UDK 539.42:669.14.018 Reviewed scientific article/Pregledni znanstveni članek ISSN 1580-2949 MTAEC9, 42(3)99(2008) ON THE DIFFERENT NATURE OF TIME-DEPENDENT AND TIME-INDEPENDENT IRREVERSIBLE DEFORMATION O RAZLIČNI NARAVI ČASOVNO ODVISNE IN ČASOVNO NEODVISNE IREVERZIBILNE DEFORMACIJE Leonid B. Getsov Saint-Petersburg State Polytechnic University guetsov@online.ru Prejem rokopisa — received: 2007-04-06; sprejem za objavo - accepted for publication: 2008-02-15 Several current models for elastoviscoplasticity use irreversible deformations without dividing them into time-dependent and time-independent components. This article presents experimental data on the difference in the mode of deformation and in the fracture conditions compared to the actual values. General functional dependences are proposed for the description of the dependence of the material characteristics from the conditions of exposure to high temperature. The interference of creep deformation and momentary deformation in conditions of static and cyclic deformations is investigated. A method is proposed for summing the irreversible deformations, taking into account their difference in nature. Key words: elastoviscoplasticity, ireversible deformation, time dependence, separation Več sedanjih modelov elastoviskoplastičnosti uporablja irevezibilno deformacijo brez ločitve v časovno odvisno in v časovno neodvisno komponento. V tem članku so predstavljeni eksperimentalni podatki o tem, da lahko to povzroči pomembno razliko v načinu deformacije in v pogojih preloma. Predlagana je splošna funkcijska odvisnost za opis karakteristik materiala v odvinosti od pogojev obremenitve pri visoki temperaturi. Raziskavna je interferenca deformacije z lezenjem in trenutne deformacije v pogojih statične in ciklične deformacije. Predlagana je metoda za seštetje ireverzibilnih deformacij, ki upošteva razliko v njihovi naravi. Ključne besede: elastoviskoplastičnost, ireverzibilna deformacija, časovna odvisnost, metoda ločitve obeh 1 INTRODUCTION Some of the current models of plasticity consider time-dependent irreversible deformations separately from time-independent deformations1. At the same time, the parameters of a number of other models for plasticity are time-dependent components of the tensor of plastic deformation. This paper presents experimental data confirming that in a number of cases it is not correct to use the second approach and it is more appropriate to use the models of thermoelastoviscoplasticity (and thermo-viscoelastoplasticity, according to the classification of Perzyna2) and the division of irreversible deformations into time-dependent and time-independent components. It should be noted that the question about such divisibility (on the basis of the notion of momentary deformation curves introduced by Yu. N. Rabotnov) was resolved positively in experimental studies of different alloys based on iron and nickel. The results of an experimental study pertaining the conditions of a uniaxial stress state were observed mainly for heat-resistant steels and alloys. 2 MICROSTRUCTURAL PECULIARITIES OF DEFORMATION PROCESSES It is known that because of the different crystallo-graphic orientation of the grains in polycrystalline metal materials, microstresses in such materials differ considerably (also because of the anisotropy of the coefficient of elasticity) from the average stresses both by the value and by the direction of the deviator vector. For this reason, the microplastic deformations differ considerably in terms of value from the average deformation and this induces residual stresses usually referred to as residual stresses of type II, which cause the Bauschinger effect and plastic hysteresis. It is evident that the time-independent microplastic deformations and microcreep deformations may take place both when deforming with stresses higher and lower than the elastic limit and may produce the relaxation of internal stresses of type II. B. I. Rovinsky and V. G. Liuttsau4 have linked the processes of micro- and macrocreep and have shown that the character of the process of microstress relaxation was similar to that of macrostress relaxation. Which deformations, microplastic or microcreep, are larger in magnitude in conditions of stresses under the elastic limit ( y), including cyclic stresses, is the question that can only be answered on the basis of experimental results. It is known, as proved by the analysis of data on the microdeformations of different materials under single loading5, that at low temperatures the microplastic deformations are considerably larger. However, in the case of cyclic deformation the process of development of microplastic deformations in many materials is slowed as the number of cycles increases, whereas the rate of accumulation of microcreep deformations under cyclic Materiali in tehnologije / Materials and technology 42 (2008) 3, 99-103 99 GETSOV L. B.: ON THE DIFFERENT NATURE OF TIME-DEPENDENT AND TIME-INDEPENDENT ... Figure 1: Cyclic creep curves for the alloy EI765 at 700 °C. (a) hard loading cycle, (b) soft loading cycle, a) Tc = 290 MPa, Ae = 1,2 %; b) Tc = 272 MPa (tc - elastic limit) Slika 1: Krivulje cikličnega lezenja za zlitino EI 765 pri 700 °C. (a) cikel trde obremenitve, (b) cikel mehke obremenitve sliding and can be overcome with microplastic deformation only at high stress with the mechanisms of lateral sliding and cutting. At the same time, during prolonged loading at the stress o < oe, the accumulation of creep deformation is controlled by dislocation creep over barriers. Besides, unlike the case of momentary loading, where shearing of grain boundaries (because of the strong off-orientation of the lattice) is not possible, by creep deformation inter-grain sliding may also occur and cause