Failure Mechanism of Multilayer Ceramic Capacitors Under Transient High Impact

applied sciences

Article Failure Mechanism of Multilayer Ceramic Capacitors under Transient High Impact

Da Yu, Keren Dai * , Jinming Zhang, Benqiang Yang, He Zhang * and Shaojie Ma

ZNDY of Ministerial Key Laboratory, School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China; [email protected] (D.Y.); [email protected] (J.Z.); [email protected] (B.Y.); [email protected] (S.M.) * Correspondence: [email protected] (K.D.); [email protected] (H.Z.)

Received: 28 October 2020; Accepted: 25 November 2020; Published: 26 November 2020

Abstract: In recent years, penetrating weapons have been used more and more to attack increasingly hard targets; therefore, the impact of such a penetrating process has increased to an extremely high level. As an important component of a fuze, the reliability of the ceramic capacitor in high-impact environments is key for the normal working of the fuze. In this paper, we found that a high-impact causes parameter drift of the multilayer ceramic capacitor (MLCC), which further causes the fuze to misfire. This paper mainly studies the internal mechanism of the MLCC’s parameter drift during high impact. Firstly, transient physical phenomena, such as capacitance fluctuation and the leakage current increase of the ceramic capacitor under a high acceleration impact, were studied experimentally by a Machete hammer, revealing the relationship between the capacitance change, leakage current change, and acceleration under different working conditions. Secondly, a mechanical model of the ceramic capacitor is established to simulate the change in capacitance value, which shows that the main factor of the capacitance change is the deformation-derived change in the facing area between the electrodes. Lastly, an equivalent circuit model is established to simulate the change in the leakage current, which shows that the main factor of the leakage current change is the piezoelectric resistance of the ceramic dielectric.

Keywords: multilayer ceramic capacitor; high impact; failure mechanism; leakage current; mechanical model

1. Introduction A penetration weapon is a kind of high-value ammunition used for attacking strategic hard targets, such as weapon depots, missile launching sites, airport runways, and command centers. A penetration fuze is the “brain” of a penetrating weapon system, which precisely controls the burst point [1]. For the penetration fuze, a reliable power supply is the basis of its normal functioning. So, the multilayer ceramic capacitor (MLCC), which is the main energy-storage component of a penetration fuze, plays an important role in the reliability of the whole penetration weapon. Because the penetration fuze experiences an extreme impact, mechanical environment (acceleration up to hundreds of thousands of gravity g, lasting for a millisecond-wide pulse) [2,3], the reliability of the MLCC under high impact is very important. Previous studies on the reliability of an MLCC under high-acceleration impact mostly focused on structural failure [4–11]. Prume et al. established a ﬁnite element simulation model for electrical, mechanical, and thermal coupling of an MLCC [12]; Lee et al. used a multi-scale homogenization modeling method to characterize the structural characteristics of multilayer ceramic capacitors [13]; Zhang et al. used the equivalent mechanical model to describe the impact-driven deformation of an MLCC and reveals that the electric ﬁeld distortion resulting from the deformation can easily cause

Appl. Sci. 2020, 10, 8435; doi:10.3390/app10238435 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 8435 2 of 14 Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 15 ceramicceramic capacitor capacitor failure failure [14]; [14]; and and He He et et al. al. discu discussedssed the the failure failure of of an an MLCC MLCC through through a a high high overload overload impactimpact dynamic dynamic experiment experiment and and analyzed analyzed the the influenc influencee of ofsuch such a failure a failure on onthe thefuze fuze system system [15]. [ 15At]. present,At present, the thedynamic dynamic impact impact experiment experiment and and me mechanicalchanical failure failure modeling modeling are are the the most most common common waysways to to study study the the failure failure of an MLCC. However,However, even therethere is is no no structural structural failure, failure, it doesit does not not mean mean that that no functional no functional failure failure occurs occurs in the inMLCC the andMLCC other and electronic other devices.electronic Current devices. research Current hotspots research are focusedhotspots on stressare focused concentration on stress and concentrationstructural damage and duestructural to high damage impact. due In actual to high working impact. conditions, In actualthe working MLCC conditions, did not have the structural MLCC diddamage, not have but thestructural penetration damage, fuze but still the misfired penetration due to fuze the parameterstill misfired drift. due This to paperthe parameter focuses ondrift. the Thisfailure paper mechanism focuses ofon an the MLCC failure under mechanism high-impact of an conditions.MLCC under In high-impact addition, it has conditions. been revealed In addition, that the ittantalum has been capacitors revealed andthat supercapacitors, the tantalum capacitors two other and kinds supercapacitors, of energy-storage two devices other kinds for a penetrationof energy- storagefuze, still devices have capacitancefor a penetration parameter fuze, fluctuationstill have ca withoutpacitance structural parameter damage fluctuation under without a high-acceleration structural damageimpact [under16]. Gao a high-acceleration et al. studied a fuze impact misfire [16]. caused Gao et by al. thestudied sudden a fuze increase misfire in caused leakage by current the sudden of the increasetantalum in capacitor leakage current under aof high- the tantalumg impact capacitor load [17]. under Therefore, a high- forg animpact MLCC load subjected [17]. Therefore, to a strong for animpact, MLCC besides subjected the structuralto a strong failure, impact, the besides functional the st failureructural problem failure, ofthe the functional parameter failure fluctuation problem is ofalso the important parameter for fluctuation practical is application. also important However, for practical the research application. in this However, area is still the relatively research in scarce. this areaIn this is paper,still relatively the changes scarce. in MLCCIn this capacitance paper, the andchanges leakage in MLCC current capacitance upon subjection and leakage to a high current impact uponare presented subjection in to real a high time, impact and the are internal presented mechanism in real time, causing and the the internal electrical mechanism parameter causing changes the is electricalstudied by parameter physical fieldchanges modeling is studied and equivalent by physical circuit field modeling, modeling whichand equivalent provides significantcircuit modeling, guiding whichtowards provides the reliable significant use of guiding an MLCC towards in a penetration the reliable fuze. use of an MLCC in a penetration fuze. 2. Experimental Study on MLCC Parameter Fluctuation Failure 2. Experimental Study on MLCC Parameter Fluctuation Failure 2.1. Structure and Principle of an MLCC 2.1. Structure and Principle of an MLCC A multilayer ceramic capacitor is mainly composed of an inner electrode, outer electrode, A multilayer ceramic capacitor is mainly composed of an inner electrode, outer electrode, and and ceramic dielectric material. A multilayer ceramic capacitor is composed of ceramic dielectric ceramic dielectric material. A multilayer ceramic capacitor is composed of ceramic dielectric membranes printed with internal electrodes (mainly made of nickel, silver, palladium, and other metal membranes printed with internal electrodes (mainly made of nickel, silver, palladium, and other materials) in a staggered manner. After one-time high-temperature sintering, the ceramic plates are metal materials) in a staggered manner. After one-time high-temperature sintering, the ceramic plates formed, and the outer electrodes are sealed at both ends of the ceramic plates to form a monolith-like are formed, and the outer electrodes are sealed at both ends of the ceramic plates to form a monolith- structure, as shown in Figure1[18,19]. like structure, as shown in Figure 1 [18,19].

