Structure of the lecture:

Structure of the lecture: • Preface • General characteristics of the problem • Classical and non-classical approaches • Griffith-Irwin concept and linear fracture mechanics • Nonlinear fracture mechanics • Problems of materials fatigue fracture • The influence of environment on corrosion resistance of materials • The influence of hydrogen containing environment • Conclusions

a b Classical and non-classical approaches Classical approaches Fc (I1, I2, I3, C1, C2, C3 …) = 0(1) I1 = σ1 + σ2 + σ3; I2, I3 are the stress (strain) invariants, Ciare the constants σ1≤σB, σ1 – σB= 0 (2) σ1›σ2›σ3 are the main stresses σB is the strength of the material under tension (3) a – classical b – non-classical (П - stage = CS- stage) n1, n2, m1, m2 are the constants which are determined on the basis of the experiment (Pisarenko-Lebedev formula)

Material Failure Model at the Crack Tip THE BASIC MODELS OF CRACKS Fig.2. Fig.1. a b c

Example. Classical and non-classical approaches. Griffith concept. 1. Tension of the plate with the elliptical hole Fig. 1 2. Griffith concept To determine the value of fracture loading for the cracked plate subjected to tension (Fig. 1 when b = 0), Griffith proposed (1924) so-called power method. It is eliminated to (6) (7) Equation (7) gives us Griffith formula: (8) γ – the effective surface energy of the body square unit

Griffith-Irwin Concept (1) (Δl<<l0) wherei, j = x, у, z in the Cartesian coordinates ori, j = r,  ,z in polar (cylindrical) coordinate system, KI0 = KI0(p, l),KII0 = KII0(p, l), KIII0 ==KIII0(p, l) are stress intensity factors (SIF), which are the functions of body configuration, crack dimensions (l) and the value of loadingp;0(1) is limited value when r0; fkij() are known functions(k = 1, 2, 3). KI0* = KI0(p*, l) = KIc(2) Local coordinates system near the crack front (line OZ) and components (I, II, III) of the vector of crack edges displacement For the case KI0 ≠ 0, KII0 = 0, KIII0 = 0

Plate containing arbitrary oriented crack criteria. Initial crack propagation occurs in the plane, for which fracture stresses σθ have the maximum SIF value. Then on the base of σθ-criteria and Irwin concept we obtain the following criteria equations Fig.1 (1)

Generalized Griffith-Irwin Concept KI(p,l) ≠ 0, KII(p,l) ≠ 0, KIII(p,l) ≠ 0 Equations (1)-(3) are proved experimentally and now present the linear fracture mechanics of materials (LFM). Tension of the plate with the arbitrary oriented crack where θ* is the angle of the initial direction of crack growth (1) (2) (3) Equations (1) and (2) were generalized (O.Ye.Andreikiv et al) for the case KI0 ≠ 0, KII0 ≠ 0, KIII0≠ 0

Linear Fracture Mechanics,Advanced Problems The Griffith-Irwin concepts and formulated equations above in previous slide form the basis of the linear fracture mechanics (LFM). • 1. Calculation of the stress intensity factors for limited bodies with cracks (structural elements) under the influence of force and temperature factors; preparation of corresponding data bases and reference books for engineering practice. • 2. Determination of crack growth resistance of structural materials (KIc, KIIc, KIIIc, g) taking into account the structure of the material and the influence of the environment, in particular under the action of H2 • 3. Experimental and theoretical verification of the LFM statements and the establishment of LFM concepts applicability in the case of limited elasto-plastic bodies (structural elements).

