UDK 539.42:669.018 Original scientific article/Izvirni znanstveni ~lanek ISSN 1580-2949 MTAEC9, 42(1)3(2008) A FAILURE CRITERION FOR SINGLE-CRYSTAL SUPERALLOYS DURING THERMOCYCLIC LOADING MERILO ZA PRELOM MONOKRISTALA SUPERZLITINE PRI TERMOCIKLIČNI OBREMENITVI Leonid Getsov1, Artem Semenov1, Alexander Staroselsky2 1St. Petersburg State Polytechnical University, Russia, St. Petersburg, Polytechnicheskaja 29 2Pratt and Whitney, MS 165-16, East Hartford, CT, 06108 USA guetsov online.ru Prejem rokopisa — received: 2007-09-12; sprejem za objavo - accepted for publication: 2007-12-18 The accumulation of deformation affects the lifetime of a monocristal submitted to low cyclic mechanical and thermal loading. An analytical method was developed considering the damages due to cyclic and axial plastic and creep deformation. The method was checked with tesst in vacuum on specimens of monocrystals with different space orientation, also specimens with stress concentrators. The distribution of stressses was FEM modelled. The fracture depends on the space orientation of the specimen and of the loading parameters. A new experimental-computational method using deformation-fracture criteria is suggested for the evaluation of the crystal life time Keywords: single crystals,cyclic and axial loading, thermal fatigue, failure criteria Kopičenje deformacije vpliva na trajnostno dobo kovine, ki prenaša malociklično mehansko in termično obremenitev. Razvita je bila analitična metoda, ki sešteva poškodbe zaradi cikličnih in enoosnih plastičnih deformacij in deformacije z lezenjem. Metoda je preverjena s preizkusi v vakuumu na vzorcih monokristalov z različno prostorsko orientacijo. Preizkusi so bili izvršeni tudi z vzorci z obliko, ki je povzročala lokalno koncentracijo napetosti. Porazdelitev napetosti je bila modelirana po metodi končnih elementov. Prelom je odvisen od prostorske orientacije in od parametrov obremenitve. Predlagana so nova deformacijsko-prelomna merila za oceno trajnostne dobe monokristala na podlagi eksperimentalno-računske analize. Ključne besede: monokristali, ciklična in aksialna obremenitev, termična utrujenost, pogoji za prelom 1 INTRODUCTION The deformation criterion DMfipli) + D2(A£ci) + D3(£pli) + D4(£ci) =1 (1) for the fracture of metal in conditions of low-cycle and thermal-cycle loading was proposed in 1 The quantitative result of the lifetime test on the basis of this criterion depends on the choice of the deformation parameters. The proposed deformation criterion is based on the summation of the damage caused by cyclic plastic deformations D1 = — ^(Aeipl)k, cyclic creep defor- C1 mations D2 =^(Aeipl)k, unilaterally accumulated 1 ^ e pl plastic deformations D3 = — and unilaterally C 3 n E r 1 ^ Epl accumulated creep deformations D4 = — C 4 n E r In the case of interference of the above-mentioned types of damage the relevant corrections are made by considering the limiting characteristics of the material, C1, C2, £r, and £cr. This criterion was tested experimentally under conditions of uniaxial and composite tension for various samples, and the GTE details made of isotropic heat-resistant steels and alloys that fracture are caused by low-cycle or thermal fatigue (see Figure 1 and [2-4 and others]). Figure 1: The correlation between the experimental and calculated values of the lifetime: I-Dj+D2, II-D3+D4, III-Dj+D2+D4, IV-D1+D3 +D4, V-Dj+D2+D3 +D4 Slika 1: Korelacija med eksperimentalnimi in izračunanimi vrednostmi za trajnostno dobo I-Dj+D2, II-D3+D4, III-Dj+D2+D4, IV-D] +D3+D4, V-Dj+D2+D3+D4 Materiali in tehnologije / Materials and technology 42 (2008) 1, 39-43 39 n 2 n L. GETSOV ET AL.: A FAILURE CRITERION FOR SINGLE-CRYSTAL SUPERALLOYS The quantitative result ot the details' lifetime test on the basis ot this criterion depends on the choice and precision ot its detormation parameters. As tor the isotropic materials, normally the role ot such