and conductivity of composites decrease as increasing the ceramic content. However, the increase of ceramic content in the composite tends to cause agglomeration of particles, which largely weakens the strengthening effect of particles. Accordingly, a more suitable ceramic content is required to obtain superior comprehensive properties (i.e. maintaining a good combination of mechanical performance and CTE and conductivity) under different preparation processes.

In the process of introducing ceramic particles into a metal matrix, the size of the ceramic particles also has a great influence on the comprehensive performance of the composite. Appropriate particle size is of great significance to further optimize the comprehensive performance of metal matrix composites. Generally, the size of ceramic particles can be classified into micron (1–100 μm), submicron (0.1–1 μm) and nanoscale (<100 nm). As shown in figure 15, the vicinity of micron particles is beneficial to form particle deformation zone, and the area with high dislocation density can be generated surrounding submicron particles due to pinned dislocations and deformation mismatch between the matrix and the particles. Meanwhile, the introduction of fine particles (i.e. in nanoscale or submicron) may delay or impede grain growth via a pinning effect on the grain boundaries [171]. However, when micron-sized or nano-sized particles are introduced into the metal matrix composites, the high particle content can easily lead to particle agglomeration, which significantly deteriorates the strength and ductility of the composite. Compared with the micron-sized particles, the nano-sized particles in metal matrix has much higher agglomeration propensity owing to the large specific area and van der Waals force. The mixture of micron-sized and nano-sized particles was reported to have a more apparent strengthening ability than monolithic size particles [172, 173]. Tian et al [174, 175] successfully prepared bimodal-sized (micron + nanoscaled) TiC/Al–Cu composites by incorporating micro-sized and nano-sized TiC. The composites with bimodal-sized TiC possess higher strength, ductility and creep resistance compared with the composites with monomodal-sized particles, which is ascribed to more significant precipitation strengthening and grain refinement of the bimodal-sized particles.

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When a metal matrix composite contains only single-scale particles and the particles are evenly distributed, the composite with relatively smaller particle size demonstrates better mechanical properties. Owing to the difference in CTE between the ceramic particles and the matrix, local deformation in the interfacial region and high-density dislocations are produced in the composites during the preparation process, leading to dislocation strengthening. When the content of the reinforced particles is constant, the increased dislocation density around the particles and the strain gradient are noted in the composite with smaller particle sizes. Such a phenomenon further enhances the dislocation strengthening effect of the composite, thereby increasing its load-bearing capacity. Ma et al [176] simulated the effect of particle size on the tensile behavior of composites by establishing the microstructure-based RVE models. The simulated stress–strain curves with different particle sizes are shown in figures 16(a) and (b), and the average S11 (stress in the X-axis) stress of Al₃Ti particles and metal matrix are compared in figure 16(c). For the same content of particles, the yield strength and elongation of the composite are enhanced slightly as decreasing the particle size. Meanwhile, the Al₃Ti particles with smaller size can bear higher S11 stress during the initial deformation. After further loading, the stress on particles remains constant, while the strength of the matrix keeps increasing. Therefore, smaller particles tend to 'be strengthened' faster and bear higher mean stress than the larger particles. Figure 16(d) shows the damage of the matrix at different moments of strains. Under the same nominal strain, the damage in the matrix with small particles evolves slowly and uniformly, while the damage extends rapidly surrounding the large ones. Therefore, cracks are always initiated adjacent to large particles in the aggregation area, due to that large particles are more prone to deformation and lead to stress and strain concentrations. Likewise, Yan et al [177] conducted the similar study using FEM in combination with Taylor-based theory of nonlocal plasticity. Both numerical and experimental results indicated that the flow stress and work hardening rate of the composites increase as decreasing the particle size when the content of the reinforcements is constant. This is mainly attributed to the fact that the strain gradient in the matrix increases as the particle size decreases.

