Abstract
Copper matrix composites reinforced with 1, 3, 5, 7 vol.% Cu-coated SiC whiskers of consistent orientation (SiCw/Cu) were prepared by powder metallurgy and hot extrusion. The microstructure of composites was investigated by scanning electron microscopy. The SiC whiskers were arranged along the direction of hot extrusion and distributed uniformly. The composites were fabricated into specimens with different whisker orientations, and their electrical conductivity was tested. The effects of SiC whiskers orientation and content on the electrical conductivity of composites were investigated through experiment. Results show that the SiC whiskers content was the major factor affecting the electrical conductivity of the composites. With increasing SiC whisker orientations angel, the electrical conductivity of composites is improved. The electrical conductivity model has been established by taking into account the SiC whiskers content, whisker orientation and microstructure parameters, and the results were in good agreement with experimental data.
Graphical abstract: Copper matrix composites reinforced with SiC whiskers of consistent orientation were prepared. The orientation of SiC whiskers changes from 0∘ to 90∘, resulting in electrical conductivity anisotropy of composites.
1 Introduction
Copper matrix composites have high strength at the room, and the electrical and thermal conductivity close to pure copper, which are widely used as high voltage dynamic/static contact, electromagnetic gun orbit, electric resistance welding electrodes, etc. [1, 2, 3, 4, 5]. Ceramic particles and whiskers with excellent thermal stability and strength are used for reinforcing copper matrix composites [6, 7, 8]. However, ceramic particles can improve the strength while reduce the plasticity of metal matrix composites [9]; Whiskers can enhance plasticity of copper matrix composites, especially at high temperatures [10], which is beneficial to the durability-damage tolerance design of composites [11]. This is due to the fact that whisker has less defects (voids, dislocations, grain boundaries, etc.), so that their strength are close to the theoretical value of intact crystals. Furthermore, whisker has high aspect ratio characteristics, which can effectively enhance the strength of metal matrix composite [12, 13, 14].
At present, most of the reported literature on whisker/fiber reinforced composites is about the effect of whisker/fiber types and interface optimization on its mechanical properties and conductivity [15, 16, 17, 18]. Results show that the strength and ductility of composites are greatly improved with SiC whiskers of consistent orientation [19]. The surface modifying can evidently enhance strength and conductivity of copper matrix composites reinforced with whiskers [12, 20]. In fact, the orientation of whiskers also can affect the electrical conductivity greatly. Klinski-Wetzel had found that the Cr particles (aspect ratio>1) alignment leads to the electrical conductivity anisotropy of Cu-Cr composites [4]. It was further supported by Yang [21] with finding that the electrical conductivity parallel along the CNTs length direction was higher than that of vertical to CNTs length direction. However, there is few literatures reported on electrical conductivity of copper matrix composite reinforce with different orientation whiskers. Besides, the established models on electrical conductivity of copper matrix composite are mostly based on various simplifying assumptions, which just consider parameters of volume fraction, electrical conductivity of each phase [22, 23]. And electrical conductivity models are applicable to isotropic composites. Therefore, value of prediction is greatly deviated from the experimental data. It is necessary to establish an anisotropic conductivity model for copper matrix composites.
In the paper, we investigated the effects of different SiC whiskers orientation on the microstructure, electrical conductivity of SiCw/Cu composites reinforced with SiC whiskers. SiC whiskers consistent orientation of SiCw/Cu composites was fabricated by powder metallurgy and hot extrusion. The composites were fabricated into specimens with different whisker orientations, and their electrical conductivity was tested. Considering the effects of orientation and volume fraction of SiC whiskers on the electrical conductivity, a model for predicting the electrical conductivity of SiCw/Cu composites was established. The results show that electrical conductivity of SiCw/Cu composites can be predicted by the model.
2 Experiment
2.1 Raw powders
Commercially available SiC whiskers (purity 99.0 wt. %, average diameter and length is 0.5 μm, 10 μm, respectively) and Cu powder (purity 99.8 wt. %, with a mean size of 75 μm). The SEM morphologies of SiCw and Cu powder are shown in Figure 1.