parameters is played by the intensities ot the total amplitudes ot the detormations Aepl = 2 [(Ae ? -Ae 2')2 + (A£pl -Ae 31)2 + (Ae 3' -Aepl)2 ] (2a) Aec = Aj-[(Ae 1 -Ae2 )2 + (Ae2 -Ae3 )2 + (Ae3 -Ae 1 )2] (2b) and the intensities ot the accumulated detormations, e p' =y f[( e 1 - e 2l)2 + ( e 2l - e 3l)2 + e Î - e I1)2 ] ec = J |[( e 1 - e 2)2 + ( e 2 - e 33 )2 + ( e3 - e1)2 ] (3a) (3b) In this research we studied the possibility ot generalizing the above-mentioned criterion tor the case ot single-crystal alloys. This generalization was based on the following relationships tor fatigue-crack initiation and growth in the reterences 5-12. According to the experimental data, the increase ot temperature 5 and the reduction in the ot trequency 6 change the mechanism ot tracture in single crystals, which means that the transition trom crack growth along crystallographic (octahedral) planes to growth in other directions does not depend on the crystal orientation, but on the conditions ot loading (according to Mode I). The non-crystallographic growth is observed predominantly on the boundary ot the ' phases. One ot the possible explanations 20 tor such a transition is the initiation ot additional damage owing to the intluence ot the environment. Oxygen-related brittle behavior in the vicinity ot the crack tip takes place according to the dittusion mechanism, and is sensitive to the temperature, the time (trequency) and the concentration ot oxygen. A comparison ot the results ot the experiments made in air 5 and in vacuum 7 has shown that the transition temperature is considerably higher in vacuum. When the trequency is decreased, the time ot the brittle behavior within the cycle increases, which promotes the turther penetration ot oxygen, and this initiates the transition trom the crystallographic mode ot crack growth to the non-crystallographic mode I. Also, the increase in the temperature accelerates the dittusion process, promoting the transition trom a crystallographic to a non-crystallographic mechanism ot crack growth. As shown in 8, the threshold value tor non-crystallo-graphic tractures, AKM, is lower than the value ot A^th(iii) tor cracks growing along a crystallographic plane, and when AKeq becomes lower than AK^m) the crack cannot continue growing according to the crystallographic mechanism and goes over to growth according to mode I. Thus, the experiments show that the transition trom the crystallographic to the non-cry- stallographic stage is controlled by the temperature T, the trequency f, and the total amplitude ot SIF, AK. For the set ot above-mentioned parameters it is possible to create maps ot mechanisms tor the growth ot tatigue cracks (analogous to the maps tor static loading in 9, showing the boundaries between the crystallo-graphic and non-crystallographic areas ot crack growth). As an example ot such a map, the reader is reterred to the map in 10 (see Figure 2), obtained on the basis ot an examination ot thermally activated slip processes in the vicinity ot the crack tip. The transition trom the crystallographic mode ot growth at high temperatures is also promoted by the decrease in the anisotropy ot the elastic and strength characteristics ot crystals. So, at high temperatures («980 °C) the growth rate ot the tatigue cracks does not, in practice, depend 11 on the orientation ot single crystals under the conditions ot a uniaxial and composite detormation mode. This probably explains the absence ot anisotropy in high-temperature multi-cycle tatigue. It is important to note that the arborescent structure also intluences the change ot the orientation ot the tatigue-crack growth and it could provoke the transition trom one crystallographic plane to another. The equalization ot the crack-growth rates tor single crystals with orientations [111 and [001 can be explained l112 by the tact that as AK grows, the tatigue-crack trajectory