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Furthermore, the thermophysical performance and electrical conductivity of metal matrix composites are also closely associated with the size of reinforced particles. Generally, the increase in particle size in metal matrix composite would increase its CTE, thermal conductivity and electrical conductivity [125, 157, 178, 179]. The decrease in particle size increases the dislocation density of the matrix, which increases the yield strength of the composite. On this basis, the thermal stress generated in the heating process is more difficult to relax and the thermal residual stress in the composite increases, which hinders the thermal expansion of the matrix. Therefore, as the particle size decreases, the CTE of the metal matrix composite decreases. At constant particle content, smaller particle size leads to more particles and smaller particle spacing in the composite, which can more effectively hinder the expansion of matrix at high temperature. Thus, small particle size in a composite would significantly reduce the increase rate of CTE with temperature [180].

For the conductivity of metal matrix composites, Efe et al [181] compared the influence of different contents and sizes of SiC particles on the relative density and electrical conductivity of Cu matrix composites. As shown in figure 17, the relative density and electrical conductivity of SiC/Cu composites increase as increasing the SiC particle size. In fact, the thermal conductivity and electrical conductivity of the material mainly depend on the movement of electrons in the matrix. However, the existence of insulating ceramic particles and scattering at the interface hinder the movement of electrons. With the decrease in particle size, the hindrance effect of particles is further aggravated and the interface proportion between particles and matrix increases, which significantly reduces the thermal and electrical conductivity of composites.

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During the preparation of Cu matrix composites, the morphology of the ceramic particles also directly affects the stress distribution of the surrounding metal matrix, which then reflects the difference in the mechanical performance of the composites. In general, the failure mode of a composite varies as modifying the particle morphology. Compared with the spherical particles, the reinforcement particles with sharp corners are more effective in pinning dislocations and have the stronger initial strain strengthening effect in composites [182, 183]. The higher load-bearing capacity is provided by the angular particles. However, both experimental and numerical simulation results [98, 183] indicated that voids tend to nucleate preferentially at the corners of the particles when the composite is loaded. Therefore, the metal matrix composites reinforced with spherical particles have larger ductility but slightly lower yield strength and work hardening rate are than those reinforced with angular particles.

Wu et al [151] developed a novel model of composite with realistic microstructure to investigate the effect of particle morphology and distribution on the deformation behavior of metal matrix composites. The deformation of the matrix is concentrated near the crack tip, which results in the destruction of the matrix when its equivalent plastic strain reaches a threshold value. As shown in figures 18(a) and (b), the cracks propagate along the direction of high stress in the matrix. Microcracks of the particles occur at corners, in which stress concentrations are prone to occur, and the matrix breaks near the crack tips. Then, the main crack passes through the particle agglomeration zone where microcracks are accumulated, while no significant particle debonding is detected and few particles fracture along the crack side (figures 18(c)–(f)). The change of the ceramic particle morphology affects the stress–strain response of the composites and the stress–strain distribution of the surrounding matrix [184, 185]. As shown in figure 18(g), with the increase in particle roundness, both the elastic modulus and yield strength of the composite decrease, while the fracture stress and strain increase. This is attributed to that the stress concentration generated at the sharp corners facilitates the improvement of elastic modulus and yield strength in the metal matrix. However, after yielding, the stress concentration at the sharp corners of the particle leads to premature softening and cracking of the matrix. As seen from figures 18(h)–(j), when the particles have larger roundness, the stresses at the sharp corners of TiB₂ particle are closer to the internal stresses, the stress distribution on the particles is more even, which obviously optimizes the stress concentration at the corner [170].

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In metal matrix composites with the same particle content, type and size, the particle morphology has little effect on the conductivity and CTE of the composites. Generally, the influence of particle morphology on the performance of composites is mainly attributed to the differences in localized stress–strain and electron conduction paths in the matrix. The previous work from the current team [100] demonstrated that spherical particles are more favorable to the transfer of thermal compare to hexagonal columnar particles, as illustrated in figure 8(d₃, d₄). Composites doped with spherical particles demonstrate improved thermal conductivity because the spherical particles enable a more uniform distribution of heat flow and reduce the accumulation of heat flow at sharp corners. At the present stage, there is a lack of targeted study on the influence of ceramic morphology on the thermophysical properties and electrical conductivity of metal matrix composites, and further exploration on this topic is still needed.