Nonlinear Fracture Mechanics , figure) • Typical linear dimensions of П-state zone in materials is great (comparable) with the linear dimensions of a crack or a considered body. – model and COD-criteria ( (1) (2) P*/σ0 (3) 1,25 Fig.1 (Griffith) 2 0,75 Fig.2 → 1 – material characteristics ! 0,25 0 2,5 5,0 7,5

EXPERIMENTAL DETERMINATION OF STRUCTURAL MATERIALS DEFORMATIONAL CRACK RESISTANCE (δc) (Investigations Of Ya.L.Ivanytsky, L.I.Muravsky et. al. ) Use of the correlation method of the specimen surface speckle images in the crack tip vicinity Fig. 1.Distribution of deformations ey(x) near the crack tip at different measuring bases (b): (1 – b = 1,28 mm; 2 – 2,56 mm; 3 – 3,08 mm) for loaded (1, 2, 3) and unloaded (1΄, 2΄, 3) D16AT alloy cracked specimen (1) Fig. 2.Dependence of the plastic zone on the crack continuation on p*/σ0 loading value for Д16АТ alloy (firm line corresponds the values in (2), dots – experimental data for different length of the initial crack (2)

in the formula, that arises from -model value is approximately determined by when , , SOME GENERALIZATIONS OFc- MODEL A diagram of stepwise interaction between the model cut edges (1) , , , ; (2) (3) (4)

1 – by Griffith formula :; 2 – according toс-model (i = 0); 3 – according to formulas (1)-(4) wheni = 0,3; 4 – according to formulas (1)-(4) wheni = 1.Points show experimental values for D16АТ aluminium alloy. SOME GENERALIZATIONS OFc- MODEL Dependence of critical stresses( p*/0), on critical process zone length (d = d*) for different lengths (i = di/d*) of the material fracture zone near concentrator

ВИСНОВКИ – CONCLUSIONS • 1. Nielinijowa mechanika pękania materiałów () na dany czas jeszcze nie ma (osiągnęła) odpowiedniego zakończenia. • 2. Ważnymi i perspektywnymi badaniami w tej dziedzinie są opracowania fizyko-matematycznych koncepcii i rozrachunkowych modeli do wyznaczenia granicznej równowagi deformowanych ciał z pęknięciami ze względem na rozwinięte (wielkie) zony plastyczności (deformacji) około frontu pęknięcia. • 1. Non-linear fracture mechanics of materials ( ) did not reach its appropriate completion yet. • 2. Development of physico-mathematical concepts and calculation models for the determination of limiting equilibrium of cracked bodies taking into account the developed (big) zones of plasticity near the crack front are important and perspective investigations.

MATERIALS FATIGUE: Crack Initiation and Propagation • The problem of materials fatigue is one of the central problems of fracture mechanics and prediction of structural elements life time (durability). Great efforts have been spent for solution of this problem since the 19th century, when this phenomenon was considered for the first time. This problem was the topic of special plenary report by J.Schijve*at the 14th European Conference on Fracture (ECF–14) on September 9 2002 in Cracow. In this problem solution the concepts of fracture mechanics are very important. They are the following. For fatigue fracture of the material two periods are determining: the macrocrack initiation period (N1) and its propagation period (N2). Determination of these periods is the main task of the science on materials fatigue and durability (life time) of structural elements. When periods N1 and N2 are known, the total life time (N*) is determined by formula N = N1 + N2 * Commentary to the report by J.Schijve“Fatigue of structures and materials in the 20th century: state of the art”. In this report the detailed list of references on the above problem is given, however the author did not consider the investigations of the East European scientists. This was done as a supplement in the Ukrainian translation of the report by the scientific editor of the “Physicochemical Mechanics of Materials” journal (“Materials Science”). – 2003. - № 3. – P. 7-27.