diverts trom the plane (111) perpendicular to the loading axis and evolves into the plane (001), where inter-dendrite areas are concentrated, i.e., to the same plane in which the tatigue cracks grow in samples with the orientation [001. As a two-dimensional model, interpreting simply the tatigue crack's growth in the area surrounding the cooling duct, the problem ot crack growth in a plate with Figure 2: Map ot tatigue-crack growth mechanisms tor monocrystals <001>/<010> PWA 1484 10 Slika 2: Shema mehanizma rasti utrujenostne razpoke za monokristale <001>/<010> PWA 1484 10 4 Materiali in tehnologije / Materials and technology 42 (2008) 1, 3-12 L. GETSOV ET AL.: A FAILURE CRITERION FOR SINGLE-CRYSTAL SUPERALLOYS a circular hole can be considered. The plate is in non-uniform temperature conditions with the minimum value of the temperature on the edge of the hole: the greater is the distance from the hole, the higher are the temperature and the SIF. The crack-growth process on the plane of parameters corresponding to the map of mechanisms of fatigue-crack growth in a single crystal is shown schematically in Figure 5 with the line ABC. When the boundary between the crystallographic and non-crystallographic stages is crossed at the point B, the crack changes its growth direction. With the change in the mechanism and the direction of the crack growth, the speed of growth also changes. Depending on the load level and the frequency, the sample orientation, the geometrical parameters of the plate with a hole and the material properties, different schemes of crack growth are possible. Among them are both the modes without a direction change (in one plane, crystallographic or non-crystallographic) and modes with one or multiple direction changes. The extrapolation of the research results described in 12 for the conditions of thermal-cycle loading and, as a final goal, the development of a new fracture criterion, have become the object of the present research. At the same time, we are not discussing here the problems of the choice of models for the visco-elastic plasticity for the calculation of parameter values of criterion (1). 2 TEST METHODS The thermal fatigue tests were performed for samples made of a single-crystal high-temperature alloy with five different orientations, including <001>, <011> and <111>. During the tests, the samples in sand-glass form were rigidly fixed in vacuum 13. A comprehensive procedure is developed in NPO CKTI for the definition of the thermal fatigue resistance of various materials and coatings, applying a special appliance that allows us to clamp flat the sand-glass shaped test pieces and to ensure their cyclic heating with a conducting current (Figure 3). The heating takes place according to a specified program (Figure 4), maintained automatically during the testing. The appliance is fixed in a vacuum chamber. The ultimate cycle temperature, defined by the rate of oxide-film formation on the sample surface, increases with the vacuum. The sample material's behavior at various surface points on the sample is observed using a microscope with a 250x magnification. During the test the following parameters are recorded: the characteristic properties of the deformation relief defining the mechanism of the accumulation of thermal fatigue damage; the number of cycles to the first microcrack formation in various elements of the metal and the coating; the growth rate of the incipient cracks; the number of cycles to sample failure and the accumulated deformations in the ruptured zone. b) Figure 3: Shape of the specimen (a) and a sketch of the specimen with a coating and with a central hole (b) Slika 3: Oblika preizkušanca (a) in shema preizkušancev s prekritjem in z osrednjo izvrtino (b) The range of the conditionally elastic stresses and the range of the total deformation Ae in the specimen's working part in the cycle were calculated from