In ceramic particles reinforced Cu matrix composites, the interface between ceramic particles and metal matrix is a bridge for particles to fully exert their reinforcing effect. Strong interfacial bonding is the key to the development of composites with excellent comprehensive performance [186–188]. The matrix/ceramic interface is generally divided into mechanical bonding and chemical bonding [189]. Compared to mechanical bonding, the chemical bonding is more critical for particle reinforced composites. The chemical bonding enables the atoms of the particles to contact the atoms of the matrix, which facilitates the exchange of electrons at the interfaces [190]. It is beneficial to weaken the interface effect on the scattering of electrons, thereby improving the thermal conductivity and electrical conductivity. However, the weak interface is prone to initiate cracks and then causes the component failure under loading, which more likely cause interface fracture, ceramic particles shedding and interface corrosion damage, thus weakening the strengthening effect of ceramic particles [191, 192]. Overall, improved bonding would increase heat transfer, electrical conductivity and facilitate load transfer between ceramic particles and Cu matrix. Synergistic enhancement of the Cu matrix with better network structure and stronger interfacial bonding is responsible for the improvement in composite properties [193, 194]. Zhang et al [195] pointed out that the enhanced interface bonding facilitates the reduction of CTE and improves dimensional stability of composites. The plastic deformation induced in the matrix around the interface is restrained by the reinforcement. When the interfacial bonding is stronger, the deformation is smaller, which is more favorable to limit the relaxation of residual stress.

Unfortunately, most ceramic particles have poor wettability with the Cu matrix and form a high contact angle, which results in weak interfacial bonding as illustrated in figures 19(a) and (b) [14, 196]. At the present stage, a variety of methods have been adopted to enhance the interfacial bonding between the ceramic phase and the Cu matrix, mainly including the surface metallization of ceramic and the matrix alloying. Furthermore, the in-situ synthesis of the ceramic phase in the matrix mentioned in section 2.4 is a more promising method to improve interfacial bonding. Tian et al [197] pretreated the surface of boron carbide (B₄C) particles by electroless Cu plating, and then mixed the Cu-coated B₄C with Cu-coated graphite to prepare a novel Cu-matrix self-lubricating composite. Compared with the composite reinforced by uncoated B₄C, Cu-coated B₄C reinforced Cu/graphite composite exhibit lower porosity, higher wear resistance and compressive strength owing to the improved wettability and interfacial bonding between the Cu-coated particles and matrix. Han et al [102] prepared reduced Cu-coated WC core–shell precursor powders by intermittent electrodeposition and SPS. This new preparation technique reduces the agglomeration of WC particles and enhances the interfacial bonding between the WC particles and the Cu matrix, which further improves the mechanical properties of the composite. Xiang et al [198] doped a small number of Ti element to optimize the interfacial bonding between the TiC and the Cu matrix and to enhance the strength of the composite. As shown in figures 19(c) and (d), the cracks propagate almost entirely along the edges of the TiC particles, and the Cu matrix does not show significant plastic deformation. This results from the poor bonding between TiC and the Cu matrix, which cannot achieve the load transfer process from the Cu matrix to the TiC particles. By contrast, for the forged 10%TiC/Cu-2%Ti samples, the interface between ceramic particles and the Cu matrix is significantly enhanced. Especially after annealing, the Cu matrix experiences significant plastic deformation and all the cracks appear within the Cu matrix or the TiC particles, suggesting an excellent interfacial bonding between the ceramic particles and the Cu matrix. During sintering process, Ti reacts with TiC particles to form non-stoichiometric TiC_x (x < 1). Meanwhile, TiC dissolves to form non-stoichiometric TiC_x and reprecipitates through the reaction of C and Ti during the succedent sintering process. Therefore, the conversion of stoichiometric TiC to non-stoichiometric TiC_x and the formation of non-stoichiometric TiC_x significantly enhance the bonding strength at the interfaces. This optimization of the interfacial bonding between the TiC particles and the Cu matrix enhances the strength and hardness of the composites by more than 40%.

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