Fuze

Energy storage module MLCC

Bomb! Inter electrode

(a) (b) (c) Outer electrode Impact Dielectric

FigureFigure 1. ApplicationApplication ofof a a multilayer multilayer ceramic ceramic capacitor capacitor (MLCC) (MLCC) in a penetrationin a penetration weapon. weapon. (a) The penetration (a) The penetrationprocess in a militaryprocess application. in a military (b )application. The MLCC is (b the) The energy-storage MLCC is the element energy-storage of a penetration element fuze. of(c) a Internal penetration structure fuze. diagram (c) Internal of the MLCC.structure diagram of the MLCC.

Appl. Sci. 2020, 10, 8435 3 of 14 Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 15

2.2.2.2. MLCC MLCC High-Impact High-Impact Test Test System System AnAn MLCC MLCC is often used asas thethe mainmain energy-storageenergy-storage element element of of a a penetration penetration fuze, fuze, which which needs needs to towithstand withstand extreme extreme environments, environments, such such as as long long pulse pulse and andhigh-g high-g impactimpact acceleration in the process process ofof launching launching and and penetrating. penetrating. The The impact impact can cause can cause changes changes in the inelectrical the electrical parameters parameters of the MLCC, of the amongMLCC, which among the which capacitance the capacitance capacity and capacity leakage and current leakage change current are changethe most are important the most to important evaluate theto evaluatecapacitance the capacitancefailure. A Machete failure. hammer A Machete is the hammer most iswidely the most applied widely experimental applied experimental system to researchsystem to such research extreme such high-g extreme impact high-g environmen impact environments,ts, whose impact whose pulse impact width pulse can reach width hundreds can reach ofhundreds microseconds of microseconds and impact and value impact can value reach can up reach to uptens to tensof thousands of thousands of ofg. g.By By adjusting adjusting the the correspondingcorresponding gear gear of of a a machete machete pawl, pawl, different diﬀerent acce accelerationleration values values can can be be obtained obtained upon upon releasing releasing thethe pawl, pawl, which which can can simulate simulate the the actual actual mechanical mechanical environment environment of of the the fuze fuze during during the the penetration penetration process.process. The The experimental experimental system system of of the the Machete Machete hammer hammer is is shown shown in in Figure Figure 22..

(a) (b) Acceleration sensor MLCC

Testing device Hammer Switch head

Gear Testing device ⚙ Base Impact

Counter weight Oscilloscope CHI600E Wayne Kerr 6500B Acceleration Leakage current Capacitance

FigureFigure 2. 2. ExperimentalExperimental system system diagram: diagram: (a) ( aschematic) schematic diagram diagram of a of Machete a Machete hammer hammer test testsystem; system; (b) installation(b) installation diagram diagram of the of capacitance the capacitance andand sensor. sensor.

FourFour kinds kinds of of ceramic ceramic capacitors capacitors with with different different capacities capacities and and different different withstand withstand voltages voltages were were usedused in in the the experiment. experiment. The The capacitors capacitors were were welded welded onto onto the Printed the Printed Circuit Circuit Board Board surface surface and fixed and tofixed the toMachete the Machete hammer hammer using thread. using thread. A piezoresistive A piezoresistive high-g sensor high-g (214-BM1009 sensor (214-BM1009 type) was type) used was to measureused to measurethe acceleration the acceleration signal during signal the during impact the process, impact process,with a sensitivity with a sensitivity of 3.0 μ ofV/g 3.0 andµV /ag maximumand a maximum range of range 30,000 of g. 30,000 A Wayne g. A Kerr Wayne 6500B Kerr se 6500Bries precision series precision impedance impedance analyzer analyzer was used was to monitorused to monitorthe change the changein ceramic in ceramic capacitance. capacitance. An electrochemical An electrochemical workstation workstation (CHI600E (CHI600E Series) Series) was selectedwas selected to monitor to monitor the thechange change in leakage in leakage current. current. The The ceramic ceramic capacitance capacitance parameters parameters and and test test parametersparameters are shown inin TableTable1 .1. The The subsequent subsequent modeling modeling and and simulation simulation in in this this paper paper are are based based on onthese these real real device device parameters. parameters.

TableTable 1. 1. CapacitanceCapacitance specifications speciﬁcations and and measurement measurement parameters. parameters.

2 Capacitor TypeCapacitor Type δ (µm) δ (µm) NN h (µhm) (µm)l ( µm) l (µm)b (µm) S (mmb (µm)) S (mm2) “J”CT41G-1210-X5R-16V-22“J”CT41G-1210-X5R-16V-22μF 3.11µF 3.11501 501 1.311.31 29452945 2059 5.342059 5.34 “J”CT41G-1210-X5R-25V-22µF 2.91 379 1.81 3165 2161 5.99 “J”CT41G-1210-X5R-25V-22“J”CT41G-1210-X5R-16V-47μF 2.91µF 1.79379 462 1.961.81 32383165 2184 6.222161 5.99 “J”CT41G-1210-X5R-16V-47“J”CT41G-1210-X5R-25V-47μF 1.79µF 2.57462 570 1.761.96 33643238 2369 7.052184 6.22 “J”CT41G-1210-X5R-25V-47Where δ—thickness of dielectricμF layer;2.57N—number of570 electrode layers;1.76h— thickness3364 of electrode layer;2369l—electrode 7.05 Wherelength; δb—electrode—thickness width; of dielectric and S—e layer;ﬀective N facing—number area. of electrode layers; h—thickness of electrode layer; l—electrode length; b—electrode width; and S—effective facing area. Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 15

2.3. Transient Variation of Capacitance Appl. Sci.The2020 capacity, 10, 8435 of a ceramic capacitor changes during the impact process. Figure 3 shows that the4 of 14 capacity of the ceramic capacitor (type: 16V-22 μF) increased with increasing impact acceleration. 2.3.Compared Transient with Variation the ceramic of Capacitance capacitors with different withstand voltages and differently rated capacities, when the peak value of impact acceleration exceeded 5000 g, the ceramic capacitance of themThe all capacityhave evident of a changes ceramic and capacitor the change changes value during increased the with impact the process.increasing Figure impact3 shows peak value. that the capacityThe measured of the data ceramic of the capacitor changes are (type: shown 16V-22 in TableµF) 2. increased Among them, with the increasing capacitance impact value acceleration. change Comparedreached 0.18 with μ theF (absolute ceramic capacitorschange); therefore, with different it cannot withstand be ignored. voltages In and addition, differently the ratedrelationship capacities, whenbetween the peakthe MLCC value ofcapacitance impact acceleration change and exceeded impact 5000acceleration g, the ceramic is nonlinear, capacitance but the of amount them all of have evidentchange changesincreases and sharply the change after the value threshold increased acceleration with the (>4000 increasing g) is exceeded. impact peak This value. indicates The that measured the datahigher of theacceleration changes arethe shown penetration in Table fuze2. Amongis subjected them, to, the the capacitance more serious value the change reliability reached problem 0.18 µF (absoluteregarding change); capacity therefore, fluctuation it can cannot be. Besides, be ignored. the larger In addition, the rated the capacity relationship and withstand between voltage, the MLCC capacitancethe greater changethe capacitance and impact fluctuation. acceleration is nonlinear, but the amount of change increases sharply after theThe thresholdexperimental acceleration results show (>4000 that, g)although is exceeded. the capacitance This indicates value changes that the at higher the moment acceleration of mechanical impact, it can restore to its original rated capacity after the impact, which verifies our the penetration fuze is subjected to, the more serious the reliability problem regarding capacity view that even if the MLCC and other fuze devices do not have structural failure, various transient fluctuation can be. Besides, the larger the rated capacity and withstand voltage, the greater the functional failures may still occur at the impact moment. capacitance fluctuation.

10000 22.01 10000 22.01 Impact Impact 8000 16V-22µF 8000 16V-22µF 22.00 22.00 6000 6000 21.99 21.99 4000 4000

2000 21.98 2000 21.98 Impact / g / Impact g / Impact

0 /µF Capacitance 0 /µF Capacitance 21.97 21.97 -2000 -2000 21.96 21.96 -4000 -4000 0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20 Time / ms Time / ms (a) (b)

10000 22.01 10000 22.01 Impact Impact 8000 16V-22µF 8000 16V-22µF 22.00 22.00 6000 6000 21.99 21.99 4000 4000

2000 21.98 2000 21.98 Impact / g / Impact g / Impact

0 /µF Capacitance 0 /µF Capacitance 21.97 21.97 -2000 -2000 21.96 21.96 -4000 -4000 0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20 Time / ms Time / ms (c) (d)

FigureFigure 3. 3.Change Change inin ceramicceramic capacitance with impact acceleration. acceleration. (a (a) )The The impact impact peak peak value value is is5209 5209 g. (bg.) The(b) The impact impact peak peak value value is 5608is 5608 g. g. (c ()c The) The impact impact peak peak valuevalue isis 63056305 g. ( (dd)) The The impact impact peak peak value value is 8297is 8297 g. g.

Table 2. Capacity change of the MLCC under a diﬀerent impact acceleration.

Capacitance Variation/µF Capacitor Type 5026 g 5608 g 6305 g 8297 g “J”CT41G-1210-X5R-16V-22µF 0.022 0.030 0.106 0.146 “J”CT41G-1210-X5R-25V-22µF 0.027 0.033 0.109 0.151 “J”CT41G-1210-X5R-16V-47µF 0.031 0.056 0.122 0.174 “J”CT41G-1210-X5R-25V-47µF 0.037 0.060 0.127 0.181 Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 15

Table 2. Capacity change of the MLCC under a different impact acceleration.

Capacitance Variation/µF Appl. Sci. 2020, 10, 8435 Capacitor Type 5 of 14 5026 g 5608 g 6305 g 8297 g “J”CT41G-1210-X5R-16V-22μF 0.022 0.030 0.106 0.146 The experimental“J”CT41G-1210-X5R-25V-22 results show that, althoughμF the0.027 capacitance 0.033 value0.109 changes 0.151 at the moment of mechanical impact,“J”CT41G-1210-X5R-16V-47 it can restore to its originalμF rated0.031 capacity 0.056 after the0.122 impact, 0.174 which verifies our view that even if the“J”CT41G-1210-X5R-25V-47 MLCC and other fuze devicesμF 0.037 do not have0.060 structural 0.127 failure,0.181 various transient functional failures may still occur at the impact moment. 2.4. Transient Change of the Leakage Current 2.4. Transient Change of the Leakage Current The leakage current of a multilayer ceramic capacitor is another key performance evaluation parameter.The leakage During current the impact, of a multilayer the leakage ceramic current capacitor of the ceramic is another capacitor key also performance changes significantly, evaluation parameter.causing ignored During energy the impact, loss. According the leakage to current Mattes of et the al. ceramic[20], the capacitorceramic dielectric also changes (BaTiO significantly,3) is not an causingabsolutely ignored ideal energy insulating loss. material According and to has Mattes a piezor et al.esistive [20], theeffect. ceramic When dielectric the capacitor (BaTiO is charged,3) is not anthe absolutelyelectron penetrates ideal insulating through material the dielectric and has layer a piezoresistive and forms the e ffleakageect. When current. the capacitorDuring the is process charged, of theimpact, electron the penetrates piezoresistive through effect the is dielectricevident, resu layerlting and in forms a sharp the increase leakage current.in the leakage During current. the process of impact,In this the study, piezoresistive both ends eff ectof the is evident, MLCC resultingare conne incted a sharp to the increase electrochemical in the leakage workstation. current. Real- timeIn monitoring this study, bothof the ends leakage of the current MLCC changes are connected by chronopotentiometry to the electrochemical mode. workstation. Under such Real-time a mode, monitoringa constant of voltage the leakage is applied current between changes the by chronopotentiometrytwo ends. When the mode.impact Under acceleration such a mode, is applied a constant to the voltageMLCC isvia applied the Machete between thehammer, two ends. the transient When the leakage impact accelerationcurrent change is applied is recorded to the MLCCby the viaelectrochemical the Machete hammer,workstation. the The transient change leakage in leakage current current change of the is ceramic recorded capacitor by the electrochemicalis closely related workstation.to its structure. The Figure change 4 in shows leakage the current leakage of current the ceramic of multilayer capacitor ceramic is closely capacitors related to with its structure. different Figurespecifications4 shows changed the leakage under current different of multilayer impacts. In ceramic the process capacitors of the withexperiment, di fferent the specifications peak value of changedthe impulse under acceleration different impacts. increases In gradually, the process and of thethe experiment, leakage current the peak of all value types of theof capacitors impulse accelerationincreases suddenly, increases which gradually, is a universal and the leakage phenomen currenton. ofMoreover, all types the of capacitors change in increasesleakage current suddenly, can whichreach isvalues a universal of up to phenomenon. 1.2 mA (absolute Moreover, change), the changeso it cannot in leakage be ignored. current In canaddition, reach valuesthe relationship of up to 1.2between mA (absolute the leakage change), current so itchange cannot and be ignored.impact accele In addition,ration rate the is relationship not linear; the between amount the of leakage change currentincreases change sharply and impactafter the acceleration threshold rate (4000 is not g) linear; is exceeded. the amount This of changeindicates increases that the sharply higher after the theacceleration threshold (4000the penetration g) is exceeded. fuze This is subjected indicates thatto, the the highermore serious the acceleration the reliability the penetration problem fuzeof an isincreased subjected leakage to, the morecurrent serious can happen. the reliability Besides, problem the greater of an the increased rated capacity leakage and current withstand can happen. voltage, Besides,the greater the the greater increase the ratedin leakage capacity current. and Note withstand that the voltage, rated capacity the greater hasthe a greater increase influence in leakage than current.the withstand Note that voltage the rated on the capacity leakage has current a greater fluctuation. influence than the withstand voltage on the leakage current fluctuation.

1.4 1.4 16V22µF 1.2 1.2 25V22µF 1.0 25V-47µF 16V47µF 1.0 25V47µF 0.8 0.8 0.6 0.6 0.4 0.4 Leakage currentmA /Leakage 0.2 Leakage current / mA 0.0 0.2

-0.2 0.0 0.020 0.025 0.030 0.035 0.040 0.045 0.050 3000 4000 5000 6000 7000 8000 9000 Time / s Impact / g

(a) (b)

FigureFigure 4. 4. RelationshipRelationship between the leakage leakage current current and and impact impact in in multilayer multilayer ceramic ceramic capacitors: capacitors: (a) (aleakage) leakage current current of of an an MLCC MLCC (25V47 (25V47µµF)F) under under 8297 8297 g impulse;impulse; ((bb)) leakageleakage currentcurrent variationvariation of of multilayermultilayer ceramic ceramic capacitors capacitors with with di differentﬀerent impacts. impacts.

3. Modeling of MLCC Parameter Fluctuation Failure The capacity of the MLCC increases with the increase in the impact peak value, which is due to the elastic deformation of the inner ﬁlm-coated electrode of the MLCC during the impact, as shown in Figure5. In the elastic range, the capacitance changes due to the change of the facing area between the electrodes. Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 15

3. Modeling of MLCC Parameter Fluctuation Failure

Appl.The Sci. capacity 2020, 10, x of FOR the PEER MLCC REVIEW increases with the increase in the impact peak value, which is due6 toof 15 the elastic deformation of the inner film-coated electrode of the MLCC during the impact, as shown in 3.Figure Modeling 5. In the of elasticMLCC range, Parameter the capacitance Fluctuation changes Failure due to the change of the facing area between the electrodes. The capacity of the MLCC increases with the increase in the impact peak value, which is due to the elastic deformation of the inner film-coated electrode of the MLCC during the impact, as shown

Appl.in Figure Sci. 2020 5. ,In10 ,the 8435 elastic range, the capacitance changes due to the change of the facing area between6 of 14 the electrodes.

Figure 5. Diagram of the facing area increase during impact.

Figure 6 shows a schematic diagram of the leakage current increase during impact. Under the mechanical pressure caused by the impact process, the electrical conductivity of the ceramic dielectric Figure 5. Diagram of the facing area increase during impact. layer increases. So, the numberFigure of5. Diagramelectrons of passin the facingg through area increase the dielectric during impact. layer increases, causing a larger leakage current. Figure 66 shows shows aa schematicschematic diagramdiagram ofof thethe leakageleakage currentcurrent increaseincrease duringduring impact.impact. UnderUnder thethe Based on the above physical mechanism, in this paper, a dynamic mechanical model is mechanical pressure caused by the impact process, thethe electrical conductivity of the ceramic dielectric established to analyze the influence of mechanical impact on capacity, and an equivalent circuit layer increases. So, So, the the number of electrons passin passingg through the dielectric layer increases, causing a model is established to analyze the influence of mechanical impact on the leakage current. larger leakage current. Based on the above physical mechanism, in this paper, a dynamic mechanical model is established+ to analyze the influence of mechanical+ impact on capacity, and an equivalent circuit model is established to analyze the influence of mechanical impact on the leakage current. + +

Impact Impact BaTiO3 e- Impact Impact Positive BaTiO3 Positive electrode Positive

Negative electrode Negative Negative e- Positive Positive electrode Positive

Negative electrode Negative Negative Free electron increase - - Figure 6. Schematic diagram of the leakage current increase during impact. Free electron increase Based onFigure the above 6. Schematic physical diagram mechanism, of thein leakage this paper, current a dynamicincrease during mechanical impact. model is established to analyze the inﬂuence of mechanical- impact on capacity, and an- equivalent circuit model is established 3.1.to Modeling analyze theof Capacitance inﬂuence ofFluctuation mechanical Based impact on Electrode on the leakage Deformation current.

3.1.The Modeling basic unit of CapacitanceFigure of a multilayer 6. Schematic Fluctuation ceramic diagram Based capacitor of onthe Electrode leakage is composed current Deformation increase of two metalduring electrodes, impact. which are separated by dielectric layer ceramics and stacked up in layers. The positive and negative charges are stored3.1. ModelinginThe the basic metal of unitCapacitance electrodes. of a multilayer Fluctuation Both ceramicends Based of capacitorthe on Electrodeelectrode is composed Deformation plate are of coated two metal in a electrodes,ceramic dielectric. which are separated by dielectric layer ceramics and stacked up in layers. The positive and negative charges are storedThe basic in the unit metal of a electrodes.multilayer Bothceramic ends capacitor of the electrode is composed plate of are two coated metal in electrodes, a ceramic which dielectric. are Therefore,separated by the dielectric equivalent layer two-dimensional ceramics and stacked elastic mechanics up in layers. problem The positive of a ceramic and negative capacitor charges electrode are storedis shown in inthe Figure metal7 .electrodes. The coordinate Both ends system of isthe length electrodel along plate the are X coated direction, in a width ceramicb along dielectric. the Y direction, and thickness h along the Z direction. When the plate is subjected to the inertial force F, the upper surface is compressed and the lower surface is stretched. The bending moment M produced by any single element under the inertial force is m, and the number of electrode layers is N. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 15

Therefore, the equivalent two-dimensional elastic mechanics problem of a ceramic capacitor electrode is shown in Figure 7. The coordinate system is length l along the X direction, width b along the Y direction, and thickness h along the Z direction. When the plate is subjected to the inertial force F, the upper surface is compressed and the lower surface is stretched. The bending moment M Appl.produced Sci. 2020 by, 10 any, 8435 single element under the inertial force is m, and the number of electrode layers7 of 14is N.

Figure 7.7. EquivalentEquivalent diagram diagram of theof the inner inner electrode: electrode: (a) schematic (a) schematic diagram diagram of the electrode; of the electrode; (b) schematic (b) schematicdiagram of diagram electrode ofequivalent electrode equivalent mechanical mechanical model. model.