thee equations: AO = ( E St1 a T max - Est2 « 2 Tmax )P Aa = (a Tmax - a2 Tmax )p (4) p = 1 - Ak / Al where Est is the static elastic modulus; Al is the free travel of the test points during heating from Tmi „ to Tmax; and k is the measured value of the displacement of the control microhardness marks, applied to the sample surface along its working-part edges during the cycle. In this calculation the values k and were used after being averaged on the basis of the hypotheses of their linear summability. Some 9-mm-wide plates of a single-crystal alloy with different orientations were prepared for the tests (see Table 1). Table 1: Sample orientation Tabela 1: Orientacija preizkušancev Number of the sample series Orientation Deviation from the exact axial orientation in degrees Azimuthal orientation of the crystallo-graphic planes in degrees 1 111 5.64 8.26 2 011 4.51 11.27 3 011 8.33 14.43 4 011 9.67 7.86 5 001 5.47 41.97 5 Materiali in tehnologije / Materials and technology 42 (2008) 1, 3-12 L. GETSOV ET AL.: A FAILURE CRITERION FOR SINGLE-CRYSTAL SUPERALLOYS Some tests were made on samples with stress concentrators in the form of holes with a diameter of 0.5 mm. The tests were conducted under different maximum temperatures in the cycle Tmax (850-1050 °C) with and without 2-5 min of holding at Tmax. The positions of the slip lines on the sample's surface were calculated and confirmed experimentally, as was the crack orientation up to the moment of the sample's rupture. The values of the irreversible deformations (characterizing the ratcheting) taking place in the central part of the samples were also determined. For the interpretation of the test results we: a) analyzed the character of the fracture from the four sides of the sample (see Figure 5) and b) carried out finite-element calculations for the change of the sample's deformation mode in order to find the orientations of the rupture surfaces with the help of methods for deformable solid-body mechanics and to compare the results with crystallographic predictions and experimental data. sample 3-2 D Figure 4: Experimentally determined distribution of the temperature along the length of the sample (à) and an example of the change of the maximum temperature in the working part of the sample during the cycle (b) Slika 4: Eksperimentalno določena porazdelitev temperature po dolžini preizkušanca (a) in primer spremembe najvišje temperature v delovnem delu preizkušanca med ciklom (b) sample 3-5 O - Crystallographic fracture, O - Non-crystallographic fracture. Figure 5: Interpretation of the fracture character of the samples 3-2 and 3-5 Slika 5: Interpretacija značilnosti preloma preizkušancev 3-2 in 3-5 6 Materiali in tehnologije / Materials and technology 42 (2008) 1, 3-12 L. GETSOV ET AL.: A FAILURE CRITERION FOR SINGLE-CRYSTAL SUPERALLOYS 3 EXPERIMENTAL RESULTS AND THEIR ANALYSIS The results ot the pertormed experiments were compared to the results ot the crystallographic analysis and the calculation ot the samples' detormation mode. The stress analysis ot the samples was performed with the help ot the PANTOCRATOR tinite-element program 14 (see http://www.pantocrator.narod.ru) based on the tollowing assumptions: 1) in the tension phase, the cleavage cracks can originate and grow, and their growth direction is determined by the orientation ot the plattorm ot the maximum principal value ot the stress tensor, 2) in the compression phase, the shear cracks can originate and grow, and their growth direction is determined by the orientation ot the plattorms ot the maximum tangent stresses. From now on the concept ot non-crystallographic tracture mode is used in the phenomenological context, as a tracture (observed at the macro-level) not coinciding with any ot the crystallographic slip planes. As an example, let us consider the place ot origin ot a shear crack on the basis ot the hypothesis ot maximum tangential