MATERIALS FATIGUE: Crack Initiation and Propagation • Problem zmęczenia materiałów – jeden zcentralnych (głównych )problemówmechaniki pękania i prognozy resursu (długowieczności(wytrzymałości) elementów konstrukcii. Na rozwiązanie tego problemu zatracono dużo wysiłków poczawszy od 19-go stulecia. Ten problem był przedmiotem specjalnego plenarnego referatu Dż.Schajwe* na 14-ej Europejskiej konferencji (ECF-14) 9 września 2002 roku w Krakowie. W rozwiązaniu tego problemu szczególne miejsce zajmują koncepcii mechaniki pękania materiałów. Oni są następne. Dla pękania zmęczeniowego materiału wyznaczalnymi są dwa periody – period zarodkowania makroszczeliny (N1) i period jej rozpowszechniania (N2).Wyznaczenie tych periodów jest głównym zadaniem nauki o zmęczeniu materiałów i długowieczności (wytrwałości)(resursie) elementów konstrukcii. Jeśli są wiadome periody N1 і N2to ogólną długowieczność można wyznaczyć za nastepną formułą: N = N1 + N2 * Komentarz do wykładu Dż.Schajwe „Zmęczenie konstrukcii i materiałów w 20-tym stuleciu: aktualny stan”. W tym referacie autor podaje wielki spis literatury naukowej z tego problemu lecz nie bierze do uwagi (pod uwagę) osiągnięć uczonych z Europy Wschodniej. To jest podane jako dodatek od naukowego redaktora tłumaczenia tego artykułu (patrz.czasopismo „Fizyko-chemiczna mechanika materiałów”- 2003. – N 3. - P.7-27)

MATERIALS FATIGUE: Macrocrack Growth Ability of the material to resist the fatigue crack initiation and growth is characterized by its fatigue crack resistance – material characteristics Fatigue crack growth resistance diagram ((v-K)-curve). 1 – sectionclose to threshold Kth; 2 – practically rectilinear section; 3 – section of quick crack growth and complete failure when KImax = Kfc

MATERIALS FATIGUE: Fatigue Crack Initiation N* is material durability; N1 is the period of fatigue damaging and macrocrack initiation; N2 is the period of macrocrack growth up to the critical value. N = N1 + N2 • The main task of the science about the material fatigue and strength of structures is the development of effective methods for assessment of fatigue crack initiation period N1 ! A scheme for calculation of N1 -period of thefatigue macrocrack formation • We have obtained certain results in this direction, in particular O.P.Ostash (PhMI) proposed in his papers a new concept in the terms of which it is possible to estimate N1 if the (n–K)-curve for this material is known (see slide 14).

– known function (diagram of material fatigue macrocrack resistance); –diagram; – unknown function. – materials characteristics, l* ~ ? Approximate Model for Determination of N1 N1 – initiation period of fatigue macrocrack of lengthl; (1) , , l (2) l = l – minimumlength of fatigue macrocrack. (3) ; ; , (4)

Kinetics of Fatigue Crack Propagation in the Zone of Two Bodies Contact (Investigations of O.P.Datsyshyn et al) Calculational modelB – direction of the contact loading movement Schemeof contacting pairs Calculation results of the surface crack propagation path under rolling (pitting formation) Damage of the subsurfase contact zone under rolling: a – the edge crack growth path (dashed line) under rolling in lubrication conditions in dependence of lubricant pressure intensity (q = rp0) on crack edges; b –cross-section of pitting on the bearing surface This is a new and important direction of the investigations in the field of materials fracture mechanics

Conclusions and Advanced Research on the Problem of Materials Fatigue 1. Determination of the macrocrack initiation period (N1) in the cyclically deformed material – the main task of experimental and theoretical investigations. 2. Construction of the fatigue crack resistance diagrams for structural materials in v0δр coordinates, that is (v-δр)-diagrams where v – macrocrack growth rate, δр – opening of crack edges at the fixed points, - new opportunities for the assessment of structural elements durability. 3. Investigations of interaction between the propagation rates of macro- and microcracks in cyclically deformed materials. 4. Development of the effective methods for the evaluation of the fatigue macrocrack minimum value for a given structure of the material. 5. Investigations of the crack fatigue propagation in the zone of two bodies cyclic contact (problems of tribology).