Under the impact acceleration aa, the, the uniformly uniformly distributed distributed load loadq isq is as as follows: follows: ρ ==FFmabhama =bhρa qq= = = (1)(1) NlNl Nl NN The deflection deﬂection function of the electrode underunder the uniform loadload qq isis asas followsfollows [[21]:21]: ρ mama 22ρa a 22 wx()w=−=−(x) = xx2 ()( ll x x)2 = x2(l xx ()) l2 x (2)(2) 24NEIl24NEIl − 2NEh 2 NEh2 2 − where thethe cross-sectionalcross-sectional areaarea ofof the the inner inner electrode electrode is is given given by byA A= b= hb·h, the, the material material density density is ρis, andρ , · andthe elasticthe elastic modulus modulus of the of materialthe material is E. is E. When xx==ll//22, the, the maximum maximum deﬂection deflection of of the the plate plate is is as as follows: follows:

ρ 44 = ρllaa wwmax = (3)(3) max 3232NEh2 2 The rotation function θθ(()xx) of of the the inner inner electrode electrode is is as as follows: follows: θ ()= ' θ(xx) = wwx(()x)0 (4)(4)

By deriving x, we obtain the following results: ρa θ ()x =−−ρa xl(2)() x l x θ(x) = 2 x(l 2x)(l x) (5)(5) NEhNEh2 − − Then, the length l of the electrode after impact is bent to the arc lengthlength ll’:’: r 2 Z l l ρaρa 2 l lxlxlxdx='1=+1 + (2)()x( −−l 2x)(l x) dx (6)(6) 0 0 2 2 0 NEhNEh − −

Then, the arc length change llis is as as follows: follows: 4 r Z l ρa 2 l = l l = 1 + x(l 2x)(l x) dx l (7) 0 2 4 − 0 NEh − − − Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 15

2 l ρa ll=−=l ' l 1(2)() +xl − x l − x dx − (7) Appl. Sci. 2020, 10, 8435 0 NEh2 8 of 14

The surface area change S of the inner electrode is obtained as follows: The surface area change S of the inner electrode is obtained as follows: 4 2 l ρ Zr a  S =+−lb= l 1(2)() ρa xl x l− x2 dx− l  b (8) S = l b =  0 1 + NEh2 x(l 2x)(l x) dx l b (8)   2   4 4 ·  0 NEh − − − ·  The capacity of the inner electrode unit of the ceramic capacitor is as follows: The capacity of the inner electrode unit of the ceramic capacitor is as follows: CSε C =εS N= 2Nkdπ (9)(9) N 22Nπkd 2 Therefore, the capacitance change C is as follows: Therefore, the capacitance change C is as follows: 4 2 εε rl ρ  NS Z l a 2  N εClblbS===ε  1(2)+−−ρaxl x( l x) dx−  (10) C = 4 = π πl b = 0 1 +2 x(l 2x)(l x) dx l b (10) 2 2Nkd4 kd  NEh 2  4 2 ·2Nπkd 4πkd· 4 ·  0 NEh − −  − ·

AccordingAccording to theto the numerical numerical calculation calculation of of the the above above mechanical mechanical model, model, the the results results are are shown shown in in FigureFigure8. The 8. The relationship relationship between between the the capacity capacity change change and and the the impact impact acceleration acceleration presents presents two two stages: stages: first,first, it changes it changes gently, gently, then then rises rapidly.rises rapidly. Further, Further, as shown as shown in Figure in9 ,Figure the first 9, stage the first has astage slow capacityhas a slow changecapacity because change the because electrode the and electrode ceramic dielectricand ceramic are closelydielectric connected are closely when connected the impact when acceleration the impact is loweracceleration than the is deformationlower than the threshold deformation of the threshold ceramic dielectric of the cerami and thec dielectric deflection and deformation the deflection is small,deformation and the facingis small, area and of thethe innerfacing electrode area of the changes inner onlyelectrode a little; changes therefore, only the a little; capacity therefore, change the is notcapacity obvious. change In theis not second obvious. stage, In the impactsecond stage, acceleration the impact exceeds acceleration the threshold, exceeds the the deflection threshold, of the thedeflection electrode of is the obvious, electrode the facingis obvious, area ofthe the facing inner ar electrodeea of the inner increases, electrode and theincreases, capacity and and the impact capacity accelerationand impact almost acceleration increase almost with in acrease linear with relation. a linear The relation. comparison The comparison between Tables between2 and Tables3 shows 2 and 3 thatshows the main that the conclusions main conclusions of both theof both simulation the simula andtion experiment and experiment are the are same, the indicatingsame, indicating that the that mechanicalthe mechanical model model proposed proposed above abov is credible.e is credible. Specifically, Specifically, the quantitativethe quantitative value value of theof the absolute absolute capacitycapacity change change of of the the simulation simulation is slightlyis slightly lower lower than than that that of theof the experiment. experiment. The The reason reason for for this this is is thatthat the the simulation simulation does does not not consider consider the the mechanical mechanic two-dimensionalal two-dimensional equivalent equivalent model model and and simplifies simplifies thethe influence influence of theof the transverse transverse strain. strain. The The variation variation in in the the electrode electrode thickness thickness direction direction is notis not an an ideal ideal factor,factor, which which leads leads to to the the deviation deviation between between the the simulation simulation results results and and the the experimental experimental results. results.

0.20 0.18 16V-22µF 0.16 25V-22µF 0.14 16V-47µF 0.12 25V-47µF 0.10 0.08 0.06 Capacitance /Capacitance µF 0.04 First stage Second stage 0.02 0.00 2000 4000 6000 8000 Impact / g

FigureFigure 8. Relationship8. Relationship between between capacity capacity change change and and impact impact acceleration. acceleration. Appl. Sci. 2020, 10, 8435 9 of 14 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 15

Electrode inertia force Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 15 Electrode Ceramic inertia force Dielectric Electrode Electrode inertia force Electrode Ceramic inertia force (a) Dielectric (b) Electrode FigureFigure 9. 9.Deformation Deformation of of the the MLCCMLCC atat didifferentﬀerent stages: ( (aa)) the the first ﬁrst stage; stage; (b ()b the) the second second stage. stage.

