Comportement rheologique, percolation et endommagement de materiaux a joints de grains visqueux, solides ou liquides

.,, , ,, , THESE , ~ présentée par Mau Chien ,,DANG , - '~énieur mécanicien de l'Institut National Polytechnique de Biélorussie URSS) pour obtenir le gradede DOCTEUR de L'INSTITUT NATIONAL POLYTECHNIQUE DE GRENO~~ ' : " (Arrêté ministériel du 30 mars 1992) , (Spécialité : Science et Génie des Matériaux) . - \~- ,/ COMPORTEMENT RHEOLOGIQUE, PERCOLATION'ET ,~ ~NDOMMAGEMENT DE MATERIAUX A JOINTS DE GRAINS VISQUEUX, SOLIDES OU LIQUIDES , ., f - • " Prof PHILmERT Président- Dr P DUVAL Rapporteur Rapporteur Prof B BAUDELET Pfu( n BOINARn Dr.'P ~·!'.iAR ANDëT Examinateur - •• 1" Prof on, SEVll LANO , , Date de soutenance : le 30 septembre 1994 _ Composition dujury : ~ - " : ' " Examinateur Examinateur ~~,} 00 sein du Laeoratoire Génie Physique ét Mécanique des ;; l Mll!hiaux (GP"'f2) ~ , nité Ôi; Recherche Associée au CNRS nO 793 , ,~ '; -«: ~ ~ ~ LA ~:~c.r èrt+-11, ,,'~ \ ~ T1', t+- Composition du jury : ,~ ~~ ; 1' ~ ; J' ~/;~~ t: \ /,\) \ , ',' '.t~ ':~.: 0,_ ~ ~, ~ >~~~~- ~ ~~\ Prof J PHILIBERT Président Dr P.DUVAL Prof J GIL SEVILLANO Rapporteur Rapporteur Prof B BAUDELET Prof D BOUVARD Dr B MARANDET Examinateur Examinateur Examinateur Thèse préparée au sein du Laboratoire Génie Physique et Mécanique des Matériaux (GPM2) Unité de Recherche Associée au CNRS n? 793 7GOG SO A n née 1994 PROFESSEURS DES UNIVE RSITES BARIBAUD Michel ENSERG BARRAUD Al ain ENSIEG BARTHELEMY Alain ENSHMG BAUDELET Bernard ENSPG BAUDIN Gérard UFR PGP BEAUFILS Jean-Pierr e ENSIEG/ILL BOIS Ph il ipp e ENSHMG BOUVIER Gé rard ENSERG BRINI Je an ENSERG BRUNET Y ve s CUEFA CAVAIGNAC J e an-Fran ỗoi s ENSPG CHARTIER Germa in ENSPG CHENEVIER Pierr e ENSERG CHERUY Ari elle ENSIEG CHOYEr A lain ENSERG ŒGNEr Gérard ENSGI COLINET Cath erin e ENSEEG COMMAULT Chr istian ENSIEG CORNUT B runo ENSIEG COULOMB Jean-Loui s ENSIEG COUTRIS Ni cole ENSPG CROWLEY James ENSIMAG DALARD Francis ENSEEG DARVE F él ix ENSHMG DELLA DORA Jean ENSIMAG DEPEY Mauri ce ENS ERG DEPORTES Jacqu es ENSPG DEROO Daniel ENSEEG DESRE Pier re ENSEEG DIARD Jean-Paul ENSEEG DOLMAZON Jean -Mar c ENSER Fr an ci s ENSEEG DURA ND J e a n-L ouis E NSPG FA UTRELLE Yves ENSHMG FOGGIA A l b e rt ENSIEG FORA Y Pi erre E NSH.L\1G FOULARD Claud e ENSIEG G AL ERIE Alain ENSEEG GA ND IN I Al e s s andro UFR/PGP GAUBERT Cl aud e ENSPG GE NT IL Pierre E NSERG GENTIL S yl v i ane ENSIEG GUERI N B ernard ENSERG GUYOT Pi err e ENSEEG IVA NES M ar cel ENSIE G JACQUET Paul ENSIM AG JALLUT Ch ri s ti an ENSEEG JANOT M arie-Thérese ENSERG JAULENT Patri ck ENSGI JA USSA UD Pierr e ENSIEG JOST R ém y ENSPG JOUBERT J e an - Cl aud e ENSPG JOUR DAIN G e ne v i ve ENSIEG KUENY J e an-L oui s ENSHMG LACHENAL D ominique UFR PGP LACOUME J e an-Loui s ENSIEG LADET Pi err e ENSIEG LE NEST J e an -Fr anỗ oi s U F R/P G P LE SlE UR M arce l ENSHMG LES PINARD G e o rg e s ENSH.L\1G LIE NARD J o ël ENSIEG LOi\'GEQUEUE J e a n-Pi erre ENSPG LORET B en j a m i n ENSHMG LOUCHET F r a nỗo i s ENSEEG LUCAZEA U Gu y ENSEEG LUX A ugu s t i n E t'iS IMAG P hil i p p e ENSPG DURA ND ~ I.