《纺织复合材料》课程参考文献（Composite materials science and applications，Second Edition）07 Electrical Properties.pdf_P11-P15

7.5 Electric Power and Resistance Heating 213 incorporating a nonstructural heating element into the structural component.For example,the nonstructural heating element can take the form of a sheet that is at or near the surface of the structural component.Examples of nonstructural heating elements include flexible graphite and carbon fiber mats,which are mechanically inadequate for load bearing.An alternate method involves using the load-bearing structural material as the heating element,so that the structural material becomes multifunctional and the need to combine a structural element with a nonstructural element is eliminated.Attractions of this alternative method include higher dura- bility(no need to worry about the detachment of the nonstructural element from the structural element,or about the possible mechanical degradation of the non- structural element),lower fabrication cost,greater implementation convenience, higher spatial uniformity of the heating,and greater volume of the heating ele- ment.Structural materials that also function as heating elements are said to be self-heating. The dominant structural materials in this context are cement-matrix composites (for buildings)and continuous fiber polymer-matrix composites(for lightweight structures such as aircraft).These materials cannot withstand high temperatures. However,heating to temperatures that are not far from room temperature is needed for deicing,comfortable living,and hazard mitigation.For example,in deicing, the relevant temperature is around 0C.This section addresses self-heating in both types of structural composites. The materials used in heating elements cannot have electrical resistivities that are too low,as this would result in the resistance of the heating element being too low and so a high current would be needed to achieve a specific power.The materials of heating elements cannot be too resistive either,as this would result in a current in the heating element that is too low (unless the voltage is very high).Materials used in heating elements include metal alloys,ceramics (such as silicon carbide), graphite,polymer-matrix composites,carbon-carbon composites,asphalt,and concrete. Resistance heating is useful for heating buildings,for deicing bridge decks,drive- ways and aircraft,for plastic welding,and for the demolition of concrete structures. On the other hand,electrical self-heating is undesirable for optimizing the perfor- mance and reliability of electrical interconnections,bolometers,superconductors, transistors,diodes,and other semiconductor devices. 7.5.2.2 Self-heating Cement-Matrix Composites Conventional concrete is electrically conductive but its resistivity is too high for resistance heating to be effective.The resistivity of concrete can be diminished by the use of electrically conductive admixtures or aggregates,such as discontinuous carbon fibers,discontinuous steel fibers or shavings,and graphite or carbon parti- cles.It can also be diminished by using an alkaline slag binder.However,the most effective method of decreasing the resistivity is to use a conductive admixture at a volume fraction beyond the percolation threshold.Percolation means the attain- ment of a continuous conductive path due to contact between adjacent conductive fibers or particles.The objective of this section is to compare various conductive

7.5 Electric Power and Resistance Heating 213 incorporating a nonstructural heating element into the structural component. For example, the nonstructural heating element can take the form of a sheet that is at or near the surface of the structural component. Examples of nonstructural heating elements include flexible graphite and carbon fiber mats, which are mechanically inadequate for load bearing. An alternate method involves using the load-bearing structural material as the heating element, so that the structural material becomes multifunctional and the need to combine a structural element with a nonstructural element is eliminated. Attractions of this alternative method include higher durability (no need to worry about the detachment of the nonstructural element from the structural element, or about the possible mechanical degradation of the nonstructural element), lower fabrication cost, greater implementation convenience, higher spatial uniformity of the heating, and greater volume of the heating element. Structural materials that also function as heating elements are said to be self-heating. The dominant structural materials in this context are cement-matrix composites (for buildings) and continuous fiber polymer–matrix composites (for lightweight structures such as aircraft). These materials cannot withstand high temperatures. However, heating to temperatures that are not far from room temperature is needed for deicing, comfortable living, and hazard mitigation. For example, in deicing, the relevant temperature is around 0°C. This section addresses self-heating in both types of structural composites. The materials used in heating elements cannot have electrical resistivities that are too low, as this would result in the resistance of the heating element being too lowandsoahighcurrentwouldbeneededtoachieveaspecificpower.Thematerials of heating elements cannot be too resistive either, as this would result in a current in the heating element that is too low (unless the voltage is very high). Materials used in heating elements include metal alloys, ceramics (such as silicon carbide), graphite, polymer–matrix composites, carbon–carbon composites, asphalt, and concrete. Resistanceheatingisusefulforheatingbuildings,fordeicingbridgedecks,driveways and aircraft, for plastic welding, and for the demolition of concrete structures. On the other hand, electrical self-heating is undesirable for optimizing the performance and reliability of electrical interconnections, bolometers, superconductors, transistors, diodes, and other semiconductor devices. 7.5.2.2 Self-heating Cement-Matrix Composites Conventional concrete is electrically conductive but its resistivity is too high for resistance heating to be effective. The resistivity of concrete can be diminished by the use of electrically conductive admixtures or aggregates, such as discontinuous carbon fibers, discontinuous steel fibers or shavings, and graphite or carbon particles. It can also be diminished by using an alkaline slag binder. However, the most effective method of decreasing the resistivity is to use a conductive admixture at a volume fraction beyond the percolation threshold. Percolation means the attainment of a continuous conductive path due to contact between adjacent conductive fibers or particles. The objective of this section is to compare various conductive

7.5 Electric Power and Resistance Heating 215 resistance.Due to the presence ofsteel fibers,the structural properties are superior to those of conventional cement-based materials. In contrast,for carbon fiber(1.0 vol%)cement of electrical resistivity 104cm, an electrical power input of 1.8 W(28 V,0.065 A)results in a maximum temperature of 56C(initial temperature 19C)and a time of 256s to achieve half of the maximum temperature rise.The high voltage(28 V,compared to 7V in the case of steel fiber cement)is undesirable due to the voltage limitations of typical power supplies.The performance is even worse for graphite particle(37 vol%)cement paste of resistivity 4071cm. The steel fibers mentioned above are only 8 um in diameter.Steel fibers of larger diameter(e.g.,60 um)are much less effective at reducing the electrical resistivities of cement-based materials and are therefore less effective for self-heating.For example,cement paste with 8um diameter steel fibers at 0.54 vol%gave a resistivity of 23 cm,whereas steel fibers of 60um diameter at 0.50 vol%led to resistivity 1.4x 103cm,steel fibers of8 um diameter at 0.36 vol%gave a resistivity of57cm, and steel fibers of 60 um diameter at 0.40 vol%gave a resistivity of 1.7 x 103cm. An alternative concrete technology involves using steel shavings(0.15-4.75mm in particle size)as the conductive aggregate in conjunction with low-carbon steel fibers as the conductive admixture.The use of 20 vol%steel shavings together with 1.5 vol%steel fibers resulted in an electrical resistivity of 75-100cm.The resistivity increased over time,reaching 350cm in six months,presumably due to the corrosion of the steel shavings and fibers.The high resistivity and the increase in resistivity with time are undesirable.In contrast,cement with stainless steel fibers(8um diameter,0.7 vol%)has a low resistivity of 0.85cm and the resistivity is stable over time.Furthermore,it does not require any special mixing equipment or procedure and does not require any special aggregate. 7.5.2.3 Self-heating Polymer-Matrix Composites Self-heating in continuous fiber polymer-matrix composites can be attained using the following methods:(a)by embedding a low-resistivity interlayer(e.g.,a carbon fiber mat)between adjacent laminae during composite fabrication and using the interlayer as a heating element,(b)by using conductive reinforcing fibers (e.g., continuous carbon fibers)to make the composite conductive and using the overall composite as a heating element,and(c)by using the interlaminar interface between adjacent laminae of conductive reinforcing fibers (e.g.,continuous carbon fibers) as a heating element. Method (a)is the one most commonly employed,as it is applicable to a broad range of composites,whether the reinforcing fibers are conductive or not.Method (b)is also feasible,but suffers from difficulties in attaining localized heating. Method(c)involves an innovative concept in which the contact resistance associ- ated with the interlaminar interface between laminae of conductive fibers allows the interface to serve as a heating element.The interface between two crossply laminae can be subdivided to provide a two-dimensional array of heating ele- ments,in addition to an x-y grid of electrical interconnections,thereby allowing spatially distributed heating(Fig.7.6)and a very small thermal mass for each

7.5 Electric Power and Resistance Heating 215 resistance. Due to the presence of steel fibers, the structural properties are superior to those of conventional cement-based materials. In contrast, for carbon fiber (1.0vol%) cement of electrical resistivity 104Ωcm, an electrical power input of 1.8W (28V, 0.065A) results in a maximum temperature of 56°C (initial temperature = 19°C) and a time of 256s to achieve half of the maximum temperature rise. The high voltage (28V, compared to 7V in the case of steel fiber cement) is undesirable due to the voltage limitations of typical power supplies. The performance is even worse for graphite particle (37vol%) cement paste of resistivity 407Ωcm. The steel fibers mentioned above are only 8μm in diameter. Steel fibers of larger diameter (e.g., 60μm) are much less effective at reducing the electrical resistivities of cement-based materials and are therefore less effective for self-heating. For example, cement paste with 8μm diameter steel fibers at 0.54vol% gave a resistivity of 23Ωcm, whereas steel fibers of 60μm diameter at 0.50vol% led to resistivity 1.4×103 Ωcm,steelfibersof8μmdiameterat0.36vol% gavearesistivityof57Ωcm, and steel fibers of 60μm diameter at 0.40vol% gave a resistivity of 1.7 × 103 Ωcm. An alternative concrete technology involves using steel shavings (0.15–4.75mm in particle size) as the conductive aggregate in conjunction with low-carbon steel fibers as the conductive admixture. The use of 20vol% steel shavings together with 1.5vol% steel fibers resulted in an electrical resistivity of 75–100Ωcm. The resistivity increased over time, reaching 350Ωcm in six months, presumably due to the corrosion of the steel shavings and fibers. The high resistivity and the increase in resistivity with time are undesirable. In contrast, cement with stainless steel fibers (8μm diameter, 0.7vol%) has a low resistivity of 0.85Ωcm and the resistivity is stable over time. Furthermore, it does not require any special mixing equipment or procedure and does not require any special aggregate. 7.5.2.3 Self-heating Polymer-Matrix Composites Self-heating in continuous fiber polymer-matrix composites can be attained using the following methods: (a) by embedding a low-resistivity interlayer (e.g., a carbon fiber mat) between adjacent laminae during composite fabrication and using the interlayer as a heating element, (b) by using conductive reinforcing fibers (e.g., continuous carbon fibers) to make the composite conductive and using the overall composite as a heating element, and (c) by using the interlaminar interface between adjacent laminae of conductive reinforcing fibers (e.g., continuous carbon fibers) as a heating element. Method (a) is the one most commonly employed, as it is applicable to a broad range of composites, whether the reinforcing fibers are conductive or not. Method (b) is also feasible, but suffers from difficulties in attaining localized heating. Method (c) involves an innovative concept in which the contact resistance associated with the interlaminar interface between laminae of conductive fibers allows the interface to serve as a heating element. The interface between two crossply laminae can be subdivided to provide a two-dimensional array of heating elements, in addition to an x–y grid of electrical interconnections, thereby allowing spatially distributed heating (Fig. 7.6) and a very small thermal mass for each

7.5 Electric Power and Resistance Heating 217 maximum temperature rise.The electrical energy used to increase the temperature by 1C during the initial rapid temperature rise(5s)is up to 3.8J.The efficiency is nearly 1.00,even in the first 5s of heating.A mat comprising metal (Ni/Cu/Ni trilayer)-coated short carbon fibers and exhibiting a volume electrical resistivity of 0.07cm provides lower temperatures(up to 79C)but a faster response (up to 14s to achieve half of the maximum temperature rise). An example of the application of method(c)involves the use of the interface be- tween two crossply laminae of a continuous carbon fiber epoxy-matrix composite. For an interface of area 5 x 5mm and a resistance of 0.067,a DC electrical power input of 0.59W(3.0A,0.20 V)results in a maximum temperature of 89C (initial temperature =19C).The time needed to reach half of the maximum temperature rise is up to 16s.The efficiency of energy conversion reaches 100%after about 55s of heating,when the heat power output is up to 4 x 104 W/m2 of the interlaminar interface. 