TableTable 3. 3.(aSimulation )Simulation capacitycapacity changechange of the MLCC MLCC under under( bdifferent di) fferent impacts. impacts. Figure 9. Deformation of the MLCC at different stages: (a) the first stage; (b) the second stage. Capacitance VariationVariation/µF/µF Capacitor ModelModel Table 3. Simulation capacity change5026 of5026 the g MLCCg 5608 5608 under g g different 6305 6305 gg impacts. 8297 gg “J”CT41G-1210-X5R-16V-22μF 0.011 0.028 0.082 0.129 “J”CT41G-1210-X5R-16V-22µF 0.011Capacitance 0.028 Variation/µF 0.082 0.129 “J”CT41G-1210-X5R-25V-22Capacitor Model μF 0.017 0.033 0.091 0.141 “J”CT41G-1210-X5R-25V-22µF 0.0175026 g 5608 0.033 g 6305 0.091 g 8297 0.141 g “J”CT41G-1210-X5R-16V-47μF 0.029 0.054 0.112 0.164 “J”CT41G-1210-X5R-16V-47“J”CT41G-1210-X5R-16V-22µFμF 0.0290.011 0.0540.028 0.082 0.112 0.129 0.164 “J”CT41G-1210-X5R-25V-47“J”CT41G-1210-X5R-25V-47“J”CT41G-1210-X5R-25V-22µμFμFF 0.0380.0380.017 0.0590.0330.059 0.091 0.1230.123 0.141 0.175 “J”CT41G-1210-X5R-16V-47μF 0.029 0.054 0.112 0.164 3.2.3.2. Modeling Modeling of of Leakage Leakage“J”CT41G-1210-X5R-25V-47 Current Current Fluctuation Fluctuation BasedBasedμF on 0.038the Piezoresistive Piezoresistive 0.059 0.123 Effect Effect 0.175 In this study, the leakage current of the ceramic capacitor returned to its original state after the In this3.2. Modeling study, the of Leakage leakage Current current Fluctuat of theion Based ceramic on the capacitor Piezoresistive returned Effect to its original state after the impact. According to the theoretical model of the equivalent circuit, the main factor affecting the impact. According to the theoretical model of the equivalent circuit, the main factor affecting the leakage leakage currentIn this study,is the theceramic leakage dielectric current ofinsulation the ceramic resistance capacitor [22].returned Therefore, to its original the key state to after solving the the currentimpact. is theceramic According dielectric to the theoretical insulation model resistance of the equivalent [22]. Therefore, circuit, the the main key factor to solving affecting the the leakage leakage current is to study the relationship between the pressure and ceramic dielectric insulation currentleakage is to study current the is relationship the ceramic dielectric between insulation the pressure resistance and [22]. ceramic Therefore, dielectric the key insulation to solving resistance.the resistance. leakage current is to study the relationship between the pressure and ceramic dielectric insulation 3.2.1. Piezoresistiveresistance. Model of Ceramics 3.2.1. Piezoresistive Model of Ceramics As3.2.1. shown Piezoresistive in Figure Model10, a static of Ceramics load is applied to the ceramic dielectric and the constant voltage As shown in Figure 10, a static load is applied to the ceramic dielectric and the constant voltage (10V)(10V) of of the theAs electrochemical electrochemicalshown in Figure workstation10, workstation a static load (CHI600E(CHI600Eis applied to Series) Series) the ceramic is is used used dielectric to to monitor monitor and the the constant the real-time real-time voltage currentcurrent changechange(10V) in in order order of the to toelectrochemical obtain obtain the the resistance resistance workstation valuesvalues (CHI600E ofof the Series) ceramics is used under under to monitor different different the pressures.real-time pressures. current The The static static pressurepressurechange test testshowed in showed order to that, that,obtain with with the theresistancethe increaseincrease values inin of pressure, the ceramics the the underinsulation insulation different impedance impedance pressures. of The ofthe thestatic ceramic ceramic pressure test showed that, with the increase in pressure, the insulation impedance of the ceramic dielectricdielectric decreased. decreased. In In Figure Figure 11 11 we we seesee thatthat the re resistancesistance of of the the ceramic ceramic dielectric dielectric began began to todecrease decrease dielectric decreased. In Figure 11 we see that the resistance of the ceramic dielectric began to decrease whenwhen the the threshold threshold pressure pressure was was 2.7 2.7 MPa,MPa, andand the resistance dropped dropped gradually gradually when when the the pressure pressure when the threshold pressure was 2.7 MPa, and the resistance dropped gradually when the pressure . reachedreachedreached 18.1 18.1 MPa. MPa.18.1 MPa. In In Figure Figure In Figure 12 12,, the12, the the relationshiprelationship relationship between between ceramicceramic ceramic conductivity conductivity conductivity and and pressure and pressure pressure is shown is isshown. shown.

Figure 10.FigureSystem 10. System diagram diagram of the of ceramic the ceramic static static pressure pressure test: test: (a ()a hydrostatic) hydrostatic machine;machine; ( (bb) )ceramic ceramic static pressurestatic diagram; pressure (c )diagram; ceramic (c static) ceramic pressure static pressure experiment. experiment. Figure 10. System diagram of the ceramic static pressure test: (a) hydrostatic machine; (b) ceramic static pressure diagram; (c) ceramic static pressure experiment. Appl. Sci. 2020, 10, 8435 10 of 14 Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 15 Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 15

Figure 11. Relationship between pressure and ceramic conductivity: (a) the change of ceramic current FigureFigure 11. 11.Relationship Relationship between between pressure pressure and and ceramicceramic conductivity: (a (a) )the the change change of ofceramic ceramic current current in static pressure experiment; (b) the relationship between ceramic dielectric pressure and resistance. in staticin static pressure pressure experiment; experiment; (b ()b the) the relationship relationship betweenbetween ceramic di dielectricelectric pressure pressure and and resistance. resistance.

Ceramic Ceramic dielectric dielectric 44 2.7MPa2.7MPa /m) /m) -6 -6 10 10 × × 33 18.1MPa18.1MPa

11 Conductivity / (S Conductivity Conductivity / (S Conductivity

00 -1-1 00 20 20 40 40 60 60 80 80 100 100 120 120 140 140 160 160 180 180 PressurePressure / MPa/ MPa

Figure 12. Relationship between pressure and ceramic resistance. FigureFigure 12. 12. Relationship Relationship between between pressure pressure and and ceramic ceramic resistance. resistance. According to Newton’s second law, the relationship between acceleration and pressure is as AccordingAccording toto Newton’sNewton’s second second law, law, the the relationship relationship between between acceleration acceleration and and pressure pressure is isas as follows: follows:follows: p(t) = ma(t)/A (11) ptpt()()== mat mat ()/ ()/ A A (11)(11) where m—mass; A—cross-sectional area. wherewhereAccording m m—mass;—mass; to theA A—cross-sectional—cross-sectional experimental results,area. area. the relationship between pressure P and resistance R (P–R equation)AccordingAccording is as to to follows: the the experimental experimental results, results, the the relationship relationship between between pressure pressure P Pand and resistance resistance R R(P– (P– RR equation) equation) is is as as follows: follows:    256,256,pp≤≤ 2.34;2.34;   256, p 2.34; R(p) =   ( (p T )/M ) ≤ ( (p T )/M ) (12) R()=p + ( 1 1 + ( −−()pT/ M2 2 R()=p R0 A1 1 e −()−−()−−pT− / M A2 1 ()e()−−−()pT2 −/ M , p > 2.34; (12)  ()()pT1111/ M 2 2 (12) Rp+−+−A· (11− eA) + +· −−e− 2 ,2.3;>> 4 Rp02A1 11eAe ,2.3;4  021 ( )        The parameters in the P-R equation are shown in Table4. TheThe parameters parameters in in the the P-R P-R equation equation are are shown shown in in Table Table 4. 4. Table 4. P–R model parameters. TableTable 4. 4. P–R P–R model model parameters. parameters. R0 A1 T1 M1 A2 T2 M2 RR0 0 AA1 1 TT1 1 MM1 1 AA2 2 TT2 2 MM2 2 457 MΩ 248 18.9 11.9 204 2.34 2.33 457457 M MΩΩ −−−248248 −−18.918.9 11.911.9 −204−204 2.342.34 2.332.33

