Electrical conduction and Joule effect in one-dimensional chains of ...

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P. Béquin, V. TournatRef. [22] forastainlesssteelAISI420.Thus,anincreasein temperature when large currents pass through the contactregion between beads leads to an increase in the electricalresistivity ρ and to a decrease in the thermal conductivityλ within the contacting material. Consequently a risein temperature increases resistivity—and Joule effect—anddecreases thermal conductivity—which reduces the abilityof the material to dissipate heat by thermal conduction. Inthe contact region between beads it is sufficient to cause asignificant heat accumulation. Moreover, it can be observedthat the saturation voltage U MAX increases with the maximumcurrent I MAX .Consequently,thetemperatureatthecontact surface increases and tends gradually towards themelting temperature of the contacting material. A softeningof the asperities is expected [13], and can lead to alocal micro-sintering. As a result, the electrical resistivityis found to decrease with current I MAX (α decreases) andthe thermal conductivity increases with current I MAX (|β|decreases).For a cycle of electric current, coefficients α ↑ (increasingcurrent) and α ↓ (decreasing current) present roughly equalvalues; in contrast coefficients β ↑ and β ↓ of thermal conductivityhave different values (|β ↓ | > |β ↑ |)thatmeasurementuncertainty cannot explain alone. In model Eq. 6, thedependencies of electrical resistivity and thermal conductivityon temperature are considered linear (Eq. 5) overthewhole range of temperature (293–1800 K). On the basis ofthe presented results, one improvement could be to seek moreelaborated relations for ρ(T ) and λ(T ). Thedependenciescan be expressed as a power series of temperature T withmore terms than used in models [12,27]. Furthermore, it isinteresting to note that a positive value of β ↑ for the increasingcurrents is deduced from Fig. 6. A thorough analysis ofthe experimental curve shows a point of inflection close toI = 0.44 A. This change of behavior could be ascribed toan initial softening of the contact surface when the currentgrows, and could partly explain the difference with the valuesin Table 3. The role of the latent heat in the possiblemicro-melting of the asperities is a highly complex phenomenonto model at this level of understanding. It has notbeen taken into account in the presented models: all the estimatedtemperatures remain significantly lower than the meltingpoint. Only softening of the contacts and micro-sinteringhave been invoked here to interpret the results. The studyof the micro-structural changes of the contact areas by othermeans could be profitable to guide the future improvementsof the models.In conclusion, these measurements show the diversity ofelectrical and thermal phenomena within the chains of beads.The simplified models based on the Wiedemann–Franz’slaw fail to describe the electro-thermo-mechanical phenomenain a chain of beads carrying currents under a small appliedcompression force ∼1 N.5ElectromagneticeffectsonachainofbeadsThe linear and nonlinear acoustic properties of granular materialsare strongly sensitive to the mechanical properties at thelevel of the contacts between beads [4]. For such studies, itcould be extremely convenient to be able to modify contactmechanical properties without any modification of the geometryof the medium. A controlled electromagnetic wave hasthe ability to produce these mechanical transformations withoutaffecting the remainder of the granular structure. In thiscontext, and as a complement to the previous part, this sectionreports an analysis of the electrical and thermal behaviors ofachainofbeadssubjectedtoastrongelectromagneticpulsecreated by a spark.This study can be viewed as a continuation of the workof Dorbolo et al. [21] whichwasdealingwiththeinfluenceof an electromagnetic wave on the electrical resistance ofthe contacts between two beads. In [21], the electromagneticperturbation is found to affect preferentially the contacts havinga resistance higher than a threshold value which dependsmainly on both the mechanical characteristics of the chain ofbeads and of the distance between the latter and the spark (theelectromagnetic source). Here, we carry out measurementswith a near field electromagnetic excitation. They confirmpartly and extend the observations of Ref. [21] madeinthefar field.5.1 Experimental set-upThe experimental set-up is presented in Fig. 9. Theelectromagneticwave is produced by a discharge across a spark gapas in Refs. [17,28].Experiments were performed using a “three-electrode system”in which the storage capacitor is kept charged at a voltage(from 0 to 20 kV) lower than the breakdown voltage ofthe gap in air at atmospheric conditions. A third electrodeis placed between the main electrodes to provide an initialionization of the air necessary to cause the spark breakdownmechanism.5.2 ResultsFigure 10 shows the voltage–current characteristics for acycle of current (0–1 A). During this cycle, 5 sparks are created(distance between the chain of beads and the electrodesr ≃ 120 mm) causing a voltage drop between the electrodesof the chain of beads. These voltage drops can be connectedto strong variations of the contact impedances. It is observedthat for increasing dc currents I ,theelectricbehaviorofthechain of beads is less and less disturbed by the electromagneticpulses.The electromagnetic radiation created by these sparksinduces an electric current I sp in the chain of beads which is123
Electrical conduction in chains of beadsFig. 11 Diameter of the contact d versus current I deduced from theellipsoidal model for the contact surface. Solid curve: model I U = d ρ —Eq. 2. Chain of 5 stainless beads (diameter 11 mm). During the cycleof current, 5 sparks were created; r ≃ 120 mm distance between thechain of bead and the sparkFig. 9 Schematic diagram of the experimental set-up to study the influenceof an electromagnetic wave pulse on the electromechanical behaviorof a chain of beads. A “three-electrode system” is used for the generationof the electromagnetic pulse. V T and V HT are the trigger voltageand the capacitor voltage. The gap distance is 10 mm and r is the distancebetween the axis of the discharge and the axis of the chain ofbeadsFig. 12 Induced current I sp versus distance r between the chain ofbeads and the spark. Values estimated at I ≃ 0.5 Aduringacycleofcurrent (0–0.5 A) on a chain of 5 stainless beads (diameter 11 mm).Dashed line corresponds to I sp ∝ 1/r 2.1Fig. 10 Voltage U as a function of current I . Chain of 5 stainless beads(diameter 11 mm). During the cycle of current, 5 sparks are producedand are indicated by the arrows. The distance between the chain ofbeads and the spark is r ≃ 120 mmadded in a quadratic way to the dc current I due to the fact thatthey are incoherent current sources. Using the model fromEq. 2 giving the diameter of the contact as a function of theadmittance I U = d ρ ,thecontactdiameterisplottedasafunctionof the current in Fig. 11.Thecurrentpulseinducedbytheelectromagnetic pulse contributes to the sudden rise of thecontact diameter between beads. After this sudden increase,the diameter remains constant as long as the dc current Ican flow without modifying the area of contact by softening[9–11,21].The value of the impulse current I sp can be estimated byidentification to the value of the dc current I necessary toobtain the same diameter of contact. With this method, theinduced current I sp for the first spark (data corresponding toFigs. 10 and 11)isestimatedtobearound0.35 A. In this currentcycle, for dc currents higher than 0.9 A, the presence ofinduced impulse currents does not further modify the contactgeometry between the beads. As was previously observed in[21], the Fig. 11 shows that the contacts having a small diameterand thus a high electrical resistance (U I = ρ d —Eq. 2)arestrongly affected by the electromagnetic perturbation.Figure 12 gives the current induced by the electromagneticpulse of a spark placed at a distance r from a chain of 5 beads.The values of this current are estimated using the methoddescribed previously. This figure shows that the induced currentdecreases monotonically as distance r increases. A firstanalysis at the distances r higher than 50 mm (distances123
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Electrical conduction and Joule effect in one-dimensional chains of ...

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