Nastanek in rast utrujenostne razpoke v korozijskem mediju Occurrence and Growth of Fatigue Cracks in Corrosion Environment L. Kosec*, F. Kosel** UDK: 620.193.01 ASM/SLA: Rlh, Rle, R2j, Q26p V prispevku obravnavamo nastanek in ravzoj poškodbe kovinskih materialov v obliki klinov iz korozijskih produktov. Analizirali smo pogoje rasti in motenj v rasti klinov, vpliv števila in velikosti klinov na intenzivnost napetosti v sistemu kovina-klin. Rezultate analize smo posplošili s tremi primeri poškodb delov orodij in naprav. 1. UVOD V kemično aktivnih okoljih nastanejo na površini kovin korozijski produkti, ki so različno trdno povezani s kovinsko osnovo. Temperaturne ali mehanske napetosti lahko poškodujejo plasti korozijskih produktov. Tesno oprijete in goste plasti korozijskih produktov upočasnijo ali povsem zavro potek korozijskih procesov. Poškodovane plasti pa te zaščite ne nudijo ali pa zgolj v omejenem obsegu. Poškodbe so različne: razpoke, luš-čenje korozijskih produktov na posameznih delih površine ob meji s kovino ali znotraj korozijskih produktov. V prispevku obravnavamo vplive temperaturnih napetosti in oksidacije kovine na razvoj in obliko poškodb, ki pripeljejo do porušitve. Analiziran je primer, ko seje zaradi mehanske nestabilnosti porušila oksidna plast na površini in je skozi nastale razpoke prišel korozijski medij v stik s kovino. Na takih mestih je prišlo do pospešene oksidacije. Zaradi posebnega načina dostopa oksidanta so na teh mestih korozijski produkti zrasli v obliki klinov. Korozijski produkti se v fizikalnih in mehanskih lastnostih bistveno razlikujejo od kovine. Zato pride pri temperaturnih spremembah do napetostno deformacijskih stanj, ki vplivajo na morfologijo ter deformacijo korozijskega produkta in kovine. Rezultate analize modela ilustriramo s tremi primeri: z elementom orodja za tlačno litje medi, cevmi pre-grevalnika pare iz termoelektrarne in anodnimi palicami akumulatorja, ki naj pokažejo relativno razširjenost pojava. O pojavu oksidnega klina in njegovem vplivu na porušitev kovine je malo strokovnih referenc. Vpliv oksidnega klina na širjenje razpok je analiziral P. T. Heald1 in ugotovil, da razpoka samo zaradi oksidnega klina ne more preiti v nestabilno rast, če sistem ni obremenjen. Razprave o pomenu oksidnega klina na razvoj poškodb strojnih delov in naprav pa najdemo tudi v naši strokovni literaturi2-3-4-5-6. The contribution treats the occurrence and grovvth of defects in metal materials in the form of corrosion pro-duct vvedges. The conditions of vvedge grovvth and crack grovvth retardation, and the effect of the number and size of vvedges on the stress intensity in the metal/ oxide system vvere analyzed. The results of the analysis vvere illustrated by three examples of this kind of defects on certain tool parts and equipment components. 1. INTRODUCTION In chemically active environment metal surfaces get covered by corrosion product coatings vvhose adhesion to the base metal is variously firm. High thermal or mechanical loads of metal/oxide systems can impair corrosion product coatings. Firmly adhered and thick corrosion product coatings can slovv dovvn or even complete-ly stop the progress of corrosion, vvhereas the injured layers can no longer protect against corrosion or can do this only to a certain extent. The defects of the injured coatings can be of various kind like cracks, splitting of corrosion products on some areas of the surface, on the boundary to the base metal, inside the corrosion product layer etc. This contribution treats the effects of thermal stresses and metal oxidation on the occurrence and development of defects leading to failure. An analysis is made of a čase vvhere due to mechanical instability, the oxide surface coating broke, and through the created cracks the corrosion medium came into contact vvith the metal. On such places an intensified oxidation took plače. Due to the special way of