1. 2 1.Preface 2.General characteristics of the problem 3.Classical and non-classical approaches 4.Griffith-Irwin concept and linear fracture mechanics.

Prezentacja na temat: "1. 2 1.Preface 2.General characteristics of the problem 3.Classical and non-classical approaches 4.Griffith-Irwin concept and linear fracture mechanics."— Zapis prezentacji:

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2 2 1.Preface 2.General characteristics of the problem 3.Classical and non-classical approaches 4.Griffith-Irwin concept and linear fracture mechanics 5.Nonlinear fracture mechanics 6.Problems of materials fatigue fracture 7.The influence of environment on corrosion resistance of materials 8.The influence of hydrogen containing environment 9.Conclusions

3 3 F c (I 1, I 2, I 3, C 1, C 2, C 3 …) = 0 (1) I 1 = σ 1 + σ 2 + σ 3 ; I 2, I 3 are the stress (strain) invariants, C i are the constants σ 1 σ B, σ 1 – σ B = 0 (2) σ 1 σ 2 σ 3 are the main stresses σ B is the strength of the material under tension a – classical b – non-classical Classical approaches n 1, n 2, m 1, m 2 are the constants which are determined on the basis of the experiment (Pisarenko-Lebedev formula) (3) (П - stage = C S - stage) b a

4 4 THE BASIC MODELS OF CRACKS a b c a b c Fig.1. Fig.2.

5 5 1. Tension of the plate with the elliptical hole 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 Equation (7) gives us Griffith formula: γ – the effective surface energy of the body square unit Fig. 1 (6) (7) (8)

6 6 (1) where i, j = x, у, z in the Cartesian coordinates or i, j = r,, z in polar (cylindrical) coordinate system, K I0 = K I0 (p, l), K II0 = K II0 (p, l), K III0 = =K III0 (p, l) are stress intensity factors (SIF), which are the functions of body configuration, crack dimensions ( l ) and the value of loading p; 0(1) is limited value when r 0; f kij ( ) are known functions (k = 1, 2, 3). Local coordinates system near the crack front (line OZ ) and components (I, II, III ) of the vector of crack edges displacement K I0 * = K I0 (p *, l) = K Ic (2) For the case K I0 0, K II0 = 0, K III0 = 0 (Δl<<l 0 )

7 7 criteria. Initial crack propagation occurs in the plane, for which fracture stresses σ θ have the maximum SIF value. Then on the base of σ θ -criteria and Irwin concept we obtain the following criteria equations (1) Fig.1

8 8 Tension of the plate with the arbitrary oriented crack K I (p,l) 0, K II (p,l) 0, K III (p,l) 0 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 K I0 0, K II0 0, K III0 0 Equations (1)-(3) are proved experimentally and now present the linear fracture mechanics of materials (LFM).

9 9 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. 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 (K Ic, K IIc, K IIIc, ) taking into account the structure of the material and the influence of the environment, in particular under the action of H 2 2. Determination of crack growth resistance of structural materials (K Ic, K IIc, K IIIc, ) taking into account the structure of the material and the influence of the environment, in particular under the action of H 2 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). 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).

10 10 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. 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 (K Ic, K IIc, K IIIc, ) taking into account the structure of the material and the influence of the environment, in particular under the action of H 2 2. Determination of crack growth resistance of structural materials (K Ic, K IIc, K IIIc, ) taking into account the structure of the material and the influence of the environment, in particular under the action of H 2 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). 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).

11 11 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. 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 (K Ic, K IIc, K IIIc, ) taking into account the structure of the material and the influence of the environment, in particular under the action of H 2 2. Determination of crack growth resistance of structural materials (K Ic, K IIc, K IIIc, ) taking into account the structure of the material and the influence of the environment, in particular under the action of H 2 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). 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).