SEM morphology of (a) Cu power, (b) uncoated SiC whiskers, (c) Cu-coated SiC whiskers, (d) XRD diffraction patterns of SiCw coated before and after
2.2 Preparation of Cu coated SiC whiskers and composite powders
The Cu coated SiC whiskers were fabricated using an electroless deposition (ED) method [24]. Table 1 shows electroless deposition chemical composition. Firstly, the cleaned SiC whiskers were put into sensitizing solution (SnCl2 20 g/L, HCl 25 mL/L) with electromagnetic stirring for 30 min. And secondly, the sensitized SiC whiskers were added into the Tollens’ reagent with electromagnetic stirring for 30 min. After then, the activated SiC whiskers were added into the ED bath with stirring. The formaldehyde and NaOH were added into the solution, and the pH of solution was maintained at 11.5-12.5 during the reaction. After the deposition was completed, the Cu-coated SiCw were washed to neutral with deionized water as shown in Figure 1c. The improvement of the wettability and density of SiC whiskers were beneficial to the homogeneously dispersion of SiC whiskers.
Electroless deposition chemical composition
| Chemical composition | Quantity |
|---|---|
| CuSO4·5H2O (g/L) | 12 |
| C4O6H4KNa (g/L) | 35 |
| Formaldehyde (ml/L) | 18 |
| Activated SiCw (g/L) | 4 |
| pH | 11.5-12.5 |
| Temperature (∘C) | 55-60 |
In order to obtain mixed powders with different SiC whiskers contents, the powders were placed into an ethanol solution with heating and stirring. Then, the suspensions become slurry, which dried in vacuum dryer for 4 h at 60∘C. Mixing was carried out on a QQM/B light ball mill for 24 h and a ball-to-batch ratio of 1:1. The mixed powders with SiC whiskers content of 1, 3, 5, 7 vol.% were prepared, respectly.
2.3 Fabrication of SiCw/Cu composites
The mixed powders were compacted by cold isostatic press at the pressure of 210 MPa, the sample was ø 50 mm×50 mm block. After then, the samples were sintered at 950∘C for 90 minutes under hydrogen atmosphere in the tube furnace, and frozen to room temperature in the furnace. The sintered samples were hot extruded into ø 14.5 mm rods at 900∘C.
2.4 Characterization tests
The density of SiCw/Cu composites was measured by Archimedes drainage method, and the relative density was calculated. Phase analysis was characterized by X-ray diffraction. The microstructures of the powders and SiCw/Cu composite were observed by Scanning electron microscope. Figure 2a shows the hot extrusion schematic diagram. The orientation of SiC whiskers was parallel to the extrusion direction by hot extrusion. This is a unique method to study the influence of whiskers orientation on the electrical conductivity of the SiCw/Cu composites, sampling as shown in Figure 2b, and the samples were ø 13 mm×3 mm. Measurements of the electrical conductivity were used by the eddy current test instrument with a ø 8 mm measuring sensor at a frequency of 60 KHz.
Schematic diagram: (a) the extrusion process experimental set-up, (b) extruded billet and samples, (c) electrical conductivity measurement method
3 Results and discussion
3.1 Microstructures and density of SiCw/Cu composition
Figure 1 shows the morphologies and the XRD diffraction patterns of SiC whiskers before and after coating Cu. It is noted that the surface of the uncoated SiC whiskers are clean and smooth (Figure 1b) and the surface of the Cucoated SiC whiskers is rough (Figure 1c). Figure 1d shows the XRD diffraction patterns of SiC whiskers before and after coating Cu. The peaks of Cu can be clearly detected from the XRD patterns of Cu-coated SiC whiskers. The results show that required Cu-coated has been deposited on SiC whiskers, and without formation of Cu2O and other byproducts.
Figure 3 shows the microstructure of SiCw/Cu composites with different volume fraction in all directions after hot extrusion. The black long rod is SiC whisker with parallel to the hot extrusion direction. The SiCw/Cu composites have a compact microstructure without defects such as pores. However, when the SiC whiskers are more than 5 Vol.%, the SiC whiskers agglomeration phenomenon can be observed. Therefore, the higher the content of SiC whiskers, the easier it is to agglomerate and the worse the performance of the composites.
SEM morphology of the extruded SiCw/Cu composite with different volume fraction: (a) 1 vol.%, (b) 3 vol.%, (c) 5 vol.%, (c) 7 vol.%. ED, ND, TD is extruding direction, normal direction, and transverse direction, respectively
The relative density of the SiCw/Cu composites before and after hot extrusion is shown in Figure 4. The relative density of the sintered SiCw/Cu composites decreases from 91.5% to 81.0% with increasing the SiC whiskers content. After hot extrusion, the relative density of SiCw/Cu composites is greater than 96.2%, which is consistent with the law of that of sintered samples in Figure 4. The relative density of SiCw/Cu composites has been increased 8.6%~18.7% compared with that of sintered state. In the hot extrusion process, the agglomerate SiC whiskers can be dispersed uniformly due to the rapid flow of copper matrix, and voids left after sintering can also be filled rapidly, which greatly improves the SiCw/Cu composites density. Additionally, the copper atomic are deposited on the surface of SiCwhiskers in the ED process, which fills the pores between copper powder and SiC whiskers that can not be filled. It also helps to improve the density of composite materials.