transfer of the oxidizing agent through the broken oxide layer, on these places the oxides grevv in the form of vvedges. Corrosion products differ essentially from metals so by their physical as vvell as their mechanical properties. As a result the properties inside such a system are very non-uniform, so the stress-strain states vvhich occur at temperature changes, cause the deformation of the corrosion products, and change their geometric characteristics. The results of a general analysis of the model repre-senting the discussed system are illustrated by three examp!es: an element of tool for die casting of brass, pipes of a steam superheater from a thermal povver plant, and anode rods of a car battery. These examples * Univerza Edvarda Kardelja v Ljubljani, FNT, VTOZD Montanistika ** Univerza Edvarda Kardelja v Ljubljani, Fakulteta za strojništvo * E. Kardelj University of Ljubljana, Faculty of Natural Sciences, Dept. of Metallur. ** E. Kardelj University of Ljubljana, Faculty of Mechanical Engineering Visokotemperaturna oksidacija je eden od pogostih načinov korozije kovin (suha korozija). Povišane in visoke temperature in nihanje temperature še dodatno močno obremenjujejo kovino, zato so poškodbe v takih okoljih še bolj pogoste in usodne. Take pogoje bomo upoštevali pri nastanku in rasti oksidnega klina. 2. NASTANEK IN RAST OKSIDNEGA KLINA Nastanek oksidnega klina sledi predhodni enakomerni oksidaciji površine kovine na primerno visoki temperaturi. Na površini nastali oksid ima različen temperaturni razteznostni koeficient od kovine. Prav tako je pomembno, da ima nastali korozijski produkt tudi znatno večji specifični volumen. Fizikalne in mehanske lastnosti oksida in kovine se s temperaturo spreminjajo. Na obravnavani pojav pa vpliva tudi trdnost vezi med oksidom in kovino. 2.1 Nastanek oksidnega klina Obravnavali bomo primer, kjer sta nastanek in širjenje oksidnega klina možna zaradi menjajočih se temperaturnih obremenitev. Na primerno visoki temperaturi nastane na površini kovine v določenem času zvezna plast oksida. Pri ohlajanju sistema kovina — oksid se zaradi različnih temperaturnih razteznostnih koeficientov v oksidu pojavijo tlačne napetosti. Zaradi njih se pri višjih temperaturah kovina in oksid plastificirata; ko pa se temperatura zniža in preide sistem iz plastičnega v elastično območje, začno v oksidu naraščati tlačne napetosti. Oksidni sloj na površini se elastično deformira. Z ohlajanjem lahko tlačne napetosti v oksidu dosežejo mejo plastičnosti. Če je trdnost vezi s kovino dovolj velika, prične oksid ponovno plastično teči. Drugače pa se lahko lokalno ukloni ali pa lušči, če je zrušilna stri-žna trdnost na meji s kovino manjša od tangencialnih napetosti. Ponavadi potekata oba pojava istočasno. Pri ponovnem segrevanju sistema se pri določeni temperaturi eventuelne preostale tlačne napetosti v oksidu izničijo zaradi različnega širjenja kovine in oksida. Nato se s segrevanjem v oksidu pojavi in narašča natezna napetost. Zaradi mehanskih poškodb, ki so nastale med ohlajanjem, se v oksidu pojavijo koncentracije napetosti. Na teh mestih se pri nadaljnem segrevanju še razmeroma krhek oksid lahko poruši z razpoko, ki je pravokotna na površino kovine. Nastane lahko več takih razpok. Te razpoke omogočajo prost in hiter dostop zraka do kovine, zaradi česar pride do omejene, lokalne oksidacije. Ta drobna oksidna zajeda je začetek oz. zarodek oksidnega klina. 2.2 Rast oksidnega klina Nastali oksid ima znatno večjo prostornino od kovine. Volumska deformacija zaradi oksidacije je tolikšna, da bi napetostno stanje daleč preseglo porušno trdnost kovine in oksida. Zato se oba (sistem) plastificirata. Napetostno stanje je v oksidni zajedi (zarodku klina) enako manjši meji tečenja ene od obeh sestavin sistema OTmin, kot je: CTTmin = min (CT?*in, a^mm) Pri ohlajanjih s Tmax bi se v oksidu pojavile tlačne napetosti, zaradi katerih sistem plastično teče. Plastično tečenje poteka vse do temperature prehoda sistema v elastično stanje pri Tp (temperatura prehoda sistema v should point to the relative frequency of the phenomen-on. In literature very few references can be found about the phenomenon of an oxide wedge. The effect of the oxide vvedge on crack propagation was analysed by P. T. Heald (1) who proved that a crack cannot start grovving unstably only because of an oxide vvedge if no load is applied. Some investigations about the import-ance of an oxide vvedge for the development of defects on various machine parts can also be found in our pro-fessional literature2 3 5 6. High temperature corrosion is one of the most fre-quently found types of metal corrosion (dry corrosion). High temperatures, raised temperatures and high temperature cycles represent an additional load for metal, making the deffects in these environments even more frequent and fatal. These very conditions will be consi-dered in our investigation of the occurrence and grovvth of an oxide vvedge. 2. OCCURRENCE AND GROVVTH OF OXIDE VVEDGE And oxide vvedge occurs after a previous uniform oxidation of a metal surface at a correspondingly high temperature. The newly formed oxide has a different thermal expansion coefficient than the metal. It is also important that this nevv corrosion product has a consid-erably larger specific volume than the metal. The physi-cal and mechanical properties of the oxide and the metal are changing vvith temperature. Besides this, the dis-cussed phenomenon is affected also by the strenght of the oxide adhesion to the metal. 2.1. Oxide Wedge Occurrence We vvill discuss a čase vvhere the occurrence and grovvth of the oxide vvedge are possible because of changing thermal loads. At a correspondingly high temperature and vvithin a certain tirne a continuous oxide layer occurs on the metal surface. During the cooling process of the metal/oxide system compressive stresses arise in the oxide due to the different thermal expansion coefficients. At higher temperatures the oxide and the metal become plastic because of the compressive stresses, but vvhen the temperature lovv-ers, and the system passes from the plastic into elastic region, the compressive stresses in the oxide start in-creasing. Now, the oxide layer on the surface undergoes elastic deformation. During the process of cooling the compressive stresses in the oxide can reach the plastic limit. If the strength of the adhesion to the metal is strong enough, the oxide starts flovving plastically. Othen/vise, it can bend locally or split in čase that the breaking shear strength on the metal boundary is smaller than the tangential stresses. Generally, hovvever, both these tvvo processes are going on simultaneously. During reheating of the system, at a certain temperature the possible remaining compressive stresses in the oxide become eliminated because of the different ex-pansion of the metal and the oxide. If heating is continu-ed, tensile stresses appear and increase in the oxide. Due to mechanical defects that occurred in the oxide during the process of cooling, different stress concen-tration areas can be found. With continued heating on these areas, a relatively brittle oxide can break vvith a crack running rectangularly to the metal surface. Several such cracks might occur. These cracks enable a free and tast transfer of the oxidant (air) to the metal, indu- elastično stanje pri tlaku). Napetostno stanje v oksidni zajedi je pri tej temperaturi enako: Ormin (Tp = amin (a°K (Tp), a? (Tp» Z ohlajenjem pa tlačne napetosti naraščajo. Če dosežejo mejo tečenja aTmin, pride do ponovnega plastičnega tečenja sistema. Naslednja stopnja v spremenljivem temperaturnem režimu je segrevanje sistema od Tmin na Tm?x. Pri tem se v začetku tlačne napetosti, nastale pri ohlajanju, zmanjšujejo in pri določeni temperaturi je sistem brez napetosti. S segrevanjem se v zajedi pojavijo natezne napetosti, ki s temperaturo rastejo. Če napetost preseže trdnost zajede pod temperaturo prehoda iz elastičnega v plastično področje (T+ — pri natezni obremenitvi), se zajeda poruši. Razpoka je nadaljevanje razpoke v zvezni površinski plasti oksida. S tem se ponovno odpre hitra pot za dostop oksidanta do kovine ter se tako pospeši rast zajede v smeri razpoke. Po večkratni ponovitvi temperaturnega cikla (Tmax-Tmin-Tmax) se zajeda izoblikuje v obliko klina mikroskopskih razsežnosti. 