7.5.2.4 Comparison of Self-heating Structural Materials Table 7.1 shows a comparison of various materials in terms of their self-heating effectiveness,as evaluated in the laboratory of the author.The carbon fiber epoxy- matrix interlaminar interface(No.6 in Table 7.1)and the Ni/Cu/Ni-coated carbon fiber mat(No.5 in Table7.1)have exceptional abilities to provide fast and significant temperature responses,though they have low power capacities.Carbon fiber mat (No.4 in Table 7.1)has an exceptional ability to deliver high power and significant temperature rises;it is superior to cement-matrix composites(Nos.1-3in Table 7.1) in terms of power capacity,temperature capacity,and fast response.On the other hand,it is much inferior to flexible graphite (not a structural material;No.7 in Table 7.1)in terms of all three attributes. A comparison of the volume electrical resistivities of the various materials in Table 7.1 shows that a low resistivity tends to be associated with good self- heating performance,although there are exceptions.The outstanding performance of flexible graphite is attributed to its outstandingly low resistivity. The maximum temperature is limited by the ability of the material to withstand high temperatures.Flexible graphite is outstanding in this ability.However,the maximum temperature is also determined by the ability of the material to sustain current.A low resistivity greatly helps this ability,as shown by comparing the performances of the three cement-based materials(Nos.1-3 in Table 7.1). The time to reach half of the maximum temperature rise increases with the maximum temperature rise,as shown by comparing the response times at differ- ent input powers for the same material.This time is expected to be reduced by a decrease in thermal mass (which relates to the mass and the specific heat)or an increase in thermal conductivity.The fast response of the carbon fiber epoxy- matrix interlaminar interface is attributed mainly to its low thermal mass,which is due to the microscopic thickness of the interface.The fast responses of the Ni/Cu/Ni-coated carbon fiber mat and the flexible graphite are attributed mainly to the high thermal conductivity

7.5 Electric Power and Resistance Heating 217 maximum temperature rise. The electrical energy used to increase the temperature by 1°C during the initial rapid temperature rise (5s) is up to 3.8J. The efficiency is nearly 1.00, even in the first 5s of heating. A mat comprising metal (Ni/Cu/Ni trilayer)-coated short carbon fibers and exhibiting a volume electrical resistivity of 0.07Ωcm provides lower temperatures (up to 79°C) but a faster response (up to 14s to achieve half of the maximum temperature rise). An example of the application of method (c) involves the use of the interface between two crossply laminae of a continuous carbon fiber epoxy-matrix composite. For an interface of area 5×5mm and a resistance of 0.067Ω, a DC electrical power input of 0.59W (3.0A, 0.20V) results in a maximum temperature of 89°C (initial temperature = 19°C). The time needed to reach half of the maximum temperature rise is up to 16s. The efficiency of energy conversion reaches 100% after about 55s of heating, when the heat power output is up to 4 × 104 W/m2 of the interlaminar interface. 7.5.2.4 Comparison of Self-heating Structural Materials Table 7.1 shows a comparison of various materials in terms of their self-heating effectiveness, as evaluated in the laboratory of the author. The carbon fiber epoxymatrix interlaminar interface (No. 6 in Table 7.1) and the Ni/Cu/Ni-coated carbon fiber mat (No.5 inTable7.1) haveexceptionalabilitiestoprovidefast andsignificant temperature responses, though they have low power capacities. Carbon fiber mat (No. 4 in Table 7.1) has an exceptional ability to deliver high power and significant temperaturerises;itissuperiortocement-matrixcomposites(Nos.1–3inTable7.1) in terms of power capacity, temperature capacity, and fast response. On the other hand, it is much inferior to flexible graphite (not a structural material; No. 7 in Table 7.1) in terms of all three attributes. A comparison of the volume electrical resistivities of the various materials in Table 7.1 shows that a low resistivity tends to be associated with good selfheating performance, although there are exceptions. The outstanding performance of flexible graphite is attributed to its outstandingly low resistivity. The maximum temperature is limited by the ability of the material to withstand high temperatures. Flexible graphite is outstanding in this ability. However, the maximum temperature is also determined by the ability of the material to sustain current. A low resistivity greatly helps this ability, as shown by comparing the performances of the three cement-based materials (Nos. 1–3 in Table 7.1). The time to reach half of the maximum temperature rise increases with the maximum temperature rise, as shown by comparing the response times at different input powers for the same material. This time is expected to be reduced by a decrease in thermal mass (which relates to the mass and the specific heat) or an increase in thermal conductivity. The fast response of the carbon fiber epoxymatrix interlaminar interface is attributed mainly to its low thermal mass, which is due to the microscopic thickness of the interface. The fast responses of the Ni/Cu/Ni-coated carbon fiber mat and the flexible graphite are attributed mainly to the high thermal conductivity