-\SS E ~ tASSE LOT é Ch ri s t ian ENSIEG ~ IA ZARE Guy ENSII\I AG ~ llC HE L G é r ar d ENS IMA G Ro gc r ENS IM AG ~ IO HR MOREAU R en é ENSHMG MORET Roger ENSIEG MOS SIERE J ac qu e s ENS IMAG OBLED Ch a r l e s · ENSHMG OZIL Pat rick ENSEEG PANANAKAK IS G e orge s ENSERG PA UL EAU Yves ENSEEG PERRET Rob ert ENSIEG PERRIER Pa scal ENSERG P IAU J e an - M ic h e l ENSHMG PIC Etienne ENSERG PLATEAU B r ig i tte ENSIMAG POUPOT C hris tian ENSERG RAMEAU J e a n - J a c qu e s EJ'lSEEG RE INISCH Ray mond ENSPG RENAUD Ma u rice U F R/ P G P RIMET Roge r ENSERG ROBERT F nỗo i s ENSIMAG ROGNON J e a n - P i er r e ENS IEG ROSSIGNOL Miche l ENS PG ROYE D anie l ENSIE G SABONNADIERE J e a n - Cl a u d e ENSIEG SAGUET P ierre ENSERG SAUCIER Gabri é le ENSIM AG SCHLENKER C Ia i re ENSPG SCHLENKER M i che l ENSPG SILVY J ac q u e s U F R/P G P SOHM J e a n - Cl a u d e ENSEEG SOLER J e a n -L o u is ENSI M AG SOUQUET J e an -Lo ui s EJ'lSEEG TICHKIEWITCH Ser ge ENSHMG TROMPETTE Philippe ENSHMG TRYSTRAM Denis EN SGI VE ILLON Gér a rd E NSIMAG VERJUS J e a n - P i err e ENS IM AG VINCE NT H enri ENSPG S ITUA T IQN PARTICULIERE PROFESSEURS D'UNIVERSITE DETACHEMENT BLOCH D an iel ENSPG BONNEr G uy ENSPG BRECHET Yves EJ"lSEEG CAILLERIE D eni s ENSW-IG GREVEN H él én e CUEFA LATOMBE J e a n-Cl au d e ENSl ivlAG P IE R R AR D J e a n-M ar ie ENSHMG DIRECTEURS DE RECHERCHE CNRS ABELLO L o u is ALDEBERT Pi e r r e ALEM ANY An t oine ALLIBERT Co lette ALLIBERT Mi c h el AN S AR A I br a hi m ARMA ND Mi ch el AUDIER M ar c AUGO YARD J e a n -Fr a n ỗ oi s AVIGNON M ic h e l BERNARD C laud e BIN DER G i lb e rt BLA IS ING J e an - J acque s BONNET R o land BORNARD G uy BOUCHERLE J e an-X a vier CA ILLET M ar c el CARRE Ren é CHASSERY J e a n- M a r c C HAT ILLO N C hr i s t ian CIBERT J o ël CLEP.MOl\'T J e a n- R ob ert COURTOIS Be r n a rd CR IQU I P at r ic k CRISTOLO VEAJ'IU S0 rin DAVID Re n é DION J e an - M i ch el DOUS SIERE J acq ue s DRIOLE Jean DUCHET P ie r re DUGARD Lu c DURAND R obe rt ESCUDIER P i err e EUSTAT HOPO ULOS N ic o la s GAR NIER Marcel GIROD J a cqu e s GLA NGEAOO Fr a n ç o i s GUELI N Pi e r r e HOPFI NGER Em il JORRA ND Ph ili p p e JOOO J e an - Charle s KAMARINO S Ge or g e s KLEITZ Mi ch el KOFMAN W al t e r LACROIX Cl au dine LANDAU I o an LAULHERE Jean -Pierre LEGRAND Mich el LEJE UNE G ér ard LEPROVOST Chri st i an MAD AR R ol a n d MARTIN J e an -M ari e tvŒRMET Jean MEU NIE R G é r ard MICHE L J e a n- M ar i e NAYR OLL ES B ern ar d PASTU REL A l ain PEUZI N J e an - C l a ud e PHAM An t o ine PIA U M on i q u e PIQUE Je a n- P a ul POINSIGNO N Ch ri s ti a ne PREJEAN Jean-J a cqu e s RENOUARD D ominique SENATEUR Jean-Pi erre SIFAKIS Jo s eph SIMON J ean-P aul SUERY Mic he l TEODOSIU C h r i sti a n VACHAUD G e o rges VA UC LI N t\l ic h el \YACK B er n ar d YAV A R I A li -R cza PERSONNES AY A NT OBTENU LE DIPLOM E D'H ABI LIT ATI ON A DIRI GER DES RECH ER CHES BALESTRA Fr an ci s BALME L o u is BECKER M oniqu e BENECH Pie r r e BIGEON Jean BINDER Zd eneck BCE L o u i s- J e a n BRECHET Y ve s CABANEL R ég i s CABON Béa t r i ce CAOOZ Cl aude CANUDAS DE WIT Ca rlo s CHAMPENOIS G ér ard CHOLLEr J e a n-Pi err e (DEY J e a n-P i err e CORNUEJOLS Ge rd COURNIL Michel CRASTES DE PAULET M iche l DALLERY Yves DESCOTES-GENON Berna rd DUGARD Lu c DURA ND M ad el eine FERRlEUX J e a n -P a u l FEUILLET R en é FORAY Pi e r r e FREIN Y ann ick GAGNOUD A n nie GAUTHIER J ea n-P aul GI-ITBAUDO Gé rd GRANGEAT P i e r re GUILLEMOT Nadi n e GUYOT Al a in HAMAR Sy l v i an e HA M AR Ro ge r HORA UD P a