Stochastic model of nonisothermal creep and long-term strength of materials

Abstract

A stochastic model of nonisothermal creep and long-term strength of metallic materials is proposed. Experimental data on the creep of the ZhS6KP alloy at temperatures equal to 900, 950, and 1000 • C are stochastically analyzed. These experimental data are used to substantiate the hypotheses applied in constructing the model. The stochastic model is checked for adequacy to the experimental data on the creep of the ZhS6KP alloy under stationary and nonstationary loading conditions. It is shown that the calculated and experimental data are in satisfactory agreement.1. The mechanical properties of materials have a clear probabilistic nature on the atomic-molecular level and on the level of a machinery or structure element, due to which the same type of products have different mechanical properties. To a great degree, this nature of material properties is manifested in rheological strains. In was noted in [1, 2] that the minimum creep rate values, obtained during creep tests for samples from the same batch, can vary by 50%. Such a difference has to be regarded as good agreement of experimental data (see [3][4][5][6][7][8][9]). The phenomenological theories of creep used in applications to estimate the safety margin of exploitation of structural elements, as a rule, have a deterministic nature and do not take into account the variation of creep and long-term strength characteristics. Therefore, a deterministic method of calculation is the first and often insufficient approximation. In engineering practice, the inaccuracies of deterministic calculation of strength and reliability can be compensated, for instance, by assignment of a safety factor, which is sometimes selected without sufficient justification and is not optimal. As a result, there are unused strength reserves or premature (compared to the estimated time) fracture of structural elements. In view of the considerations mentioned above, we needed to develop stochastic models of isothermal creep and long-term strength [6-8, 10, 11]. The need to develop stochastic rheological models is also due to the development of the creep theory, which is used, in particular, to solve stochastic boundary-value problems of creep [12][13][14][15]. The main element in formulating such problems is the governing (physical) relations. In the present work, we generalized the results of [7,10,11] to the case of nonisothermal creep and constructed a corresponding stochastic model of creep and long-term strength.2. In accordance with [10], it is assumed that the strain of the sample ε(t) is an additive component of two random functions:is the mathematical expectation operator). In view of these conditions, ε 2 (t) is considered as some noise superimposed onto a random function ε 1 (t), which describes stable random properties of the material. Thus, the role of the random function ε 2 (t) is reduced to creating minor fluctuations of each

Прогнозирование Индивидуальных Деформационных Характеристик Элементов Конструкций По Изделию-Лидеру

“…характеризуются большим разбросом деформационных характеристик. Так, для наблюдаемой экспериментальной деформации ползучести металлических материалов величина разброса составляет 20-50 %, для длительной прочности величина разброса -30-100 % [8][9][10], а для геометрических характеристик, описывающих, например, величину зазора между сопрягаемыми цилиндрическими деталями в условиях трения, величина разброса может составлять до 100 % [11]. В связи с этим классические статистические теории [1,2,[12][13][14]28] и современные подходы линеаризации нелинейных регрессионных уравнений для идентификации параметров моделей [29,30], основанные на моделировании деградации материала элементов конструкций и необратимом накоплении поврежденности, ориентированы на генеральную совокупность однотипных изделий с использованием стандартных (и модифицированных) методов обработки статистической информации [15,16] и дают широкую полосу разброса для математических ожиданий соответствующих выходных деформационных характеристик и времени безопасной эксплуатации по параметрическим критериям отказа.…”