Thermodynamic Reliability

Transcription

1 Thermodynamic Reliabiliy Dr. Alec Feinberg 04 ASQ Reliabiliy Division

2 Thermodynamics Reliabiliy Alec Feinberg, Ph.D. DfRSof This Talk is available a: Selec -> Free Publicaions On his webpage scroll down o: ASQ Talk Thermodynamic Reliabiliy For ASQ members he video and he slides are also available a: hp:// Equaions in his alk are incorporaed in DfRSof sofware described a he websie DfRSof

3 Table of Conens: Thermodynamics: a fundamenal Science for Physics-offailure Equilibrium Damage Assessmen Mehod Non Equilibrium Damage Assessmen Mehod Conclusions Appendix Examples 3

4 NEW BOOK: Only reference for his maerial The Physics of Degradaion in Engineered Maerials and Devices Edior: Dr Jonahan Swingler, Herio-Wa Universiy, England Major Conribuor: Dr Alec Feinberg Published by: Momenum Press Due ou a he end of his year 4 6/6/04

5 Book Overview: The Physics of Degradaion in Engineered Maerials and Devices Chaper : Inroducion, Dr Jonahan Swingler Chaper : The Hisory of he Physics of Degradaion, Dr Jeffrey Jones, Chaper 3: Thermodynamics of Engineering, Prof Michael Bryan Chaper 4: Thermodynamic Damage wihin Physics of Degradaion, Dr Alec Feinberg Chaper 5: Monioring Degradaion in he Field., Dr Xiandong Ma, Chaper 6: Physics of Degradaion in Polymers Elecronics, Prof Hari e al Chaper 7: Physics of Degradaion in Ferroelecric Devices,Prof Paul Weaver 5

6 Wha is Thermodynamic Reliabiliy? A relaively new evolving science now being recognized a he universiy level I merges hermodynamics wih reliabiliy I can help Undersand why maerials degrade Lead o new ways o make beer and more meaningful measuremens Help in he making of new maerials Provide new approaches o solving and deecing degradaion Can be used a he sysem and componen level To overlook he poenial his science has in is abiliy o conribue o reliabiliy physics would be a misake 6

7 Thermodynamics: a fundamenal Science for Physics-of-failure Thermodynamics Second Law can be used o describes aging damage Second law in erms of device hermodynamic damage: The sponaneous irreversible damage processes ha ake place in a device ineracing wih is environmen, do so in order o go owards hermodynamic equilibrium wih is environmen. 7

8 Examples Semiconducor componen, seel beam, or a bicycle ire Each sysem ineracs wih is environmen The ineracion beween he sysem and environmen degrade he sysem in accordance wih our second law Degradaion is driven by his endency of he sysem/device o come ino hermodynamic equilibrium wih is environmen Air in bike ire will deflae, seel beam will rus/corrode, semiconducor diffusion will sar o occur 8 6/6/04

9 Order in he Sysem Decreases Causing Damage Toal order of he sysem plus is environmen ends o decrease The sponaneous processes creaing disorder are irreversible Air will no go back ino he bike ire Semiconducor will no sponaneously purify Seal beam will coninue o corrode The original order creaed in a manufacured produc diminishes in a random manner, and becomes measurable 9 6/6/04

10 Assessing Damage in Equilibrium Thermodynamics Thermodynamic sae variables define he equilibrium sae of he sysem Sae variables examples: emperaure, volume, pressure, energy, enropy, mass, volage, curren, elecric field, vibraion displacemens... Enropy or Free Energy are key variables o help assess damage 0 6/6/04

11 Damage Causes a Loss of Abiliy o do Useful Work Disorder is associaed wih device damage Enropy change measures damage If enropy does no increase, here is no degradaion No all enropy increase causes damage Adding or removing hea, increase or decrease enropy. Ye device damage may no occur Heaing a ransisor does no always cause permanen damage. We can pu air back in he ire bu we canno repair a corroded seel beam. 6/6/04

12 Enropy Damage The enropy generaed associaed wih device damage, is, enropy damage Enropy Generaed S gen S gen =DS oal =DS device +DS env 0 We can wrie enropy change in erms of he Non Damage and Damage? DS device =DS damage +DS non-damage 0 6/6/04