stresses tor a sample ot the 3rd group tested in the mode 150-900 °C. We tound that there are two equal, centrally symmetric maximums rmax = 856 MPa with a bias located at a distance ot 0.64 mm trom the center (see Figure 6), and the stresses localized in the lateral zones (with a maximum on the center line) (see Figure 6b). For the same sample, we identitied the tensile-crack initiation point using the hypothesis ot maximum principal stresses. We tound that there are two equal, centrally symmetric maximums o1 = 1559 MPa at a distance ot 0.45 mm trom the centre (see Figure 7); there is also a localization ot stresses in the lateral zones (with a maximum at the edge) (see Figure 7b). An analysis ot the calculation results showed that the distribution ot stresses x and the locations ot the maximum stress zones are very ditterent tor ditterent groups ot samples. An example ot the experimental data analysis is shown in Table 2, containing the results tor sample 2-1 tested under the mode 150-900 °C. For this sample the crystallographic and the tinite-element results are similar and show only an insigniticant ditterence compared to the experiment (a Figure 6: Distribution ot the tields ot maximum tangential stress (sample 3-0, 3rd cycle) Slika 6: Porazdelitev polj največjih tangencialnih napetosti (preizku-šanec 3-0, 3. cikel) Figure 7: Distribution ot tields ot maximum principal stress (sample 3-0, 3rd cycle) Slika 7: Porazdelitev polj največjih glavnih napetosti (preizkušanec 3-0, 3. cikel) 7 Materiali in tehnologije / Materials and technology 42 (2008) 1, 3-12 L. GETSOV ET AL.: A FAILURE CRITERION FOR SINGLE-CRYSTAL SUPERALLOYS Table 2: Comparison of the experimental data with the results of the crystallographic and finite-element analyses of specimen 2-1 Tabela 2: Primerjava eksperimentalnih podatkov in rezultatov kristalografske analize in analize po metodi kon~nih elementov za preizku{anec 2-1 Experiment crystallography FEA cleavage mode shear mode A 84/49 84/51 (1-11) 90 / 90 88 / 45 B 90/47 84/51 (1-11) C 86/49 84/51 (1-11) D 86/49 84/51 (1-11) maximum of 4°). Symbolically, we designate fractures of this type as "Mode 90 / 45". Owing to the absence of pure modes of crystallo-graphic or non-crystallographic fracture and, in some cases, to the ambiguities of the choice between the modes caused by the neighboring prognoses of the crystallographic and the finite-element analysis, in order to map the fracture mechanisms we use the classification of modes on the basis of the orientation of the middle fracture "plane" instead of the concepts of crystallo-graphic or non-crystallographic fracture modes the four modes are considered: Mode 90 / 45 Mode 90 / 90 Mode 45 / 45 Mode 45 / 90 }crystallographic or SSS } crystallographic In Table 3 the results of the analyses of the fracture modes for the samples from group 3 are shown. The results show that the sample's rupture occurred in the Table 3: Dominant fracture modes of the samples of the 3rd group (r-duration of cycle) Tabela 3: Prevladujo~i na~ini preloma preizku{anca iz 3. skupine ( -trajanje cikla) Non-FE, non-forecasting with the finite-element analysis 8 Materiali in tehnologije / Materials and technology 42 (2008) 1, 3-12 L. GETSOV ET AL.: A FAILURE CRITERION FOR SINGLE-CRYSTAL SUPERALLOYS 800 Sample series 3 <011> 700 U o < 600- 500- ■ \ 0 0 Simples: 3-0 v Samplea: 3-1 Samplea: 3-2 Mode 90/90 \ Mode 90/45 "Non-Crystallographic" \ "Crystallographic"? (11-1) 86/51 ■ \ 0 0 Sample«: 3-5 Samples: 3-3 Sampla«: 3-4 900 950 1000 T /°C * max' 1050 Figure 8: Map of the fracture mechanisms for the samples of the 3rd series Slika 8: Shema mehanizma preloma za preizkušance iz 3. serije crystallographic, the non-crystallographic and the mixed modes. The conditions for the occurrence of the crack type (dominant type (mode) of fracture) are generalized with the help of maps of fracture mechanisms plotted in