12 12 Typical linear dimensions of П-state zone in materials is great (comparable) with the linear dimensions of a crack or a considered body. 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 (, figure) 1,25 0,75 0,25 1 2 02,55,07,5 – material characteristics ! (1) (2) (3) Fig.2 Fig.1 (Griffith) P*/σ0P*/σ0

13 13 (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)

14 14 A diagram of stepwise interaction between the model cut edges, (1) (2) (3) value is approximately determined by in the formula, that arises from-model (4)(4),, when,,;

15 15 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. Dependence of critical stresses( p * / 0 ), on critical process zone length ( d = d* ) for different lengths ( i = d i /d * ) of the material fracture zone near concentrator

16 16 1. Non-linear fracture mechanics of materials ( ) did not reach its appropriate completion yet. 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. 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. 1. Nielinijowa mechanika pękania materiałów ( ) na dany czas jeszcze nie ma (osiągnęła) odpowiedniego zakończenia. 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. 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.

17 17 * 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. 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 14 th 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 (N 1 ) and its propagation period (N 2 ). Determination of these periods is the main task of the science on materials fatigue and durability (life time) of structural elements. When periods N 1 and N 2 are known, the total life time (N * ) is determined by formula 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 14 th 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 (N 1 ) and its propagation period (N 2 ). Determination of these periods is the main task of the science on materials fatigue and durability (life time) of structural elements. When periods N 1 and N 2 are known, the total life time (N * ) is determined by formula N = N 1 + N 2

18 18 * 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) Problem zmęczenia materiałów – jeden zcentralnych (głównych ) problemów mechaniki 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 (N 1 ) i period jej rozpowszechniania (N 2 ). Wyznaczenie tych periodów jest głównym zadaniem nauki o zmęczeniu materiałów i długowieczności (wytrwałości)(resursie) elementów konstrukcii. Jeśli są wiadome periody N 1 і N 2 to ogólną długowieczność można wyznaczyć za nastepną formułą: Problem zmęczenia materiałów – jeden zcentralnych (głównych ) problemów mechaniki 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 (N 1 ) i period jej rozpowszechniania (N 2 ). Wyznaczenie tych periodów jest głównym zadaniem nauki o zmęczeniu materiałów i długowieczności (wytrwałości)(resursie) elementów konstrukcii. Jeśli są wiadome periody N 1 і N 2 to ogólną długowieczność można wyznaczyć za nastepną formułą: N = N 1 + N 2

19 19 Ability of the material to resist the fatigue crack initiation and growth is characterized by its fatigue crack resistance Fatigue crack growth resistance diagram ((v-K)-curve). 1 – section close to threshold K th ; 2 – practically rectilinear section; 3 – section of quick crack growth and complete failure when K Imax = K fc – material characteristics

20 20 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 N 1 ! 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 N 1 ! N = N 1 + N 2 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 N 1 if the ( –K )-curve for this material is known (see slide 14). 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 N 1 if the ( –K )-curve for this material is known (see slide 14). N 1 A scheme for calculation of N 1 - period of the fatigue macrocrack formation N * is material durability; N 1 is the period of fatigue damaging and macrocrack initiation; N 2 is the period of macrocrack growth up to the critical value.

21 21 l = l l = l – minimum length of fatigue macrocrack. N 1 l N 1 – initiation period of fatigue macrocrack of length l ; – materials characteristics, l * ~ ? – known function (diagram of material fatigue macrocrack resistance); – diagram; – unknown function. (1) (2)(2) (2)(2) (3)(3) (3)(3) (4)(4) (4)(4),,,, ; ; ; ;,, l l

22 22 (Investigations of O.P.Datsyshyn et al) Scheme of contacting pairs Calculational model B – direction of the contact loading movement Calculation results of the surface crack propagation path under rolling (pitting formation) 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 = rp 0 ) 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

23 23 1. Determination of the macrocrack initiation period (N 1 ) 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 v 0 δ р coordinates, that is ( v-δ р )-diagrams where v – macrocrack growth rate, δ р – 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).