Wnioski i nowoczesne (nowe) badania problemu zmęczenia materiałów 1. Wyznaczenie okresu zarodzenia się makroszczeliny (N1) w cyklicznie-deformowanym materiale – główne zadanie eksperymental-nych i teoretycznych badań. 2. Budowa diagramu zmęczeniowej odporności na pękanie konstruk-cyjnych materiałów w koordynatach v0δp ,czyli (v - δp) –diagramów, gdzie v – szybkość rozwarcia brzegów szczeliny(pęknięcia) w punktach fiksowanych – nowe możliwości do oceny długowieczności (wytrzymałości) konstrukcyjnych materiałów. 3. Badania wzajemnego oddziaływania (współdziałania) szybkości rozpowszechniania się makro- i mikro szczelin w cyklicznie-deformowanym materiale. 4. Opracowanie efektywnych metod wyznaczenia minimalnego znaczenia (wielkości) zmęczeniowej makroszczeliny dla materiału o pewnej(wyznaczonej) strukturze. 5. Zbadanie rozpowszechniania się zmęczeniowej szczeliny w zonie cyklicznego kontaktu dwuch ciał (problemy trybologii)

Korozyjne zmęczenie konstrukcyjnych materiałów Nagromadzenie uszkodzeń korozyjnych Zarodkowanie i wzrost (rozwój) krutkich szczelin Wzrost długich szczelin do krytycznego rozmiaru Wniosek w proces pękania korozyjnego Rujnacja materiału Glówne stadium procesu pękania korozyjnego (korozyjnej rujnacji)

Influence of Initial Testing Conditions on Corrosion Crack Growth Behaviour Influence of initial level of stress intensity factor Kion corrosion crack growth rate ( ) ( ) ( ) ( ) ( ) ( ) Stress intensity factor, K

– curve will be invariant when , The methods and equipment for , evaluation were developed in PhMI. Simultaneous Influence of Stresses and Environment Peculiarities of Physical-Chemical Situation Near the Crack Tip (schematically) (1) (2) (3)

Equipment and Methods for , Measuring c a b Equipment for evaluation of the material fatigue fracture characteristics: a – scheme of location of the gauges-microelectrodes in the specimen for local electrochemical investigations; b – scheme of the automatic testing equipment; c – general view of the equipment.

Basic Diagrams for Pressure Vessel Materials Fatigue crack growth diagram (v-K curves) for pressure vessel metal; 1, 2 – according to ASME method; 3, 4 – according to Bamford (generalized experimental data); 5 – basic curve, plotted in terms of the proposed concept

Influence of hydrogen containing environment Problems: 1. Hydrogen transport to the metal 2. Surface interaction and hydrogen penetration into the metal 3. Hydrogen state and behavior inside the metal 4. Hydrogen influence on the fracture microprocesses 5. Hydrogen influence on the crack growth resistance of metals and welded joint Each of these problems is a separate section of the science about the interaction between the deformed metal and hydrogen. Scientists and engineers from different countries work at the solution of these problems. Investigations of some aspects of these problems are planned in the frames of Polish-Ukrainian scientific collaboration. Consideration of specific investigation of these problems will be the subject of future lectures.

Wpływ wodórmieszczących środowisk Problemy (zadania): 1. Przeniesienie wodoru do metalu 2. ІІ – współdziałanie powierzchni i przedostawanie się (przeniknięcie) wodoru do metalu ІІІ – stan wodoru i jego zachowanie wewnątrz metalu 3. Wplyw wodoru na mikroprocesy rujnacji 4. Wplyw wodoru na odpornosc metali I spawanych łączni wzrostu szczeliny Każdy z tych problemów jest oddzielnym rozdziałem nauki o wspłódziałaniu deformowanego metalu z wodorem. Nad rozwiązaniem tych problemów pracują pracowniki naukowe i inżynierowie. Badania oddzielnych aspektów takich problemów planujemy realizowac w ramkach naukowo-technicznej ukrainsko-polskiej wspólpracy. Rozpatrzenie konkretnych badan z tego problemu będzie przedmiotem następnych wykladów.