the coordinates Tmax - A T (see, for example, Figure 8). With the help of such maps of fracture mechanisms it is possible to separate the loading conditions. Fracture criterion. The above-mentioned facts make it evident that, depending on the fracture mode of single-crystal alloys, in each concrete case it is necessary to choose the corresponding deformation-fracture criteria: • criterion 1: D^Aypl) + D2(Ayc) + DJyJ + Dfy) = 1 (4) • criterion 2 Di(A£pli) + + D3(£pli) + D(eJ = 1 (5) Namely, for crystallographically oriented fracture modes, the following criterion parameters must be chosen: shear deformations and their total amplitudes pl and pl ( c, c), and for non-crystallographic fracture modes, the tensile deformations and their total amplitudes £pli, A£pli, £ci, and A£d. Let us take as a basis the fact that the performed thermal fatigue tests are described, on the one hand, by the total number of cycles and, on the other hand, by the level of the ratcheting deformation. Table 4: Comparison of the ratcheting deformation £max with the thermal fatigue and plasticity (short-time plasticity £r and creep-rupture plasticity cr ) at high temperature Tabela 4: Primerjava prelomnih deformacij £max s termično utrujenostjo in plastičnostjo (kratkotrajna plastičnost £r in plastičnost pri prelomu z lezenjem cr) pri visoki temperaturi Orientation T /°C L max' Time of stay, min £max/% ^•max1/ £max2 N N2/N1 r % at Tmax cr % at Tmax D3 D4 001 900 0 9.0 0.75 560 0.17 27 12.8-16.4 0.1 0 1000 0 12 95 19 8-23 0.25 0 111 900 0 10.7 24.3* 823 50 19,5 14-24 0.22 0.5 0 2 21 140 0 0.35-0.6 5 18.3 16 0 0.3-0.52 1000 2 23.7 194 21,5 7.2-23.8 0 0.4-1.3 011(2) 850 0 9.3* 2952 900 0 15.3 100 1000 0 20 0.67 472 0.67 5 29.7 317 0 10.6* 0.77 187 0.33 2 13.7* 62 011(3) 900 0 10.3 951 950 0 4.3 0.4 2535 0.18 950 0 10.7 450 1000 0 7.3 0.6 1220 0.05 1000 0 12 63 1050 0 14.7 356 011(4) 900 0 10 0.47 0.55 308 0.06 0.08 900 2 21.3 17 900 5 18 26 900 0 9.7* 25 950 0 9.7 0.94 626 0.20 950 2 10.3 128 *-specimen with concentrator Materiali in tehnologije / Materials and technology 42 (2008) 1, 3-12 9 L. GETSOV ET AL.: A FAILURE CRITERION FOR SINGLE-CRYSTAL SUPERALLOYS Table 5: Calculation of damage by means of (5) Tabela 5: Izračun poškodb z uporabo (5) Orientation The minimum temperature of a cycle, °C The maximum tempera ture of a cycle, °C Time of cycle, sec Number of cycles before formation of the main crack, nm Ae % 2 + A21 H < 010 > ■ + A22 n < 010 > nz A13 H < 100 >+ A23 H < 010 > + A31 H < 001 > ■ + A32 n < 001 ; + A33 H < 001 > (10) and l = Al + Al + Al "1r < 100 > ^ ^211 < 010 > ^ < 001 > 1 = Al + Al + Al y "^12 1 < 100 < 010 32 < 001 > l = Al + Al + Al z 131, < 100 "^23' < 010 r^33l < 001 > components of the strain tensor are obtained from the experimental data and the non-diagonal components are taken from the finite-element simulations. The results of the calculation of damage with the use of criterion (4) are shown in Table 8. For the definition of the damage size the following relations were used: D = Cr £ (Ay ipl)k; D2 = -L £ ( Ay f)k; C 3 n C a D3 = 0.4y ma '4 n /y r; D4 = 0.4y m^,/y c (12) Shear-strain computation. The criterion (4) requires a shear-strain (Aypi, Ayc, ypi, and yc) computation. The shear strain yn at the plane with the normal vector n in the slip direction l is defined on the basis of the strain tensor £ by the relation y „i = 2£ „i = 2n-£ • l (8) or, by using a presentation with components y ni = 2£ ni = 2(nx £ xxlx + nx £ xyly + Hx £ Jz. + + ny £ xylx + ny £ yyl y + ny £ yzl z + (9) +nz £ Jx + nz.