Relative density of SiCw/Cu composites
SiCwhiskers are added to the copper matrix composite as a second phase, which are distributed around or gaps between the copper particles in the mixing process. During the densification process, they hinder the movement of copper phase to fill pores, and weaken the deformation, diffusion and rearrangement between copper particles, especially in the case of high SiC whiskers content [25, 26].
3.2 Electrical conductivity anisotropy of composites
Figure 5 displays the electrical conductivity of SiCw/Cu composites with different SiC whiskers content. As seen from Figure 5, the electrical conductivity of the SiCw/Cu composites decreases with increasing SiC whiskers content, but they are higher than 76.5 %IACS. In general, the electrical conductivity of copper matrix composites is related to the microstructure, density and content of the composites, etc. There are two main factors affecting the electrical conductivity of SiCw/Cu composites. On the one hand, the electrical conductivity of SiC whiskers is lower than that of copper. With the increase of SiC whiskers volume fraction, the copper matrix participating in conductivity decreases. The electrical conductivity of the SiCw/Cu composites decreases. On the other hand, the aspect ratio of SiCwhiskers leads to the microstructure and electrical conductivity anisotropy of the composites, as shown in Figures 3 and 5.
The electrical conductivity of cross and longitudinal sections of SiCw/Cu composites with different SiC whiskers content
During hot extrusion process, the SiC whiskers changes from a random arrangement to align along the axial direction, as shown in Figure 3. It is conducive to study the influence of SiC whiskers orientation on electrical conductivity anisotropy of composites. The electrical conductivity of the cross section (θ=0∘C) and the longitudinal section (θ=90∘C) was investigated. The results show that the electrical conductivity of longitudinal section is higher than that of cross section, that is, when the current direction is parallel to SiC whiskers, the electrical conductivity is higher, as shown in Figure 5. The aligned CNTs reinforced ceramic composites also leads to electrical conductivity anisotropy, and the values of electrical conductivity along the length direction of the CNTs is higher [21]. The results are consistent with those of SiCw/Cu composites. For composites with different SiC whiskers volume fractions, the electrical conductivity increases with increasing the angle θ, as shown in Figure 6. Therefore, the knowledge of conductive mechanism can be used to prepare copper matrix composites, which can achieve a good match between electrical conductivity and mechanical properties.
Relationship among electrical conductivity, SiC whiskers spatial distribution and volume fraction in the SiCw/Cu composites
Figure 7 displays a schematic diagram of the electronic path through the SiCw/Cu composite conductor under the action of electric field. We assume that the resistance in the material is caused by the interaction of drifting electrons
Schematic representation of the electron path through the SiCw/Cu composite conductor under the action of an electric field
with some defects in the material. (Such as impurity atoms, second phase, grain boundaries, etc.).
The electrical conductivity σ of metal can be deduced by classical electronic theory [27].
Where, τF is a relaxation time (the average time between two consecutive collisions), n is the number of electron (per unit volume), e is the elementary electric charge, m is the mass of an electron. As shown in Figure 7, the volume fraction and spatial distribution of SiC whiskers affect τF. When content of SiC whiskers is fixed, the aligned SiC whiskers are parallel to axial direction. It is conducive to reduce the consecutive collisions between electrons and SiC whiskers, so the electron relaxation time is large, and the electrical conductivity increases. On the contrary, when the aligned SiC whiskers is vertical to axial direction, the consecutive collisions between electrons and SiC whiskers increase, so the electron relaxation time decreases, and the electrical conductivity decreases. Figure 7 and Eq. 1 show that the electrical conductivity is large for a large relaxation time τF.
3.3 Establishment of the electrical conductivity model
The electrical conductivity of metal materials mainly depends primarily on the composition, structure and defects of the materials. The resistivity of copper matrix composites mainly comes from electron scattering, including phonon scattering, impurity/reinforced phase scattering, dislocation scattering and interface scattering [28, 29, 30, 31]. If the content is constant, the electron scattering effect caused by the reinforced phase is much lower than that of atoms (impurities) in solid solution, which can be neglected [5]. The effects of phonon scattering and dislocation scattering on the resistivity of composites are also minimal [28, 30]. However, the interface scattering is a main factor affecting resistivity of composites. It is related to the volume fraction, size, shape and distribution of reinforced phases and microstructure.