13 Measuring Enropy Damage Devise a genle measuremen process f, o measure enropy change in a ime period D. Make an iniial measuremen a ime DS f = S +D-S ime Expose he device o aging unil ime hen make a nd measuremen DS f = S +D-S, where >> Enropy damage: DS f-damage, =DS f -DS f 0 Noe: Equal o 0 => no Damage 3 6/6/04

14 Measuring Enropy Damage Con. We can also look a he aging raio Aging Raio= DS f /DS f wha is an accepable %?? Noe he measuremen process iself should no cause significan damage compared o aging damage Aging sress mus be limied o wihin reason so ha we can repea our measuremen in a consisen manner. See Seleced Examples 4 6/6/04

15 Complex Sysems Enropy Damage The oal enropy of a sysem is equal o he sum of he enropies of he pars. If we isolae an area enclosing he sysem and is environmen such ha no hea, mass flows, or work flows in or ou, hen he enropy generaed is S Gen DS Toal This is an imporan resul for hermodynamic damage. If we can keep abs on DS Toal over ime, we can deermine if aging is occurring even in a complex sysem. See Seleced Examples N i DS i DS Sys DS Surroundin gs 0 6/6/04 5

16 Seleced Resuls in Equilibrium Thermodynamics 6

17 Example & DS Simple Resisor Aging Damage, mc pavg T Ln T 4 3 A Agingraio Ln T3 T Ln T4 T Where C p-avg average specific hea of resisor, m=resisor mass, T room emperaure Time :T 3 emp. rise when curren I passes hrough Time Monh Laer: T 4 emp rise when curren I passes hrough i Example : Complex bu similar Resisor Bank o Ex A Agingraio Ln T3 T Ln T4 T 7 6/6/04

18 Example 3 Sysem of similar pars incompressible consan volume DS Toal T Ln T N N DS mic Avg i i i Where C Avgi average specific hea of pars, m i = mass A Agingraio Ln T3 T Ln T T A Iniial Time T =Iniial Temperaure of Sysem T =T +Temperaure rise of sysem in operaion iniially A a ime laer when aging has occurred T =Iniial Temperaure of Sysem T 3 =T +Temperaure rise of sysem in operaion a laer ime 8 6/6/04

19 Numeric Example 4 Prior o a sysem being subjeced o a harsh environmen, we make an iniial measuremen M + a ambien emperaure. Then he sysem is subjeced o an unknown harsh environmen. We hen reurn he sysem o he lab and make a measuremen M + in he exac same way ha M was made. Find he aging raio where M: T=300 o K, T=360 o K, Soluion: A M: T=300 o K, T3=400 o K Agingraio Ln Ln Sysem has aged by a facor of.58. We nex need o deermine wha aging raio is criical. + Noe: In he sric hermodynamic approach M and M should be made wih he sysem hermally insulaed. However, if we can make a measuremen in a repeaable way say wih a hermal couple on a specific surface of ineres we should ge reasonably accurae resuls. 9

20 Example 5 Noise can be considered a sysem level sae variable Noise Degradaion of isolaed sysem and environmen wih sysem exhibiing whie noise Thermodynamic enropy analysis resuls show noise variance is a key sae variable. Where DS Damage A Iniial Time S s -iniial =Iniial sandard deviaion of whie noise A a ime laer when aging has occurred s X S X DS, log s s -final =Final or laer ime value of he sandard deviaion of whie noise 0

21 Numeric Example 6 Prior o a sysem being subjeced o a harsh environmen, we make an iniial measuremen M + of an engine vibraion flucuaion profile. Then he sysem is subjeced o an unknown harsh environmen. We hen reurn he sysem o he lab and make a measuremen M + in he exac same way ha M was made. Find he aging raio where M: Engine exhibis a consan PSD characerisic of 3Grms in he bandwidh from 0 o 500 Hz M: Engine exhibis a consan PSD characerisic of 5Grms in he bandwidh from 0 o 500 Hz Sysem noise damage raio is hen: noe variance=grms for whie noise noise_ raio Log5 Log3.47 Damage

22 Assessing Damage in Non Equilibrium Thermodynamic Equilibrium hermodynamics provides mehods for describing he iniial and final equilibrium sysem saes, wihou describing he deails of how he sysem evolves o final sae. While, non-equilibrium hermodynamics describes in more deail wha happens during he evoluion o he final equilibrium sae.

