Crac ack k Pr Propagati opagation on Model odel from om Cou - PowerPoint PPT Presentation

Crac ack k Pr Propagati opagation on Model odel from om Cou oupled pled Atom omis istic tic-Cont Continuu inuum m Simulations ulations Som omnath nath Ghosh osh Grad aduate uate St Stud udents: nts: Jia iaxi i Zhan ang g an and Su Subh bhen endu du Chak akrabo rabort rty Depar artm tments ents of Civ ivil il, Mechani anical cal an and Mat ateri rials als Sc Scie ience ce &Engine gineeri ering ng Jo Johns ns Hopkins kins Un Univ iversity sity Bal altimore imore, , USA SA Ackno nowl wledge dgeme ments nts: : Nat atio iona nal l Sc Scie ience e Found undat ation ion NIST ST Works rkshop hop on Atom tomis isti tic c Si Simul ulat ations ions for r Industri ustrial al Needs Gai aithersburg, ersburg, MD Aug ugust ust 2, 2, 20 2018 18

Mod odelin eling Fa Fati tigue gue and nd Fa Failu ilure e in n Crys ystalline talline Materials erials Ti Ti-624 6242 Al Al- 7075 7075-T65 T651 Williams, Sinha, Mills, Hochhalter et al. (2010) Bhattacharjee, (2006)

Short ort and nd Lon ong g Crack ack Pr Propagation opagation in Po Polycrystalline ycrystalline Micros crostructure tructures Stag St age I – Sh Short rt Crac ack k Growt owth Stag St age II – Long ng Crac ack k Grow owth • Plastic • Insen tic zone one at grain in scale e ensiti sitive ve to o micr crost ostruc ructure ture • Strong • Paris’ Law ong microstru ructure e de depe pend ndenc ence, e, grain in boundary, oundary, di disloc ocati ation n struc ucture, ure, slip p , etc. c. http://fcp.mechse.illinois.edu

Short ort Crack ack Ev Evol oluti tion on Coh ohesiv esive e zon one e mod odels els Separation between material surfaces resisted by cohesive tractions Needleman (1990), Ortiz and Pandolfi (1999), Park Paulino, Roesler (2009) Spearot, McDowell (2004), Yamakov, Saether E, Glaessgen E (2008) Process Zone  Parameters ameters of cohesi esive ve potent ential al are e typ ypically y calibr brated ated by y ex exper erimen ments ts  Inter eracti action on bet etween een crack ck growth wth and local al plast stici city y ev evolut lution on which h affected ted by y the e local l mi microstruct ostructur ure e is not include ded

ሶ ሶ Ph Phase ase-Field Field Mo Model delin ing Clayton and Knap (2015), Conti tinu nuous us Aux uxil iliary iary Fie ield ld to Miehe, Hofacker, and Welschinger (2010), Approxim roximate ate Sh Shar arp p Crac ack k Ambati, Gerasimov, and Lorenzis, (2015). Discon Di conti tinu nuit ities. ies. s 𝑦 = 𝑓 −|𝑦|/𝑚 𝑑 (s) 𝑚 𝑑 𝑚 𝑑 Diffused crack 𝑡 is the phase field variable (order parameter): 𝒕 ∈ [𝟏, 𝟐] ; ; 𝒕 = 𝟏 perfect ct soli lid; d; 𝒕 = 𝟐 fully cracked d Helmhol lmholtz tz stor ored energy rgy and d crack k di dissipat pation are mod odeled eled wi with h ph phase e field: Ψ = Ψ 𝑓 (𝑭 𝑓 , 𝑡) + Ψ 𝑒 (𝜽, 𝑡) + Ψ 𝑔 (𝑡, 𝛼𝑡) Stored free energy: 𝐸 = 𝑋 𝑓𝑦𝑢 − Ψ e + ሶ Ψ d + ሶ Ψ f Dissipation rate: Energy gy fun unctional tionals s ar are typica ically lly not t roo ooted ed in in the at atomis misti tic sour urce e of the frac acture ture regi gion on

Objec jective tive of of th this s Stu tudy dy  Upscaling Upscaling of of varia variabl bles fro from ato atomi mic-sc scale ale molecul molecular ar dyn ynam amics ics si simu mula lati tion ons in in a se self lf-con consiste sistent nt mo model el.  De Develop velop phys ysics ics-base based, d, integrated integrated fra frame mewor work of of crack ack evolut volution ion and nd de defor formation mation mode models ls for for cr cryst ystal alline line ma materi terial als that that can an be be used sed in in co conjunc njuncti tion wit ith cr crys ystal tal pla last stici icity ty fin init ite ele lemen ment mo models els.

Seq equence ence of of Ste teps s in n Buil uildin ing th the e Mod odel el • Char arac acterizin erizing g me mechan anisms isms in at atomi mist stic ic si simu mulation ations ( Zhang, Ghosh JMPS, 2013) • Self-con consi sistent stent coupled pled at atomi mistic stic-con conti tinu nuum m mo model el ( Zhang, Chakraborty, Ghosh IJMCE 2017, Ghosh Zhang IJF 2017) • Crack propa paga gatio tion n using coupled led model • Hyperdy rdynam namics ics for time me-sca scale le ac accelerati leration on (Chakraborty, Zhang, Ghosh CMS 2016, Chakraborty, CMS Ghosh 2018) • Extracting ting crack growth th mo models els, , e.g. phas ase e fie ield ld ene nergies gies (Ghosh Zhang IJF 2017, Chakraborty, CMS Ghosh 2018)

I. Atomistic omistic Si Simu mulations lations wi with h Me Mech chan anism ism Chara racteriz cterization ation and Quanti tificat ication ion MD D sim imul ulat ation ion prov ovid ides es tool ols s to cap apture ure defor ormati ation on mechan anism isms s whic ich domin minate ate crac ack k tip ip pla lasti ticit ity an and af affect t crac ack k propag opagati ation on proc ocess ess. J. Zhang hang and d S. Gho hosh, , JMPS PS , Vol ol. 61, 1670 – 1690, 690, 2013 Crack propagation dislocation micro structure twinning evolution

I. Charact aracterization erization and d Qu Quanti antification fication of of I. Mec echan hanisms isms in Molecu olecular lar Simul mulation ion Crack ck sur urface ace Dislocati ocation on Extrac racti tion on (DX DXA) A) Deformatio rmation n gradien ent for or twi wins Di Dislo locat cation ion CNA, , DX DXA Di Dislo locat cation ion densit ity, , Bur urge gers rs vector tor Twin in De Defor orma mation tion Twin volume ume fractio tion gr grad adient ient Crac ack k sur urface face Equi uiva valen lent t ell llip ipse Crack k length, h, openi ning ng

A MD MD Mo Model el to to St Study dy Ev Evol oluti tion on of of Crac ack k and d Ass ssoc ociat iated ed Mec echanisms hanisms • Nick ckel l Singl gle e Crys ystal tal: : MEAM M po potential ntial • NPT T ensem emble ble ~1K 100 nm m x 60nm nm x 25nm(10 m(10 million n atom oms) s) Periodic dic bou ound ndary ary con ondi dition tion Initial al small ll cr crack ck in the he ce center er Tensil nsile e loa oadi ding, ng, strain in con ontrolle led d rate ~ 10 7 s -1 Strain in-rate

A. Ev Evol oluti tion on of of De Deform ormation ation Mec echan hanisms isms Stabilized Dislocation Structure at 2.7% Strain. • After er cr critica cal stress, s, pa partial al di disloc ocati ation emiss ssio ion n from om crack-tip p slip caused ed by dislocat ation on gliding ng blunt unts s crack k tip an p and d redu duces s stress ss con oncentrat entration Dislocation segments • No o brittle e cr crack ck pr prop opaga agation n by bond ond cl cleava vage ge colored by magnitude of Burgers vector • Crack ck evol oluti ution n for or thi his or orienta ntation n is gov overne erned by 1  bl e u : b 112 { 111 } hy hydr drost ostat atic strain n and d slip, p, resemb embli ling ng voi oid d growt owth 6 1  r e d : b 110 { 111 } • 6 For ormatio mation n of of di disloc ocatio ation n jun unct ctio ions, ns, jun unct ctio ion n length gth 1  take kes s 30% % of of tot otal lengt gth gree n : b 100 { 111 } 3

B. Ev Evol olut ution ion of of De Deform ormation ation Me Mechan hanisms isms • Deformatio ation mechanism sms s divided d into two categor gorie ies, s, (i) twin n partials ials contri tributi buting ng to slip (ii) disloca ocatio tion n motion n contrib tribut uting ng to slip. • Tw Twins s forme med at at crac ack k tip by sequential tial lead ading par artial ial dislocatio cations ns nucleate eated d on adjace cent nt {111} plane • All twin n partial ials s are edge partials als with h no cross ss-sl slip ip • At ∼ 3.3% 3% tensil ile strain, n, dislocatio cation n loop starts rts to emit from the crack k tip, , gliding g in the {111} plane. • Tw Twin bounda daries ries imp mpede disloca ocatio tion n mo motion, n, simi milar ar on jun unction to dislocati cation Dislocations interact with twin boundary forming stair-rod dislocations Dislocation segments colored by magnitude of Burgers vector 1 𝑐𝑚𝑣𝑓: 𝒄 𝟐 = 6 112 111 1 𝑠𝑓𝑒: 𝒄 𝟑 = 6 110 111 1 𝑕𝑠𝑓𝑓𝑜: 𝒄 𝟒 = 3 100 111

Decomposition omposition of Ene nergy y Associ ssociated ated wit ith Ener En ergy gy Pa Partitio titionin ning g Ass ssoc ociat iated ed with th Deforma rmati tion on Mechanisms anisms Def efor ormati mation on Mec echanisms hanisms 𝒆𝑿 = 𝒆𝑽 𝐟𝐦 + 𝒆𝑽 𝒋𝒐𝒇𝒎 + 𝒆𝑹 Disloc ocation ation do domina inated ed Energy rgy evol olution n pr prof ofile e ca can sug ugges gest t the he de deform ormation n mechanism! anism! Twi win n first the hen di disloc ocation tion Heat transfer coefficient 𝑅 𝜈 ≜ 𝑅+𝑉 𝑗𝑜𝑓𝑚