3. NAPETOSTI ZARADI OKSIDNEGA KLINA Rast oksidnega klina v kovini uravnava predvsem hiter prenos kisika po razpoki do kovine, v smeri normalno na steno klina, pa difuzija skozi oksid. Na ta način nastane in se ohranja trikotna oblika klina. Vsaka razpoka skozi primarni oksidni sloj je lahko začetek oksidne zajede oz. klina. Zato je na kovinskih delih, ki so izpostavljeni menjajočim se temperaturam, veliko mikroskopskih poškodb v obliki oksidnih klinov. Napetostno stanje, ki se pojavi v sistemu med rastjo oksidnega klina, raziskujemo na poenostavljenem modelu, tako da izberemo tanek sloj polprostora, ki ga predstavlja polravnina z več oksidnimi klini. Napetostno stanje je odvisno od temperaturnih obremenitev in ga bomo analizirali pri treh značilnih mejnih temperaturah. 3.1 Napetostno stanje pri najvišji temperturi, Tmgx. Pri tej temperaturi oksidni klin najhitreje raste. V njem se pojavijo tlačne napetosti, ki dosežejo minimalno mejo tečenja ene od sestavin sistema oTmin. Ker pa se oksid in kovina razlikujeta tudi v drugih lastnostih, se pojavijo še dodatne temperaturne napetosti. Te napetosti so v temenu klina, to je na meji polravnine razmeroma velike tlačne napetosti in so vzporedne z mejo polravnine. Pod mejo polravnine delujejo na klin znatne strižne in normalne napetosti pravokotno na smer polravnine5. Primerjalna napetost v sistemu kovina-oksid je znatno večja od meje tečenja, zato je hitrost plastične deformacije velika in napetostno stanje ne preseže aTmin. Rezultanta sil zaradi tlačne napetosti na plašču klina (aTmin) deluje proti meji polravnine. Zaradi nje in temperaturnih napetosti se sistem značilno deformira. Teme oksidnega klina se pri tem zoži, kovina pa s plastičnim tečenjem zavzame ta prostor. Posledica re-zultirajočih napetosti je izbočitev meje polravnine okoli temena oksidnega klina (si. 1). Zelo izraziti primeri plastične deformacije sistema so takrat, ko na temenih oksidnih klinov izpade del oksida in se poruši ravnotežno napetostno stanje na tem delu polravnine (si. 2, 3). Oksidni klin vpliva na stabilno oz. nestabilno rast razpoke v kovini zaradi tlačnih napetosti, ki so enake meji tečenja oTmin (Tmax). Dejanska širina korena razpoke je (2): cing a limited local oxidation. This tiny oxide flaw repre-sents the beginning of an oxide wedge. 2.2. Oxide Wedge Growth The newly formed oxide has a much larger volume than the metal. The volume deformation due to oxidation is so extensive that the stress state exceeds by far the rupture strength of the metal and the oxide. Therefore both of them (the metal/oxide system) become plastic. The stress state in the oxide flaw (vvedge embryo) is equal to the lower yield point of one of the system's components as follovvs: aymin = arnin (ay°*in, ayMmln) (1) During cooling from Tmax, compressive stresses ap-pear in the oxide due to vvhich the system exceeds the yield point. The plastic flovv continues down to the temperature of the transition of the system from the plastic into elastic state, Tp (temperature of the system's transition into elastic state under pressure). The stress state in the oxide flavv at this temperature is: ay min (TP) = o min (a°K (Tp), ayM (Tp)) (2) With continued cooling the compressive stresses in-crease. If they attain the yield point aymin, this induces a repeated plastic flovv of the system. In changing temperature conditions, the next stage is heating up the system from Tmin onto Tmax. Here, at