£yzly + nz £ Jz ) The presented equations are valid for all cases, pl, c, pl and c, with a special choice of the strain tensor for each case. The components of the normal vector n and the slip direction l in the global coordinate system are related to the components in the crystallographic coordinate system by the following relations nx = A11 n < where the values of the constants C3, C4, yr, and ycr were defined using the ratio C3 = 2.25 Q; C4 = 1.66 C2; yr = 1.5 £r; ycr = 1.5 £r (13) For the orientation 111 , the sum of the damage agrees with the criterion (4) at the moment of formation of the main crack, and appears to be much more than 1.0, while calculations that use this criterion (5) are in good agreement with the experiment. Thus, criterion (4) gives, in this case, an underestimated number of cycles. At the same time the use of this criterion for two samples with the orientation 001 gives the best agreement with the experiment in comparison to criterion (5), and for one specimen the agreement is worse. The use of diagrams of maps of destruction (see Figure 8) allows us to predict the criterion of destruction during the thermal cyclic loading of objects made from single-crystal alloys. The use of the forgoing modification of the deformation fracture criterion will make it possible to solve reliably the problems of the prediction of the conditions of initiation of the thermal-fatigue cracks in the turbine blades made of single-crystal alloys. (11) 4 CONCLUSIONS where Aj is the matrix of crystallographic orientations, which is different for each specimen. The results of the computations of ynl for all the specimen series are given in Table 7. The diagonal The performed experimental investigation and the analysis led to the following conclusions: 1. The character of fracture of single-crystal alloys under thermal-cycle loading depends on the cry-stallographic orientation of the material and on the Table 8: Calculation of damages by means of (4) Tabela 8: Izračun poškodb z uporabo (4) Orientation The minimum tempera ture of a cycle, °C The maximum temperature of a cycle, °C Time of cycle, s Number of cycles before formation of the main crack, Nm pl,c % D1(Aypi) D2( c) D3( pl) D4( c) 2Di 111 150 900 72 190 1.57 2.19 0 0.62 0 2.81 247 50 1.40 0 3.6 0 0.99 4.59 378 12 1.57 0 0.16 0 1.47 1.63 500 1000 149 80 1.53 0 11.7 0 1.13 12.83 001 150 900 72 500 0. 345 0.027 0 0.144 0 0.171 250 1000 48 40 0.71 0.37 0 0.36 0 0.73 500 1000 28 1400 0.28 2.34 0 0.36 0 2.70 Materiali in tehnologije / Materials and technology 42 (2008) 1, 3-12 11 L. GETSOV ET AL.: A FAILURE CRITERION FOR SINGLE-CRYSTAL SUPERALLOYS temperature and time parameters of the loading mode. 2. The difference of the fracture mechanisms for each case of crystallographic orientation of the material can be represented with the help of the proposed fracture maps using the coordinates Tmax -AT. 3. New definitions for the deformation fracture criteria of single-crystal alloys in conditions of thermal-cycle loading have been proposed; they make it possible to evaluate the lifetime of blades made of single-crystal alloys using a computational-experimental approach. In summary, the use of the deformation criterion for the calculation of fracture conditions for single-crystal alloys submitted to thermal-cycle loading requires, on the one hand, a knowledge of the creep and plasticity characteristics of the material for different crystallo-graphic orientations in the working temperature range, and, on the other hand, the appropriate choice of the thermo-visco-elasto-placticity model. 5 REFERENCES 1 L. B. Getsov: Problems of creation of the "universal" theory of destruction of materials. 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PANTOCRATOR - Finite-element program specialized on the solution of non-linear problems of solid body mechanics; Proc. V-th Int. Conf. "Scientific and engineering problems of predicting the reliability and service life of structures and methods of their solution", St-Petersburg, 2003, 466-480 15 Thermal strength of machine details. The theory. Experimental researches. Calculation. Editor Birger I. A. and Shorr B. F. Mechanical engineering, 1975 (In Russian) 12 Materiali in tehnologije / Materials and technology 42 (2008) 1, 3-12