CONCLUSIONS AND PERSPECTIVES 1. Fundamentally new tools for studying of surface-active and corrosion-aggressive environments influence on the physico-mechanical characteristics of cracked materials are developed. 2. New conditions of a given system “metal-corrosive environment”, when the value of crack growth rate in the cyclically deformed metal reaches its maximum, are determined. 3.Methodology for plotting of metals corrosion cracking basic diagrams, used for the assessment of high-pressure vessels reliability in service, is worked out. 4. Perspective and important for engineering practice is the plotting of corrosion cracking basic diagrams for different material classes and corrosion environments. 5. Perspective and important are the investigations of the interaction between deformed metals and hydrogen. Here we have a number of sub-problems, which must be investigated and solved considering the strength of long-term operation structures.

Crack Tip Opening Displacement Estimation Under Tention of an Infinite Plate с, mm (experim.) с, mm d*/l0 d*, mm l0, mm dі/d* № 0 0,2 Distribution of Deformations Near the Crack Tip on the Basis of Digital Specle Correlation Method of the Specimen Surface Image Base (mm): 1 – 1,28; 2 – 2,56; 3 – 3,84.

DETERMINATION OF CRACK RESISTANCE VALUES Test investigations of Ya.L.Ivanytsky et. al. An outline of a speciman for the determination of the materials crack resistance (KIIc) [8, 9]: 1, 2 – circular concentrator; 3, 4 – symmetric cracks; 5, 6 – the places of the specimen grips during turning or tension An outline of the specimen for the determination of the materials crack resistance (KIIIc) [8, 9]

= 1 = 1 CRITERION OF LINEAR FRACTURE MECHANICS UNDER COMPLEX LOADING CONDITIONS (КІ ≠ 0, КІІ ≠ 0, КІІІ ≠ 0) Griffith-Irwin criterion (1) Generalized criterion for the case of complex loading (КІ ≠ 0, КІІ ≠ 0, КІІІ ≠ 0) is as follows: (2) where KIc, KIIc, KIIIc, ni (i = 1, 2, 3) – parameters that characterize material near the concentrator, that is there, were П-states of the material appear. These states are determined experimentally or on the bases of certain model calculations. KI, KII, KIII values are calculated for each case in the frames of the crack mathematical theory. Under the complex loading conditions criterion (2), КІ ≠ 0, КІІ ≠ 0, КІІІ= 0 and mixed mechanism (I + II) of fracture is realized, is as follows: (3) In the case when КІ = 0, КІІ ≠ 0, КІІІ ≠ 0 and mixed mechanism (II+III) of fracture is realized, we have (4) where ni equals 4 or 2.

SOME EXPERIMENTAL RESULTS A criterion in the case of complex loading has such a form: (1) where: ni(1, 2, 3) - material characteristics received from the experiment or on the bases of theoretical calculations; KIC, KIIC, KIIIC - characteristics received from the experiment Diagrams of the deformed body limiting-equilibrium state the conditions of mixed (I+II), (I+III) fracture mechanisms Curve 1 – according to formula (1) when KIII = 0 and ni = 4, curve 2 according formula (1) when KIII = 0 and ni= 2 Curves 1 and 2 are plotted according to formula (1) when ni = 4 and ni=2 correspondingly Experimental data: - 40KhN steel, hardening in oil under 1123 K, tempering under 833 K; - 30KhGSA steel, normalizing; - 40KhN steel, hardening in oil under 1133 K, tempering under 773 K (test results of Ya.L.Ivanytsky); - 4340 steel (test results of A.A.Chuzhuk); aluminum alloy 2219 (E87) (test results of A.A.Chuzhuk); - 9KhF steel: - hardening in oil under 1133 K, tempering under 873 K; - tempering under 773 K; - tempering under 673 K (test results of Ya.L.Ivanytsky)

Structure of the lecture: