17-equations-that-changed-the-world-part-ii - dfr solutions文档

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1、17EquationsThatChangedtheWorld-There’sMoreThanThat!!!Part2GregCaswellBackgroundMathematicshasbeenapartofourlivesforeverandisusedinnumerouswaysinoureverydaylives.Recently,createdbyIanStewart,listedonDr.PaulCoxon’sTwitteraccountanddiscussedonmathematicsbloggerLarryPhilip’ssiteisalisto

2、fthe“17EquationsthatChangedtheCourseofHistory,”manyofwhichhavebeenmentionedontheBigBangTheoryTVseries.However,thelistisincomplete.TherearenumerousequationsthathelptodeterminethereliabilityofelectronicsproductsthatDfRbelievesshouldbeincluded.TheseformulasareallintegraltoDfR’sSherlock

3、softwareandarethebasisforthevalidationoftheresultsobtainedinanADAanalysis.LastmonthwelookedaseveraloftheminPart1ofthiswhitepaper.PartIIdelineatestherestoftheformulas.FlexCrackingofMultilayerCeramicCapacitorsMultilayerCeramicCapacitors(MLCC),alsoknownasChipCapacitors,areamongthemostc

4、ommon,andmostfragile,ofcomponentsusedinCircuitCardAssemblies(CCAs).Flexcracking,causedbyexcessivebendingoftheprintedcircuitboardundertheMLCC,isoneofthemostcommonreasonsforfieldfailuresinelectronicdevicesandisalmostexclusivelydrivenbydesigndecisions.Theworkthatrelatesthefailuresofcer

5、amicsduetoprintedcircuitboardbendingcoincideswiththeacceptanceofusingsurfacemountcomponentsonorganicbasedsubstratesinthemid-eighties.(1)Beforethis,surfacemountdevicesweretypicallyonlyusedonceramicsubstratesandactualfailuresduetobendingwerequiterare.Insteadmostpublicationsthatevaluat

6、edcrackingincapacitorstendedtofocusonthosedrivenbythermalshockconditions.PriorWorkOneofthefirstpaperstoaddressthestructuralreliabilityofleadlessceramiccomponentsonanorganicsubstratewaswrittenbyCozzolinoandEwell(2)in1980.Thepaperwasthefirsttoapplyaphysicsoffailurebasedapproachtocapac

7、itorcracking.Criticalmaterialpropertiesweremeasuredthroughavarietyofexperimentaltechniques,includingindentationtocalculatefracturetoughness,straingagestomeasureresidualstrains,andultrasonicmethodstoobtainelasticproperties.Cozzolinoalsoprovidedabasisforapplyingfracturemechanicsthroug

8、htheuseoffiniteelem