3.2.2. Theoretical Model of Equivalent Circuit for Multilayer Ceramic Capacitor The characteristics of an MLCC are not ideal due to the parasitic effects. Many scholars use the following equivalent circuit model to describe the capacitance [23], as shown in Figure 13a. This paper Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 15 Appl. Sci. 2020, 10, 8435 11 of 14 3.2.2. Theoretical Model of Equivalent Circuit for Multilayer Ceramic Capacitor The characteristics of an MLCC are not ideal due to the parasitic effects. Many scholars use the focuses onfollowing the influence equivalent of circuit the mechanical model to describe impact the capacitance on the MLCC [23], as(mainly shown in Figure determined 13a. This by paper the ceramic dielectricfocuses resistance, on the Rp),influence which of the is mechanical not significantly impact on related the MLCC to the(mainly parasitic determined effects. by the So, ceramic the equivalent circuit modeldielectric is simplified resistance, Rp), as Figure which is 13 notb: significantly related to the parasitic effects. So, the equivalent circuit model is simplified as Figure 13b:

Figure 13.FigureMLCC 13. MLCC equivalent equivalent circuit circuit model:model: (a) ( ageneral) general equivalent equivalent circuit model circuit of modelthe MLCC; of ( theb) MLCC; simplified equivalent circuit model of the MLCC. (b) simpliﬁed equivalent circuit model of the MLCC.

Where C is MLCC capacity, Ck is the storage capacity of one pair of positive and negative Whereelectrodes,C is MLCC ESR(R capacity,s) is the equivalentCk is the storage series resistance, capacity and of one Rp is pair the of equivalent positive andresistance negative of the electrodes, ESR(Rs) isceramic the equivalent dielectric: series resistance, and Rp is the equivalent resistance of the ceramic dielectric: AccordingAccording to the to equivalent the equivalent circuit, circuit, the the mathematical mathematical model model can can be established be established as follows: asfollows: += IRls,0 V p ,0 U 0 (13) Il,0Rs + Vp,0 = U0 (13) VV CRUVpk,,+=− pk VkspkΔ V ! 0, (14) p,ktRppk,,k Ck + Rs = U0 Vp,k (14) ∆t nnR − 111p,k 111  −  + tt−  + Δ U CRR CRR  = 0 Pn kpkskk==11,, kpksPn  (15) Vepk, 1 ( 1 + 1 ) t Z[] e1 ( 1 + 1 ) dt∆t U C R Rs  C R Rs CR0ks− k = p,k 4 − k = p,k Vp,k = e k 1 [ e k 1 dt] (15) CkRs − UV0,pk I = (16) lk, U0 Vp,k Rs Il,k = − (16) Rs where U0 is the constant voltage applied to the MLCC, Vp,k are the voltages of the ceramic dielectric where U0betweenis the constantthe kth pair voltage of positive applied and negative to the electrodes, MLCC, V andp,k arethe conductivity the voltages of ofRp varies the ceramic with thedielectric betweenimpact. the kth pair of positive and negative electrodes, and the conductivity of Rp varies with the impact. After combining the equivalent circuit model (Equations (13)–(16)) and the P–R model (Equations (11) and (12)), perform the process calculation in Figure 14 to obtain the relationship Afterbetween combining acceleration the equivalent and leakage circuit current: model (Equations (13)–(16)) and the P–R model (Equations (11) and (12)), performThe piezoresistive the process effect calculation of the ceramic in Figure dielectric 14 tois the obtain main the factor relationship that causes betweenthe change acceleration in and leakageleakageAppl. current: Sci. current. 2020, 10, xThe FOR PEERimpact REVIEW acceleration has the characteristics of a pulse signal. Therefore,12 of the15 corresponding impact stress waves at different moments of the impact have different pressures on the ceramic dielectric, which in turn causes pulsed changes in the leakage current. Acceleration : Input a（t）

Pressure : p(t)=m*a(t)/A

p(t) > 2.34

Dielectric resistance : Rp=256MΩ Dielectric resistance : P-R equation

Equivalent circuit equations ：Equation 13-16

Leakage current ：Output Ileak

FigureFigure 14. Flow 14. Flow chart chart of of the the leakage current current calculation. calculation.

According to the static pressure data model of the ceramic dielectric and the mathematical model of an equivalent circuit, the relationship between the conductivity of the ceramic dielectric and the leakage current is presented, as shown in Figure 15. As the conductivity increases, the leakage current increases.

1.2 Ceramic dielectric

1.0

0.8

0.6

0.4 Leakage current / mA / Leakage current 0.2 4,000g 8,000g 0.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 Conductivity / (S×10-6/m)

Figure 15. Relationship between leakage current and ceramic conductivity.

In addition, the leakage current variation of a multilayer ceramic capacitor under different impacts is simulated, as shown in Figure 16. The results show that the leakage current increases approximately exponentially with the increasing impact acceleration, which is in good agreement with the experimental results (Figure 4). The sudden increase in leakage current of the ceramic capacitors causes the loss of energy storage, which makes the detonator energy insufficient. Therefore, the design of the fuze’s energy-storage capacitor must consider the leakage current during the impact and increase the design margin to ensure the reliability of the fuze effect. Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 15

Acceleration : Input a（t）

Pressure : p(t)=m*a(t)/A

p(t) > 2.34

Dielectric resistance : Rp=256MΩ Dielectric resistance : P-R equation

Equivalent circuit equations ：Equation 13-16 Appl. Sci. 2020, 10, 8435 12 of 14

Leakage current ：Output Ileak The piezoresistive effect of the ceramic dielectric is the main factor that causes the change in leakage current. The impact acceleration has the characteristics of a pulse signal. Therefore, the corresponding Figure 14. Flow chart of the leakage current calculation. impact stress waves at different moments of the impact have different pressures on the ceramic dielectric,According which in to turn the static causes pressure pulsed changesdata model in theof the leakage ceramic current. dielectric and the mathematical model of Accordingan equivalent to the circuit, static the pressure relationship data model between of the the ceramic conductivity dielectric of andthe theceramic mathematical dielectric modeland the ofleakage an equivalent current circuit, is presented, the relationship as shown in between Figure 15. the As conductivity the conductivity of the increases, ceramic dielectric the leakage and current the leakageincreases. current is presented, as shown in Figure 15. As the conductivity increases, the leakage current increases.

1.2 Ceramic dielectric

1.0

0.8

0.6

0.4 Leakage current / mA / Leakage current 0.2 4,000g 8,000g 0.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 Conductivity / (S×10-6/m)

Figure 15. Relationship between leakage current and ceramic conductivity. Figure 15. Relationship between leakage current and ceramic conductivity. Appl.In Sci. addition, 2020, 10, x the FOR leakage PEER REVIEW current variation of a multilayer ceramic capacitor under diﬀerent impacts13 of 15 In addition, the leakage current variation of a multilayer ceramic capacitor under different is simulated, as shown in Figure 16. impacts is simulated, as shown in Figure 16. The results show that1.4 the leakage current increases approximately exponentially with the increasing impact acceleration, which is in good agreement with the experimental results (Figure 4). The sudden increase in leakage1.2 current 16V-22µF of the ceramic capacitors causes the loss of energy storage, which makes the detonator energy insufficient. 25V-22µF Therefore, the design of the fuze’s energy-storage 1.0 capacitor must consider the leakage current 16V-47µF during the impact and increase the design margin to 25V-47µF ensure the reliability of the0.8 fuze effect.

0.6

0.4 Leakage current / mA / current Leakage 0.2

0.0 3000 4000 5000 6000 7000 8000 9000 Impact / g

Figure 16. Relationship between leakage current and impact acceleration of the MLCC. Figure 16. Relationship between leakage current and impact acceleration of the MLCC. The results show that the leakage current increases approximately exponentially with the increasing 4. Conclusions impact acceleration, which is in good agreement with the experimental results (Figure4). The sudden increaseIn inthis leakage paper, current the transient of the ceramic change capacitors (and its causesmechanism) the loss of of the energy electronical storage, parameters which makes of themultilayer detonator ceramic energy insucapacitorsﬃcient. Therefore,during high- theg design impacts of the was fuze’s analyzed energy-storage via Machete capacitor hammer must considerexperiments. the leakage Further, current by establishing during the a impact mechanical and increase model theand design equivalent margin circuit to ensure model, the the reliability capacity ofand the leakage fuze eﬀ ect.current changes were studied, and a numerical simulation was carried out to verify the experimental results. To sum up, the experimental and simulation results indicate the following issues: (1) Under high-g impact acceleration, in the MLCC occurs the phenomenon of parameter drift, in which the capacitance value becomes larger and the leakage current increases. Besides, the larger the rated capacitance and withstand voltage of the MLCC, the greater the capacitance change and leakage current drift. With impact acceleration of no more than 9000 g, the influence on the capacity and leakage current are reversible. (2) The facing area deformation is the dominant factor in the transient change of the capacity value. A mechanical model based on the facing area is established to calculate the capacity change. The numerical calculation results are consistent with the experimental results, and the relationship between the impact and capacity changes can be described semi-quantitatively. (3) The piezoresistive effect of the ceramic dielectric is the dominant factor in leakage current variation. The insulation resistance begins to decrease when the threshold pressure exceeds 2.7 MPa. With increasing pressure, the insulation impedance of the ceramic dielectric decreases continuously, and when the pressure reaches 18.1 MPa, the resistance drops gradually. By combining the P-R model and the equivalent circuit model, the relationship between the leakage current and impact acceleration can be simulated, which is an approximately exponentially increasing relationship. (4) The sudden increase in the leakage current of the ceramic capacitor causes the energy storage loss of the MLCC, which makes the detonator energy of the fuze insufficient. The design of the fuze’s energy-storage capacitor must consider the leakage current during the impact and increase the design margin to ensure the reliability of the fuze. By analyzing the relationship between the different impact accelerations and parameter drift, and by calculating the failure threshold of the different specification parameters of the MLCC according to the mechanical model and equivalent circuit model, effectively provides guidance for the design of a penetration fuze’s MLCC, to ensure the reliability of the fuze. Appl. Sci. 2020, 10, 8435 13 of 14

4. Conclusions In this paper, the transient change (and its mechanism) of the electronical parameters of multilayer ceramic capacitors during high-g impacts was analyzed via Machete hammer experiments. Further, by establishing a mechanical model and equivalent circuit model, the capacity and leakage current changes were studied, and a numerical simulation was carried out to verify the experimental results. To sum up, the experimental and simulation results indicate the following issues:

(1) Under high-g impact acceleration, in the MLCC occurs the phenomenon of parameter drift, in which the capacitance value becomes larger and the leakage current increases. Besides, the larger the rated capacitance and withstand voltage of the MLCC, the greater the capacitance change and leakage current drift. With impact acceleration of no more than 9000 g, the influence on the capacity and leakage current are reversible. (2) The facing area deformation is the dominant factor in the transient change of the capacity value. A mechanical model based on the facing area is established to calculate the capacity change. The numerical calculation results are consistent with the experimental results, and the relationship between the impact and capacity changes can be described semi-quantitatively. (3) The piezoresistive effect of the ceramic dielectric is the dominant factor in leakage current variation. The insulation resistance begins to decrease when the threshold pressure exceeds 2.7 MPa. With increasing pressure, the insulation impedance of the ceramic dielectric decreases continuously, and when the pressure reaches 18.1 MPa, the resistance drops gradually. By combining the P-R model and the equivalent circuit model, the relationship between the leakage current and impact acceleration can be simulated, which is an approximately exponentially increasing relationship. (4) The sudden increase in the leakage current of the ceramic capacitor causes the energy storage loss of the MLCC, which makes the detonator energy of the fuze insufficient. The design of the fuze’s energy-storage capacitor must consider the leakage current during the impact and increase the design margin to ensure the reliability of the fuze.

By analyzing the relationship between the different impact accelerations and parameter drift, and by calculating the failure threshold of the different specification parameters of the MLCC according to the mechanical model and equivalent circuit model, effectively provides guidance for the design of a penetration fuze’s MLCC, to ensure the reliability of the fuze.

Author Contributions: D.Y. and K.D. conceived and designed the experiments; D.Y., J.Z. and B.Y. performed the experiments; D.Y. and K.D. analyzed the data; H.Z. and S.M. contributed analysis tools; D.Y. wrote the paper. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded in part by Key Basic Research Projects of Basic Strengthening Plan of China (Grant number 2017-JCJQ-ZD-004), in part by National Natural Science Foundation of China (Grant number 52007084), in part by the Natural Science Foundation of Jiangsu Province under Grant (BK20190470), and in part by the Central University Special Funding for Basic Scientific Research (Grant number 30918012201). Conflicts of Interest: The authors declare no conflict of interest.

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