24 24 1. Wyznaczenie okresu zarodzenia się makroszczeliny (N 1 ) w cyklicznie-deformowanym materiale – główne zadanie eksperymental- nych i teoretycznych badań. 2. Budowa diagramu zmęczeniowej odporności na pękanie konstruk- cyjnych materiałów w koordynatach v 0 δ p,czyli (v - δ p ) –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) 1. Wyznaczenie okresu zarodzenia się makroszczeliny (N 1 ) w cyklicznie-deformowanym materiale – główne zadanie eksperymental- nych i teoretycznych badań. 2. Budowa diagramu zmęczeniowej odporności na pękanie konstruk- cyjnych materiałów w koordynatach v 0 δ p,czyli (v - δ p ) –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)

25 25 Wniosek w proces pękania korozyjnego Korozyjne zmęczenie konstrukcyjnych materiałów Nagromadzenie uszkodzeń korozyjnych Zarodkowanie i wzrost (rozwój) krutkich szczelin Wzrost długich szczelin do krytycznego rozmiaru Rujnacja materiału

26 26 Stress intensity factor, K Influence of initial level of stress intensity factor K i on corrosion crack growth rate ( )

27 27 Peculiarities of Physical-Chemical Situation Near the Crack Tip (schematically) The methods and equipment for, evaluation were developed in PhMI. – curve will be invariant when, (1) (2) (3)

28 28 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. ab c

29 29 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

30 30 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. 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 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

31 31 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 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.

32 32 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.

33 33 112,50,9612,00,1120,1250,1200,24 212,61,012,60,1180,1310,1220,22 313,00,9712,60,1180,1310,1250,25 414,50,7310,60,0990,1100,1080,25 518,10,7213,00,1210,1350,1280,22 613,00,8511,00,1030,1140,1100,26 d*/l0d*/l0 d*/l0d*/l0 l 0, mm l 0, mm d *, mm d *, mm с, mm 0,2 0 0 Base (mm): 1 – 1,28; 2 – 2,56; 3 – 3,84. Distribution of Deformations Near the Crack Tip on the Basis of Digital Specle Correlation Method of the Specimen Surface Image Distribution of Deformations Near the Crack Tip on the Basis of Digital Specle Correlation Method of the Specimen Surface Image с, mm (experim.) dі/d*dі/d* dі/d*dі/d*

34 34 An outline of a speciman for the determination of the materials crack resistance (K IIc ) [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 (K IIIc ) [8, 9] MaterialsThermal processing К ІС К ІІС К ІІІС ІС ІІС ІІІС mm 1. 40 KhN steel hardening,tempe- ring under 733 K 641241650,110,411,49 2. 40 KhN steel hardening,tempe- ring under 833 K 74136120,130,481,56 3. 30KhGKhA steelnormalizing 531481690,140,481.39 4. 40 KhN steel hardening,tempe- ring under 833 K 751391760,130,491,41 5. 20Kh13 steelstate of delivery 42–170––– Test investigations of Ya.L.Ivanytsky et. al.

35 35 (К І 0, К ІІ 0, К ІІІ 0) Griffith-Irwin criterion Generalized criterion for the case of complex loading (К І 0, К ІІ 0, К ІІІ 0) is as follows: where K Ic, K IIc, K IIIc, n i (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. K I, K II, K III values are calculated for each case in the frames of the crack mathematical theory. Under the complex loading conditions criterion (2), К І 0, К ІІ 0, К ІІІ = 0 and mixed mechanism (I + II) of fracture is realized, is as follows: In the case when К І = 0, К ІІ 0, К ІІІ 0 and mixed mechanism (II+III) of fracture is realized, we have where n i equals 4 or 2. (1) (2) = 1 (3) = 1 (4)

36 36 A criterion in the case of complex loading has such a form: where: n i (1, 2, 3) - material characteristics received from the experiment or on the bases of theoretical calculations; K IC, K IIC, K IIIC - 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 K III = 0 and n i = 4, curve 2 according formula (1) when K III = 0 and n i = 2 Curves 1 and 2 are plotted according to formula (1) when n i = 4 and n i =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) (1)