tr i ce JACQUET Paul KEVORKl AN Antoine LATOMBE Cl audin e LE HUY H o an g LE GORREC B e rn ard LOZANO-LEAL R oge lio MACOVSCHI Mih aïl MAHEY Philipp e METAIS Oliv ier MONMUSSO N-PICQ G eo rgett e MORY M athieu MULLER J ean MULLER J e an-Miche l NGUYEN TRONG Bernadette NIEZ Jean -Jacques PERRIER Pas cal PETRIN J o cel yne PLA F ern and RAUCH E dg ar RECHENMA NN Fr a n ỗoi s RIVEILL M i ch el ROGNON J e an -Pierre ROUGER Je an ROUX J e a n-Claud e SKOTNICKI To masz TCHUENT Ma u r i ce THOMAS Ol ivie r TlXADOR P a s c al VAHLAS C on st antin VALETTE Ser ge VERGER-GAUDRY J e an-Loui s per colation may occu r ove r long di stan ces This is demonstra ted by t h a t du r ing compression the liqu id inter ph a se is a lm ost compl ete ly expelled fr om a reas in t ri ax ial comp ression (top a nd bottom of th e specime n) an d flows into th e cen tral par t of th e spe cim en wh er e a comb ination of biaxial ten sion and u nia xia l com pr es sion exi sts [13] C cn ver sely, th e pe rcolation is limit ed t o distan ce compa ble t o gra in siz e (loca l per cola tio n) u nder simiJa r dit ions wh en the int erp se is in visco u s solid sta te [14] Consequen tly, in spit e of sho r t t im e, th e pr opor tion of th e int erp h as e in th e centr a l part of th e spec ime n test ed at T > T cs is hi gh er (Fi g l b) th a n th a t of th e spe cime n tested at T < Tco (F ig l a ) compres sio n axis into GB parall ei with ax is ; and vi se ver sa in the case of ten: [14J These re sul t s clearly indica t e existe nce of a n et work of ch annels betw th e pocket s of interphase th at all ows ea sy flow of this ph a se The kin etics of percola tion process viscou s solid inte r ph a se ' w a s stud ied t occu re nce of percolation dep ends on m agnitud es of tim e, t, and a pp lie d st r ess a t a given tem pera ture In th e logari t scale of (t, cr), th e zones without and \\ per cola tio n can be sepa r ated by a strai lin e (F ig ) - n o percola tion low percolation o high per colation e o T = 465' C 10 APPLŒD STRESS (MPa) I O~ F ig The dep e nd ence of th e occu r r en ce per colation on th e m agn itud es of t im e, t, a a pplied str ess, cr, is sh ow n in the logaritl sca le ; ( + , , ) in com pressio n, ( , , ) t ension The tim e-str ess behavio u r observ ed see t o follow a h yp erbolic r el a t ion : t c = K, wh r K is a const a nt for a gi ven t em peratu nea rly equ al t o 600 -100 MPa s a t 46 5'C Fig SE:'.r mic r ographs sho winc- th e per colation of inte r phase du r ing com p;essive tests perforrn ed a t : (a ) cr = ",rPa , t = 1600 s T = 465 'C (solid GB) and (b) cr = MPa , t ~ 160 s, T =4S0'C (liquid GE) As shown in th e figure, th e interph a se wa s squeez ed ou t of GB perpendi cula r t o th e 3.2 Grain s h a pe as a function of st a and proportion of interphase The percola tion of t h e in terpha se (j redistribu t ion of th is pha se) m ay m odify t micr ostructu re a nd gr ain sha pes As seen F ig l , th e int er ph a se su r ro u nds th e gr m cornp le te ly and sorne solid cont a ct s (necl exist bet ween gr ns The num ber of the neck s decr ea ses wit h in cr ea sing a rnount th e in terphase Wh en ail n eck s are di ssolv th e cohe si on of m ateria l is n o lon] maintain ed [13] Th e microstructur e with necks is pr esented in F ig which shows the decohesion at necks and sorne rem ain ing facets before complete ruptur e m , a nd no grai n deformatio n (Tab, 1) The GES is eva luated by th e shift of scrat ch es at GE and by surface relief of gr ains (Fig 4) Table Deformation beh aviour as a fu nction of strain rate and state of interp has e Strain St a te of interphase rates -1 - Fig SE ;:"'! micrograph of th e intergra nul ar fractu re aft er a compressive test at 4S0'C (Iiquid GEl, i: = 3.10-' ỗ l for E = 0.3 The Iiqui d int er ph ase is seen to smooth out th e angles of gr a ins a nd, conseque ntly to change an gular grains into rou nd ed ones (Fig lb) F u th ermore, grains become "ball like" in th e zone wit h high pr opor tion of the liquid inte rp hase [13] The change in grain shape seems to be negligible when the interphase is viscous solid (Fig l a ) The change in gr a in shape is ca used by the dissol ution and depositi on of the solid phase Th e ki netics of the pr ocesses depen ds on whether the inter pha se is solid or liqu id These proces ses occur more pidl y in th e liquid inte r pha se a nd lead to the smooth en ing of grain su rfaces 3.3 Deformation behaviou r Th e deformation behaviou r depends on :he state of th e interphase and st rain r a tes Tab, 1) At T < Tcs ' th e rnat erial exhibits a c-e) behaviour with a stea dy state plateau ) 2] At T > T cs a nd at h igh str ain rates th e c-e) curves exhibit a maximum followed by a strong decrea se associ ated with dam a ge vhe reas thes e curv es in crea se slowly a nd :ontinuous ly with st rain at low stra in rat es Th e exis t ence of GES is rela ted to hi gh zalues of strain te se nsit ivity coefficie nt, m =0.3±0.1 · m = 0.9±0.1 * - no GES - GES with gr ain - no grain deform a tion deform ation * Low - m = 0.8±0.1 · m = 0.9±0.1 - GES · GES - no grain - no gr ain deforma tion de formation * tests per fonn ed und er hydr ost atic pr essure in order to avoid dam age [12] High Fig SE"-! microgr aph sh owing GES (in ten sion at 465 ·C, i: = 5x10-5 s" for E = 0.25), 3.4 D ama ge a) Cavi ty nu cleation and gr owth When GES is ab sent cavities nucl ea te a t GE facet s oriented perpend icular to the ten sion axis Subsequently, th ey grow and coal esce a long th e same GE (Fig 5) I n th e case when GES occurs , cavities nucl eate at multi ple point s for both vi scous solid [14] and liquid int erphase (F ig 3) b) Effect of th e interph a se sta te on th e dam age Th e dependence of th e damage on th e sta te of inte rphase , type of solicita tion (te nsion or compres sion) and strain rate is sh own in Tab The damage of the rnaterial with viscous solid interphase produces intergranular fracture of angular grain s (14] whe reas that of r ounded grains has be en observed when in terphase is liquid (Fig 3) Additionally, whe n the proportion of liquid interphase is hi gh grain shapes becorne "ball-like " [13] T= 480·C È=3.10-' s-' ~ e 0- 2VI VI Fig SEM rnicrograph of pre -polish ed specim en surface showing ca vity nucl eation and growth at GB facets (in ten sion at Ë = 5x 10-' S -I, T = 465'C an d E = 0.15) LU e: VI .J ~ ~ Tabl e Final stages of damage observe d in ten sile and compressi ve tes ts for materials with solid or liguid GB Type of Strain Final stages of damage solicitation rates liguid GB solid GB Tensile high failure failur e zrowth " failure low fail ure Compr essive high gr owth"" low no-cavitation**growt h* * * tensile tests up to 100% deforma tion ** compre ssive tests up to 60 TGB (12] Less liquid in te rphase lead s to more ext ensive dama ge (Fig 6), as exhibited bv the more pidly decrea sing cr with in cr ea si ng E e) Fracture su rfaces 0.L ~-~ ~ ~-_ J 0.00 0.0 o.oa 12 0.16 0.20 TRUE STRAIN Fig Strain dependence of stress for specim ens su bmitted to different in-situ annealings at 480'C prior to compressive tests : (1 ) - 10 mn, (2) - hrs, (3) - 15 hrs 4, DISCUSSION 4.1 Percolation and viscosity of interphase The perc olation of interphase is dr iven by gr adient of st res ses wh ich is proportional to th e applied st ress es [14] This is supported by experirnental results obse rved above (Figs and 2) Th e ki netics of the flow of a viscous phase ca n be considered accord ing to a simple model for the flow of a Newtonian liqu id of viscosit y 1] and original thickness ho from bet ween two flat plates of radius r pre ssed together at constant stress cr (9] as : (1) where hl is the th ickness of liquid mm which decreas es with time, t The relation (1) describ es a hyperbolic law bet ween t and cr, which agrees with experimental re sults (Fig 2) The viscosity of the viscous solid interphase, TJs' is calculated according to equation (1) to be 103-10' Ns/rnê [14] These values are significantly higher than that for liquid metals, TJ L - 10-3 Ns/m" [29] The fact that TJS/TJL = 10 G-107 and ta oc TJ [equation (1)] allows to extrapolate the percolation time correspo nding ~ for liquid interphase For the same order of the magnitude of an cr, it was found th at ~ = 10-G-1O-7 t s, whe re t is percolatio n time for viscous solid interphase at 465 'C a nd equal to 100 s [14] Th e resul ti ng va lue of ~ = 10-' -10-5 S is in good agree me nt wit h th at suggested [9] 4.2 D amage induced b y loc al t ensile stresse s at th e GB Th e critical tensile stress for th e cavity formation withi n th e vis cous inte rphase at GB facets or multiple poi nts ma y provide the basis for interpre ting the cavity nucleat ion and growth [13 , 21] The cavitation is promoted by tensile local stresses , crGS acting on GB [17, 22, 30, 31] and the ' cavi ty nuclea tion occurs when th is stress exceeds the critical stress This was confirmed in experiments which sho wed that in t ensio n the evolution of damage is strongly faste; than that in compr ession under similar conditions (Tab, ·2) Dam age occurs al so in specimens tested in compression because certain local tensile crGS may be produced due to h eterogeneous deformati on asso ciated with compressive tests [32] So, cavitation may only sta rt at GB with highest crGs ' As a r esul t, cavities are observed at GB n early perpendicul ar t o th e tension axis (Fig 6) or parallel with the comp r ess ion axis [13] The preferen tial nuclea ti on of caviti es at multipl e junctions in th e case of presenc e of GBS may be interpret ed by two hypoth eses : one is associated with hi zh stressas induced by GBS at mu lt i;le ju nct ions [13, 21, 24, 27, 31] ; th e ether is rela ted to the difficul ty in maintaini ng the cohesion of mater ial at solid ta cts betwee n grains whe n GBS occurs [13] The fact that the damage is more extensive when the interphase is liquid (Ta b.2) suggests that the critical tens ile stress for cavity formation in a liquid ph a se is lower as compared with that in the viscous solid phase When a hydrostatic pressure is additionally applied during compressive tests, it decreases the local tensile stress on GB by a value equal to the applied hydrostatic pressure [13] and as a result damage is r educed This effect was obs erv ed expe rimentall y for hydr ost a tic pre ssure high er than 0.5 MPa [12] The a GS may be par t iall y r elea sed by accommodation mechanisms su ch as percola tion of inter ph a se an d/or diffu sion in th is ph a se [13, 15] This is suppo r te d by observation of (cr-e) behaviour in specimens wit h differ ent proportions of liqu id int erph a se as seen in F ig Specificall y, each (cr-e) curve consists of two parts separated by a maximum poi nt I n th e left part, strain r esul t s predominatly from GBS (Tab 1) wh ere as in th e r igh t part, pr odu ction of st r n is pr obab ly as sociated with dam ag e [12] The most interesting feature of th ese curves is that less proportion of liquid phase leads to a h igher left part and a lower right part of th e (cr-e) curve This faet suzzests that when the pr oportion of liquid interphase is less the GBS becomes more difficult (due to the increase in ne ck surfa ces at GB) and the stress relaxation process by liquid interpha se decr eases, lead ing to extensive damage As necks betw een grains are essential to main tain the mater ial cohesion durinz deform ation (§ 3.2 ) a n optimum proportion of liquid phase is necessary t o allow the eas y deform ation of th e m ater ial without r emarka ble damage form a tion CONCLUSIONS Th e perco la tion of vi scou s interphase depends on time, t , and ap plied stress, cr, according to th e hyperbolic r elation ta = K, where K is a temperature constant and depend stro ngly on th e state of interph a se Th e cavities are always seen to develop within the viscous in terp h ase.' 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viscosité de rinterphase L'endommagement se produit dans les joints sè>1ï4cs visqûeuxou liquides et dépend de la contrainte locale en traction 'exe-:cant sur ces joints Cette contrainte en traction peut être compensée par la pression effective au cours de déformation en compression triaxiale, ce qUi réduit l'endommagement Comme la percolation est un mécanisme · Cfaœommodation, moins il y a de.liquide, plus la percolation est difficile et · pll!! !'e!!~o~agemei1t est important -'- , - Mors-eLES - Alliage - d'alununium ; Joints solides v11::;ueu~ liauides · ~'.nuJaire ; Comportement r:héologique,lmécanill'; c; Otis! ';' joipts ; Percolation ; Endommagement ; Pression hydre ',' ~cation_; Dissolution-diffiJsion-précipitation Phase Thtr vlën DH Bach •• Kh08 111111111111milmllllllllllllllllllllllllllllllllllllili ... ABDEL-RAZEK Adel AKSAS Haris ALLA Hassane AMER Ahmed ANCELLE Bernard ANGENIEUX Gilbert ATMANI Hamid AYED! Hassine Feri A. BADR Osman BACHIR Aziz BALANZAT Emmanuel BALTER Roland BARDEL Robert BARRAL Gérard... PERCOLAnON ET ENDOMMAGEMENT DE MATERIAUX A JOINTS DE GRAINS VISQUEUX, SOLIDES OU LIQUIDES RESUME Nous avons entrepris une étude systématique sur le comportement rhéologique, la percolation et l 'endommagement. .. POIGNET J e a n - Cl au d e PONS M ich el POU Ton g Eck 12 RAHAL Salah RAMA SEABRA Fernando SANTOS RAVAINE Denis RAZBAN-HAGHIGHI Tchanguiz RAZZOUK Micham REGAZZONI Gilles RIQUET Jean-Pierre ROBACH