23 Assessing Damage in Non Equilibrium Thermodynamic Here we are concerned wih he aging pah. How does aging occur over ime as opposed o jus assessing he sysem s sae a any ime poin. We can use he prior mehod and sample more o race ou an aging pah However, using his mehod, we need o keep rack and measure a number of saes hroughou he aging process. Ofen we are able o model he degradaion damage so we do no have o make many measuremens. 6/6/04 3 Aging pah

24 Conjugae Work & Free Energy Approach The work done on he sysem by he environmen has he form W a Y a dx Associaed wih work causing damage by he environmen on he device is a loss of free energy F a or W X X Y dx D Fx Work =F final -F iniial 4 6/6/04

25 Damage: Enropy Increases or Free Energy Decreases Non Equilibrium Thermodynamics Aging Sae dstoal d 0 0 d d Enropy definiion Free energy definiion Equilibrium Thermodynamics dstoal 0 d Enropy is as large as possible Non Aging Sae d 0 d Free energy is as small as possible

26 Conjugae Work Variable Some common hermodynamic work sysems Common Sysems W Generalized force Y Generalized Displacemen X Mechanical Work W=YdX Gas Pressure -P Volume V -P dv Chemical Chemical Poenial m Molar number of aoms or molecules N Spring Force f Disance x f dx Mechanical Wire/Bar Tension J Lengh L J dl Mechanical Srain Sress s Srain e s de Elecric Polarizaion Polarizaion -p Elecric Field E -p de Capaciance Volage V Charge q V dq Inducion Curren I Magneic flux Id Magneic Polarizabiliy Magneic Inensiy H Magneizaion M H dm Linear Sysem Velociy v Momenum m v dm Roaing Fluids Angular velociy w Angular momenum L wdl Resisor Volage V Curren I VI d m dn 6 6/6/04

27 Thermodynamic Damage Raio Mehod for Tracking Degradaion Toal work some work cause damage and some work is due o damage inefficiencies unrelaed o sysem work damage. In heory we can rack he rue damage, he ypes of damage Damage The work damage raio: This consiss of he work performed o he work needed o cause sysem failure. In sysem failure, we exhaus he maximum amoun of useful sysem work. All work found mus be aken over he same work pah. m d i i i and Effecive Damage W w d m W w T T i 7 6/6/04

28 Damage Raio Con. Cyclic damage can be wrien over n cycles as Damage Y n dx n n W Failure Parial cyclic work Toal cyclic work ocyclic Non cyclic damage Same Work Pah Damage YdX W Failure Parial work Toal work needed for failure 8 6/6/04

29 Deermining Acceleraion Facors Using Damage Raio When he degradaion pah is separable for ime Damage beween wo differen environmenal sresses Y and Y, and failure occurs for each a ime and hen he damage value of requires ha Then damage can be wrien AF 6/6/04 9,,,,,,,,, a E k Y f a E k Y f AF or a E k Y f a E k Y f Damage E k Y f d d dx Y w a f i,,,,,,,,,,, AF a E k Y f a E k Y f a E k Y f a E k Y f Damage

30 Seleced Resuls in Non Equilibrium Thermodynamics Ex. 7: Creep s is mechanical sress, e p srain 6/6/04 30 i p i i p i i i AF Damage, p M T T K E c B a e AF / s s p M p M P P B T d p B d d d d w s s e s e s

31 Seleced Resuls in Non Equilibrium Thermodynamics Ex. 8: Mechanical Abrasive Wear non emperaure sress relaed w Damage AF F dx i dd F d d i i i A kp kp d HA HA i AF, i P, A P V=removed volume of he sofer maerial, P=normal load lbs, L is he sliding disance fee, H=hardness of he sofer maerial in psi, wear volume V=AD where A is he area and D is he deph of he removed. Then wriing L= for wo sliding surfaces rubbing agains each oher a a consan velociy, failure ime. 3 6/6/04

32 Cyclic Work How Much Damage/Cycle? Cyclic Work cause damage each cycle Compress-Decompress To esimae he amoun of damage we firs need o find he oal amoun of cyclic work done i.e. he sum of all he cyclic work performed for each cycle For sress and srain ype cyclic work he oal work is given by wcycle The damage is he raio n i Area i Sde Damage n Sde i Area i W Failure Sum work per cycle Toal work needed for failure 3

