PSI - Issue 28

Vasilii Gorokhov et al. / Procedia Structural Integrity 28 (2020) 1416–1425 Author name / Structural Integrity Procedia 00 (2019) 000–000

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3. Results of numerical simulation of high-temperature creep of structural elements made of heat-resistant alloys The proposed model and obtained material functions were verified by reconstructing the original creep curves based on numerical simulation in the temperature range melt T T (0.607 0.679)   , as such showing good agreement between experimental data and numerical results. On the basis of the model proposed above, a numerical technique for solving problems of high-temperature creep of structures made of heat-resistant alloys under conditions of neutron irradiation has been developed and implemented within the framework of CC UPAKS (Computing complex UPAKS (2002)). The problems of studying the behavior of structures made of heat-resistant alloy under consideration are solved within the framework of the general methodology used in CC UPAKS for studying the deformation and fracture processes in structures under quasi-static thermo-force loads by step-by-step integration of incremental equations with the help of a combined step scheme (Kapustin et al. (2015)). Nonlinear problems at a step are solved in the form of the initial stress method. The numerical solution of linearized problems is carried out on the basis of FEM using universal models of isoparametric quadratic FE with sirendip approximation of the displacement field (Kapustin et al. (2015)). To verify and illustrate the capabilities of the developed methodological and software tools, a number of problems of modeling the processes of high-temperature creep and fracture of structural elements made of the considered heat-resistant alloy were solved. In the first problem, numerical modeling of creep processes is performed in the working part of the irradiated specimen made of a nickel-based heat-resistant cast alloy, heated to a temperature melt T T 0.607  for the level of constant stresses Y σ 0.35σ  ( Y σ is the yield stress of the material at melt T T 0.607  ), applied along its ends. The problems were solved by the FEM in an axisymmetric formulation. The process of loading the irradiated specimen was represented in the form of two steps: the first step - heating up to melt T T 0.607  , and application of end stresses; in the second step the specimen is exposed to load for a specified time under neutron flux irradiation. The calculation results in the form of curves of creep strain as a function of time ( ) e e t c c  are shown in Fig. 1. Solid line corresponds to experimental curve, while the results of numerical simulation are represented by dashed line. The presented results show that, for the stress level Y σ 0.35σ  the results of numerical simulation are in good agreement with experimental ones: they describe with an acceptable accuracy the steady-state creep rate, the value of the creep strain accumulated during the time   t t 0.217 (  t is the characteristic time of operation) and the predicted time of the brittle fracture onset. In the second problem, numerical modeling of the deformation process of a bellows fragment made of the considered heat-resistant alloy was performed, the geometric dimensions and the scheme of finite element discretization of which are given in (Antipov et al. (2016)), under high-temperature force loading conditions. Due to the presence of the axis of symmetry in the geometry of the fragment, 1/16 of it was considered along the circumference (22.5º). The following loading option is considered: loading with internal pressure of Y p 0.003σ  and heating of the bellows fragment to temperature melt T T 0.643  (step 1); time under irradiation of   t t hours at constant pressure Y p 0.003σ  and temperature melt T T 0.643  (step 2). At the first step, stresses are observed to arise in the bellows as a result of loading, the zone of maximum intensity of which was located on the outer surface of the lower bend. In the indicated zone, the stress intensity reached the value Y и 0.551σ σ  . After exposure time   t t , a significant relaxation of stresses due to creep and their redistribution in depth along the thickness occurred in the outermost fibers of the fragment. As such, the maximum stress intensity decreased to Y и 0.215σ σ  . As a result of calculations, a significant nonstationarity of the bellows deformation process was established. In particular, the maximum creep rate at the most loaded point was observed from the beginning of exposure time, and creep rate was observed to decrease monotonously with time. Fig. 2 presents a graph of creep strain as a function of time at the most loaded point of the bellows, showing a sharp decrease in the creep rate during time delay.