The classical rule of mixture (ROM) (Eq. 2) [32] and Maxwell’s equation (Eq. 3) [33] predicted that the electrical conductivity of SiCw/Cu composites is larger than the experimental data, as shown in Figure 8. They only consider the electrical conductivity and volume fraction of each phase. Maxwell model is applicable to isotropic composites. Therefore, the models are not enough to accurately predict the electrical conductivity. Besides the electrical conductivity and volume fraction of the each phase, the microstructure parameter (np) is very important for predicting the electrical conductivity of copper matrix composites. It is assumed that the microstructure parameter is the characteristic parameters and arrangement of phases.
The calculated electrical conductivity of SiCw/Cu composites in comparison with the experimental data
Where vm is the volume fraction of SiC whiskers, σw (about 0 %IACS) and σm (100 %IACS) are the electrical conductivity of SiC whiskers and copper.
Fan [34] proposed an electrical conductivity model based on topological microstructure of composites and the equivalent electrical circuit analysis technique. The electrical conductivity of composites can be predicted by combining the electrical conductivity, volume fraction of each phases and microstructure parameter (np). The electrical conductivity of SiC whiskers is significantly less than that of copper,which is almost zero. The electrical conductivity model of SiCw/Cu composite the can be expressed as:
Where σc is the electrical conductivity of composites, np is the microstructure parameter. The smaller the value of np (np ≥ 1), the more continuous of the matrix. It should be emphasized that in order to accurately predict the electrical conductivity of composites, the np must be measured experimentally. The experimental data are substituted into Eq. 4, and the np value obtained can be expressed by Eq. 5, the np is given as:
Where, θ (0∘≤ θ≤ 90∘) is the angle between whisker orientation and vertical direction. When np(0∘)=3.5 and np(90∘)=2.5, can describe two extreme cases distribution of whiskers in copper matrix, as shown in Figure 8. The model can well reflect the relationship among electrical conductivity, microstructure and volume fraction of SiCw/Cu composites.
The electrical conductivity of composites with different orientation angles (0∘, 30∘, 45∘, 60∘, 90∘) were calculated and compared with experimental data in Figure 9. The electrical conductivity of composites is between two extreme cases, and its mathematical expression predicts the electrical conductivity of composites more accurately than Eq. 2 and 3.
The electrical conductivity of composites with different SiC whiskers orientation angles was calculated and compared with experimental data
4 Conclusions
SiCw/Cu composites with volume fraction of 1~7% were prepared by powder metallurgy and hot extrusion. The microstructure and electrical conductivity were investigated. The density and electrical conductivity of composites are closely related to the SiC whiskers volume fraction. They decrease with the increase SiC whiskers volume fraction. The consistent orientation of SiC whiskers leads to microstructure and electrical conductivity anisotropy of the composites. The electrical conductivity of the longitudinal section is higher than that of the cross section. Based on the microstructure parameters and volume fraction, a simple SiC whiskers reinforced copper matrix composite electrical conductive model was established, and the results were in good agreement with experimental data.