the accumulation of creep damage. Thus, the analysis of the microstructural behavior of materials during deformation shows that it is useful to divide irreversible deformation into creep deformation and time-independent plastic deformation. alternating loading increases with the number of cycles (Figure 1). At high temperatures the microcreep deformations are considerably larger than the microplastic deformations. These conclusions were confirmed by the author's electron microscope observations of the deformation relief on heat-resistant alloy samples with precipitation strengthening after momentary tension in vacuum under high temperature up to stresses that were considerably lower than the elastic limit (a), after keeping it in such conditions for a short period of time (b) and after a creep test (c). After unloading, the deformation relief of the alloy EI826 (ChN70WMTAlV) formed at 850 °C was investigated after momentary and prolonged loading up to o = 220 MPa - 0.6 Oc (Figure 2). After a longer loading time (1-4 h) and a creep test, the accumulation of a microcreep deformation of 0.1 % and the intense development of fine slip lines were discovered in the overwhelming majority of grains. (Figure 2b). By difference, in conditions of momentary loading (with a rate of 180-2400 %/h) after loading-unloading the packets of slip lines were found in only 30 % of grains (Figure 2a). Particles of the second phase in heat-resistant alloys are efficient barriers for the development of conservative Figure 2: Microstructure of the alloy EI826 after momentary loading (a) and after prolonged loading (b) = 220 MPa at 850 °C Slika 2: Mikrostruktura zlitine EI 826 po trenutni (a) in po podaljšani (b) obremenitvi 3 CREEP DEFORMATION CAPACITY OF MATERIALS The deformation accumulated in a material at the moment of rupture, is, as a rule, considerably different in the cases for momentary loading and after a creep test. As an example, in Table 1 the values of the residual elongation for two groups of steels and alloys after a short time deformation up to rupture and after long-term strength tests (in creep conditions) are shown. The alloys of group A have values close to the residual elongation after short-term tension and after a long-term strength test. This confirms the conclusion, considering the deformation at rupture, that for the materials of group B the equal residual deformation accumulated by momentary loading (e) and in creep (p), may lead to considerably different values of damage (e/cf and p/cc). Thus, for such materials, the use of irreversible deformations without the separation into time-dependent and time-independent deformations may produce considerable errors in the determination of the margins of safety. Table 1: Residual elongation after creep and after momentary loading Tabela 1: Sposobnost za deformacijo v primeru lezenja in trenutne obremenitve Residual elongation (%) under Material Group Temperature, °C Long-time rupture (100-1000 h) Momentary tension 22K 500 21-23 24 15ChM A 520 15-31 21 12Ch1MV 500 34-41 21-22 10Ch18N10T 650 9-45 27-37 25Ch2M1V 550 1,0 14 EI481 600 1 -3 12 EI612 600 1 -3 15-25 EI765 B 700 10-13 20 EI826 800 4-7 14 EI827 800 2-6 18 EP220 900 2-3 10 100 Materiali in tehnologije / Materials and technology 42 (2008) 3, 99-103 GETSOV L. B.: ON THE DIFFERENT NATURE OF TIME-DEPENDENT AND TIME-INDEPENDENT Table 2: Influence of a long ageing time on the residual deformation Tabela 2: Vpliv dolgega staranja na rezidualno deformacijo Material Temperature and time of preliminary aging Stress, temperature and time to rupture in the creep test Residual deformation (%) T/°C r/h /MPa T/°C Tf/h Momentary loading, f Creep, ec EI787 - - 350 650 8000 20 1,6 650 50000 350 650 442 6 15,0 EP99 - - 200 800 374 50.2 24 800 5000 200 800 193 5.0 20.4 EP126 - - 100 800 684 41 28,8 800 5000 100 800 151 16 10.0 EI481 - - 300 650 1000 23 4 650 40000 300 650 72 20 30 4 INFLUENCE OF EXPOSURE TO HIGH TEMPERATURES ON THE DEFORMATION CAPACITY Special experiments were carried out to determine the influence of preliminary aging without any load on the alloy microstructure and its resistance to deformation in the cases of momentary loading and in creep condi-tions6 (Table 2). It was found that the microstructural changes caused by long-term aging affect differently the residual elongation after momentary deformation and after creep and, as shown in Table 2, on the deformation capacities f and c. Thus, the microstructure of the material is related to its mechanical state, which is a microstructural parameter. Metallographic studies were also carried out during the deformation of samples of the alloy EI787 after aging for 50000 h at a temperature of 650 °C (state 2) in comparison with the initial state (state 1). For both states of material approximately equal values of yield stress (880 MPa and 900 MPa) were established with tensile tests (in the case of momentary loading). At the same time, the values of the plasticity and the time-to-rupture below 650 °C and a stress of 350 MPa were considerably different (Table 3). Table 3: Influence of microstructure of the alloy EI787 on it deformation characteristics Tabela 3: Vpliv stanja mikrostrukture zlitine EI787 na deformacijske značilnosti Temperature of tests, T/°C 650 700 State 1 2 1 2 Stress, Material T/°C Without creep With creep in both semi-cycles 20Ch23N18 400 4.3 1.8 EI868 600 2.0-2.9 1.8 700 2.5 1.8 EI765 700 1.9 1.4-1.7 EP220 900 1.9 1.3 The acceleration of creep from cycle to cycle is observed in case of cyclic deformation with creep in one semi-cycle (Figure 5). It was also found that the creep has a softening effect on the curve of cyclic deformation in the next semi-cycle: 1) the cyclic elastic limit decreases by the value (Smax/2) - CTcteep (