33 Faigue Damage Using Miner s Rule Miner s rule is a popular approximaion for finding damage Work W is a funcion of he cyclic area. Miner s empirically figured ha sress S, cycles n were he main facors for damage In our framework his means W n =WS, n Miner also empirically assumed ha he work for n cycles of he same cyclic size is all ha is needed in our framework his means W n = n WS Miner s assumpion=realiy is work is reduced each S cycle Failure Failure Failure W S n W W S nw W S n W S nw Damage S W N S W N S W N Failure W i i N n i N n N n N n S W N S W n S W N S W n S W N S W n Damage

34 Example: Miner s Rule Then Miner s rule can be modified as Ni = AF, i N Effecive Damage n N n AF, N n 3 AF,3 N k n i i AF, i N 34 6/6/04

35 Non Equilibrium Thermodynamics, Example 9 Miner s Rule for Secondary Baeries Miner s rule using he n cyclic sum over he Deph of Discharge % DoD% i h level sress for baery life peraining o a cerain failure permanen volage drop such as 0% of he iniially raed baery volage and hen he effecive damage done in n i DoDs% can be assessed when N i is known for he i h DoD level. 35 Effecive Damage i k n i N i 6/6/04

36 Thermally Acivaed Time-dependen TAT device degradaion models Arrhenius Aging Due o Small Parameric Change due o a changes in he free energy da d da d a exp K BT where y and y are given by For small parameric change we have ay T exp KBT y a a 0 ay y T 0 a and 0 o exp KBT y... 0 a 36

37 Solving a DP A ln[ B ] P A K T y and B B T y K T B Examples of Ln+B ime aging law wih a similar o primary and secondary creep sages and b similar o primary baery volage loss. Oher key examples include Type II wear, ransisor aging. 37

38 Wear Modeling Common wear ypes Type I wear model is covered by he well known Archards linear Wear Model. When logarihmic-in-ime aging occurs as is illusraed in Type II wear shown in he Figure ofen observed in meals. Here we apply he TAT model. This is characerized by an iniially high wear rae hen, a seady sae low wear rae. Type I shows he case of seady wear in ime, Type III ypically observed in lapping and polishing for surface finishing of ceramics. 38

39 Example 0 : Wear TAT Modeling for Type II Mass removal M per uni ime for an acivaed process dm d T o 0 m M exp K BT T exp m M K B T m as he acivaion chemical poenial per uni mass, is he acivaion energy for he process and is he wear ampliude described in he book chaper. 39

40 Model Resuls M=A ln+b A K B m T and B T m K B T Noe he logarihmic-in-ime dependence in he acivaion wear case differs from he Archard s linear dependence i.e. l=v. Here we find ha when B is less han or of he order of, he removal amoun is large a firs hen is less as ime accumulaes - a non linear in ime removal. However when B>>, he removal is in ln dependence. Also since ln+x~x for X<<, hen his can be approximaed as M AB =gt for B<<, which upon subsiuion agrees wih he Archard s wear equaion. 40

41 Oher TAT Model Resuls Described in he Book Reference Ex. : TAT Transisor Aging Model Bea degradaion of ransisors D Aln[ B ] MESFET Gae Leakage I Gae-Source Model DI I GS GS Ex. : Creep Model primary & secondary phases in one model DL e L A Aln[ ln[ B ] B ] 4

42 FET Model o Daa Resuls 4

43 Conclusion We presened wo mehods for finding damage Equilibrium hermodynamic assessmen Concep of using enropy as a measure of degradaion, how o make such measuremens, and he capabiliy o assess damage of complex sysems wih an energy approach using enropy damage measuremens Non equilibrium hermodynamic assessmen Using conjugae work an energy approach o assess damage boh cyclic and non cyclic over ime, an improved mehod for deermining acceleraion facors wih he work damage approach Provide enough informaion so hose ineresed in his physics of failure approach can decide if hey wish o pursue his approach 43 6/6/04

44 Appendix Misc. Examples 44 6/6/04

45 Seleced Resuls in Non Equilibrium Thermodynamics Ex. 3: Corrosion where I is he corrosion curren I Damage corrosion AF, Damage corrosion I Ex. 4: In baery corrosion I I De exp R T T, hen Noe I can opionally be defined in a more sophisicaed way AF AF p Where C p is he baery capaciy, is he failure ime, I is he corrosion curren a a one-ampere discharge rae per Peuker s Law I I C C p I I Y 45 6/6/04

46 Conac Informaion Alec Feinberg