Acknowledgement
This work was supported by the National Natural Science Foundation of China (Grant Nos. U1502274 and 51605146), China Postdoctoral Science Foundation (No.2018M632769), and Henan Plan Project for College Youth Backbone Teacher (2018GGJS045)
References
[1] Zhang X.H., Zhang Y., Tian B.H., An J.H., Zhao Z., Volinsky A.A., Liu Y., Song K.X., Arc erosion behavior of the Al2O3-Cu/(W, Cr) electrical contacts, Compos. Part B, 160, 110-118.10.1016/j.compositesb.2018.10.040Search in Google Scholar
[2] Song K.X., Xing J.D., Dong Q.M., Liu P., Tian B.H., Cao X.J., Optimization of the processing parameters during internal oxidation of Cu-Al alloy powders using an artificial neural network, Mater. Des., 2005, 26, 337-341.10.1016/j.matdes.2004.06.002Search in Google Scholar
[3] Shojaeepour F., Abachi P., Purazrang K., Moghanian A.H., Production and properties of Cu/Cr2O3 nano-composites, Powder Technol., 2012, 222, 80-84.10.1016/j.powtec.2012.02.001Search in Google Scholar
[4] Klinski-Wetzel K.V., Kowanda C., Heilmaier M.,Mueller F.E.H., The influence of microstructural features on the electrical conductivity of solid phase sintered CuCr composites, J. Alloys Compd., 2015, 631, 237-247.10.1016/j.jallcom.2014.12.249Search in Google Scholar
[5] Guo X.H., Song K.X., Liang S.H., Zhou Y.J., Wang X., Relationship between the MgOp/Cu interfacial bonding state and the arc erosion resistance of MgO/Cu composites, J. Mater. Res., 2017, 32, 3753-3760.10.1557/jmr.2017.321Search in Google Scholar
[6] Zhang Z.G., Sheng Y.Y., Xu X.W., Li W., Microstructural features and mechanical properties of in situ formed ZrB2/Cu composites, Adv. Eng. Mater., 2015, 17, 1338-1343.10.1002/adem.201400532Search in Google Scholar
[7] Fathy A., Investigation on microstructure and properties of Cu-ZrO2 nanocomposites synthesized by in situ processing, Mater. Lett., 2018, 213, 95-99.10.1016/j.matlet.2017.11.023Search in Google Scholar
[8] Akbarpour M.R., Mousa M.H., Alipour S., Microstructural and mechanical characteristics of hybrid SiC/Cu composites with nano- and micro-sized SiC particles, Ceram. Int., 2019, 45, 3276-3283.10.1016/j.ceramint.2018.10.235Search in Google Scholar
[9] Shalabya E.A.M., Churyumov A.Y., Solonina A.N., Lotfya A., Preparation and characterization of hybrid A359/(SiC+Si3N4 composites synthesized by stir/squeeze casting techniques, Mater. Sci. Eng. A, 2016, 674, 18-24.10.1016/j.msea.2016.07.058Search in Google Scholar
[10] Zhang X.N., Geng L., Xu B., Compressive behaviour of Al-based hybrid composites reinforcedwith SiC whiskers and SiC nanoparticles, Mater. Chem. Phys., 2007, 101, 242-246.10.1016/j.matchemphys.2006.04.004Search in Google Scholar
[11] Oh K., Han K., Short-fiber/particle hybrid reinforcement: Effects on fracture toughness and fatigue crack growth of metal matrix composites, Compos. Sci. Technol., 2007, 67, 1719-1726.10.1016/j.compscitech.2006.06.020Search in Google Scholar
[12] Yin J.W., Yao D.X., Xia Y.F., Zuo K.H., Zeng Y.P., Enhanced thermal conductivity of Cu matrix composites reinforced with Ag-coated β-Si3N4 whiskers, Mater. Des., 2014, 60, 282-288.10.1016/j.matdes.2014.03.047Search in Google Scholar
[13] Guo X.L., Wang L.Q., Wang M.M., Qin J.N., Zhang D., Lu W.J., Effects of degree of deformation on the microstructure, mechanical properties and texture of hybrid-reinforced titanium matrix composites, Acta Mater., 2012, 60, 2656-2667.10.1016/j.actamat.2012.01.032Search in Google Scholar
[14] Ghesmati T.S., Sajjadi S.A., Babakhani A., Lu W.J., Analytical and experimental investigation of the effect of SPS and hot rolling on the microstructure and flexural behavior of Ti6Al4V matrix reinforced with in-situ TiB and TiC, J. Alloys Compd., 2017, 692, 734-744.10.1016/j.jallcom.2016.09.026Search in Google Scholar
[15] Jiang Q.,Wang X., Zhu Y.T., Hui D., Qiu Y.P., Mechanical, electrical and thermal properties of aligned carbon nanotube/polyimide composites, Compos. Part B, 2014, 56, 408-412.10.1016/j.compositesb.2013.08.064Search in Google Scholar
[16] Zhang C.X., Yao D.X., Yin J.W., Zuo K.H., Xia Y.F., Liang H.Q., Zeng Y.P., Effects of whisker surface modification on microstructures, mechanical and thermal properties of β-Si3N4 whiskers reinforced Al matrix composites, Mater. Des., 2018, 159, 117-126.10.1016/j.matdes.2018.08.055Search in Google Scholar
