Nonlinear stochastic creep problem for an inhomogeneous plane with the damage to the material taken into account

Попов, Николай Николаевич; Радченко, Владимир Павлович

doi:10.1007/s10808-007-0034-7

J Appl Mech Tech Phys

2007

DOI: 10.1007/s10808-007-0034-7

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Nonlinear stochastic creep problem for an inhomogeneous plane with the damage to the material taken into account

Николай Николаевич Попов

Владимир Павлович Радченко

Abstract: DAMAGE TO THE MATERIAL TAKEN INTO ACCOUNT UDC 539.376 N. N. Popov and V. P. Radchenko An analytical method for the solution of two-dimensional nonlinear creep problems is developed using as an example the biaxial extension of a plane from a stochastically inhomogeneous material with damage accumulation and the third stage of creep taken into account. The governing creep relation is adopted in accordance with the energetic version of the nonlinear theory of viscous flow. The stochasticity of the material is def… Show more

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Cited by 7 publications

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“…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.…”

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

Радченко

Саушкин

Goludin

2012

J Appl Mech Tech Phy

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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

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confidence: 99%

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

Радченко

Саушкин

Goludin

2012

J Appl Mech Tech Phy

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Метод расчeта ресурса стержневых конструкций на основе энергетического варианта ползучести и длительной прочности

Шершнева¹,

Shershneva²

2012

J. Samara State Tech. Univ., Ser. Phys. & Math. Sci.

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Предложен аналитический метод оценки ресурса стержневых элементов конструкций в условиях ползучести по деформационному критерию отказа. Выполнена линеаризация стохастических реологических уравнений энергетического типа, получены оценки времени безотказной работы при ограничениях на предельные значения деформации ползучести. Выполнена проверка адекватности метода экспериментальным данным по ползучести образцов из стали 12Х18Н10Т при T = 850 ℃. Наблюдается соответствие расчётных и экспериментальных данных. Ключевые слова: ползучесть, предел длительной прочности, стохастическая модель, вероятность безотказной работы, деформационный критерий отказа.

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Оценка надeжности элементов конструкций в условиях ползучести на основании стохастических обобщeнных моделей

Радченко¹,

Шершнева²,

Shershneva³

et al. 2012

Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки

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Nonlinear stochastic creep problem for an inhomogeneous plane with the damage to the material taken into account

Cited by 7 publications

References 3 publications

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

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

Метод расчeта ресурса стержневых конструкций на основе энергетического варианта ползучести и длительной прочности

Оценка надeжности элементов конструкций в условиях ползучести на основании стохастических обобщeнных моделей

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