the beginning, the compressive stresses induced by cooling, are reduced and at a certain temperature the sys-tem is free of stress. With heating up the system, tensile stresses appear in the flavv, increasing vvith temperature. If the stress exceeds the strength of the flavv belovv the temperature of the transition from the elastic into plastic state (T+ — under tensile load), the flavv breaks. The newly occurred crack continues the crack in the primary surface layer of the oxide. In this way, the oxidant has again a fast access to the metal reopened, stimulating the grovvth of the flavv in the direction of the crack. After several repetitions of the temperature cycle (Tmax — Tmjn — Tn,ax) i the flavv grovvs into a vvedge of micro-scopic dimensions. 3. STRESSES INDUCED BY OXIDE VVEDGES The grovvth of the oxide vvedge into the metal de-pends especially on hovv rapid is the access of the oxi-dant to the metal along the crack, and in the direction normally to the vvedge face, on hovv strong is the diffusion through the oxide. In this way the vvedge grovvs in the form of a triangle and keeps this form. Any crack through the primary oxide layer can mean the onset of an oxide flavv or vvedge. As a result, on metal parts vvhich are exposed to changing temperature conditions, a great number of microscopic defects in the form of oxide vvedges can be found. The stress state occurring in the system during the process of oxide vvedge development, is investigated on a simplified model by choosing a thin layer of semi-space, representing the semi-plane vvith several oxide vvedges. The stress state as function of thermal loads will be analysed only for three extreme temperatures. 3.1. Stress State at the Highest Temperture (Tmax) At this temperature the oxide vvedge grovvs the most rapidly. Compressive stresses appear in it, attaining the Slika 3 Deformacija kovine in oksidnega klina zaradi odluščenja oksida na temenu klina; 40 x Fig. 3 Deformation of the metal in the oxide vvedge due to oxide split-ting on the vvedge back face; 40 x minimum yield point of one of the system's components aTmin. But since the oxide and the metal differ also in other properties, additional thermal stresses appear too. On the back face of the oxide vvedge, i. e. on the semi-plane boundary, these stresses are compressive, and relatively high, acting in the direction parallel to the se-mi-plane. Under the semi-plane boundary considerable shear and normal stresses act on the vvedge in the direction rectangular to the semi-plane (5). The compara-tive stress in the metal-oxide system is considerably higher than the yield point, therefore, the rate of plastic deformation is high, and the stress state does not ex-ceed the aymin. The resultant of the forces arising from compressive stress on the vvedge faces (aymin), acts in the direction tovvards the semi-plane boundary. Because of this and due to temperature stresses, the system un-dergoes a typical deformation. The back face of the oxide vvedge narrovvs, its plače being taken by the plastically flovving metal. The conse-quence of the stresses resulting from this is the buck-ling of the semi-plane boundary around the oxide vvedge, (Fig. 1). Very distinct cases of plastic deformation of the system can be observed if on the back face of the vvedge a tiny piece of the oxide splits off and de-stroys the equilibrium stress-state in this part of the semi-plane (Fig. 2, 3). The oxide vvedge has an influence on the stable or unstable crack grovvth in the metal ovving to compressive stresses being equal to the yield point oymin (Tmax). The actual vvidth of the crack tip is (2) tan 0 + ti oy min (Tmax) .1 -v (3) fl(c)= c(1~v) 4 7t |x au (Tn vvhere 0 is the vvedge angle of the crack in the metal, v Poisson's number and n shear module. And the critical vvidth of the crack tip at unstable grovvth is: # (c) and unstable and leading to failure if QCcp(C). Če pa je