[17] Dong S.H., Zhou J.Q., Hui D., Wang Y., Zhang S., Size dependent strengthening mechanisms in carbon nanotube reinforced metal matrix composites, Compos. Part A, 2015, 68, 356-364.10.1016/j.compositesa.2014.10.018Search in Google Scholar
[18] Lamanna G., Battigelli A., Ménard-Moyon C., Bianco A., Multifunctionalized carbon nanotubes as advanced multimodal nano-materials for biomedical application, Nanotechnol. Rev., 2012, 1, 17-29.10.1515/ntrev-2011-0002Search in Google Scholar
[19] Wang C.A., Huang Y., Zhai H.X., The effect of whisker orientation in SiC whisker-reinforced Si3N4 ceramic matrix composites, J. Eur. Ceram. Soc., 1999, 19, 1903-1909.10.1016/S0955-2219(98)00289-1Search in Google Scholar
[20] Li M., Chen F.Y., Si X.Y., Wang J., Du S.Y., Huang Q., Copper-SiC whiskers composites with interface optimized by Ti3SiC2 J. Mater. Sci., 2018, 53, 9806-9815.10.1007/s10853-018-2255-ySearch in Google Scholar
[21] Yang J.S., Downes R., Schrand A., Park J.G., Liang R., Xu C.Y., High electrical conductivity and anisotropy of aligned carbon nanotube nanocomposites reinforced by silicon carbonitride, Scr. Mater., 2016, 124, 21-25.10.1016/j.scriptamat.2016.06.023Search in Google Scholar
[22] Landauer R., The Electrical resistance of binary metallic mixtures, J. Appl. Phys., 1952, 23, 779-784.10.1063/1.1702301Search in Google Scholar
[23] Frank H., Hans-Jörg S.M., Günter G., Analytical modeling of the electrical conductivity of metal matrix composites: application to Ag-Cu and Cu-Nb, Mater. Sci. Eng. A, 2003, 347, 9-20.10.1016/S0921-5093(02)00590-7Search in Google Scholar
[24] Wang H., Zhang Z.H., Zhang H.M., Hu Z.Y., Li S.L., Cheng X.W., Novel synthesizing and characterization of copper matrix composites reinforced with carbon nanotubes, Mater. Sci. Eng. A, 2017, 696, 80-89.10.1016/j.msea.2017.04.055Search in Google Scholar
[25] Zhang C.X., Yin J.W., Yao D.X., Zuo K.H., Xia Y.F., Liang H.Q., Zeng Y.P., Enhanced tensile properties of Al matrix composites reinforced with β-Si3N4 whiskers, Compos. Part A, 2017, 102, 145-153.10.1016/j.compositesa.2017.07.025Search in Google Scholar
[26] Yin J.W., Yao D.X., Hu H.L., Xia Y.F., Zuo K.H., Zeng Y.P., Improved mechanical properties of Cu matrix composites reinforced with β-Si3N4 whiskers, Mater. Sci. Eng. A, 2014, 607, 287-293.10.1016/j.msea.2014.04.021Search in Google Scholar
[27] Rossiter P.L., The electrical resistivity of metals and alloys, 1991, Cambridge University Press, Cambridge,.Search in Google Scholar
[28] Xiong L.Q., Shuai J., Liu K.W., Hou Z.C., Zhu L., Li W.Z., Enhanced mechanical and electrical properties of super-aligned carbon nanotubes reinforced copper by severe plastic deformation, Compos. Part B, 2019, 160, 315-320.10.1016/j.compositesb.2018.10.023Search in Google Scholar
[29] Tian L., Anderson I., Riedemann T., Russell A., Modeling the electrical resistivity of deformation processed metal-metal composites, Acta Mater., 2014, 77, 151-161.10.1016/j.actamat.2014.06.013Search in Google Scholar
[30] Verhoeven J.D., Downing H.L., Chumbley L.S., Gibson E.D., The resistivity and microstructure of heavily drawn Cu-Nb alloys, J. Appl. Phys., 1989, 65, 1293-1301.10.1063/1.343024Search in Google Scholar
[31] Guo X.H., Song K.X., Liang S.H., Wang X., Zhang Y.M., Effect of Al2O3 Particle Size on Electrical Wear Performance of Al2O3/Cu Composites, Tribol. Trans., 2016, 59, 170-177.10.1080/10402004.2015.1061079Search in Google Scholar
[32] Han D.G., Choi G.M., Computer simulation of the electrical conductivity of composites the effect of geometrical arrangement, Solid State Ionics, 1997, 106, 71-87.10.1016/S0167-2738(97)00484-0Search in Google Scholar
[33] Maxwell J.C., A Treatise on electricity and magnetism, 1881, Clarendon Press.Search in Google Scholar
[34] Fan Z.Y., A new approach to the electrical resistivity of two-phase composites, Acta Metall. Mater., 1995, 43, 43-49.10.1016/0956-7151(95)90259-7Search in Google Scholar
© 2019 J. Feng et al., published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 Public License.
