Determination of the distribution function of the parameters of a creep equation of state

Badaev, A. N.

doi:10.1007/bf01537996

Cited by 5 publications

(4 citation statements)

References 3 publications

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“…As a result, we have a number of implementations for the random function p = p(t), the time before fracture t * , and the strain p * at the time of fracture, for which we can estimate the mathematical expectation, variance, root-mean-square deviation, and statistical moments of any order. We tested the effectiveness of the proposed model and its adequacy to the experimental data with the use of the results of [5,6], which provide the necessary statistical information on the creep curves for the heat-resistant ZhS6KP alloy at temperatures T = 900, 950, 1000 • C (solid curves in Fig. 1).…”

Section: ω(T) = ασ(T)ṗ(t)mentioning

confidence: 99%

“…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.…”

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confidence: 98%

“…Calculated and experimental data for the ZhS6KP alloy at σ0 = 135 MPa and T = 900 • C in the stationary loading mode: the dashed curve is the averaged creep curve; the points are the experimental data for five samples[5]; the dot-and-dashed curves are the boundaries of the 95% confidence interval; the fracture area is marked by the rectangle.…”

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confidence: 99%

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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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Section: ω(T) = ασ(T)ṗ(t)mentioning

confidence: 99%

mentioning

confidence: 98%

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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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“…This problem is of utmost importance for creep strain, for which the spread of experimental values is as high as 50-70% and one has to consider these results as acceptable [3][4][5].…”

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confidence: 99%

Solution of the Stochastic Boundary-Value Problem of Steady-State Creep for a Thick-Walled Tube Using the Small-Parameter Method

Dolzhkovoi

Попов

Радченко

2006

J Appl Mech Tech Phys

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The physically and statistically nonlinear problem of steady-state creep for a thick-walled tube loaded by internal pressure is solved in the third approximation using the small-parameter method. The variances of random creep strain rates and displacements are calculated. The results obtained are compared with the solution of the same problem in the first and second approximations. A reliability assessment method for the tube using the strain failure criteria is proposed. 1.The substantial effect of random perturbations of the mechanical characteristics of materials on the stress and strain fields and the need for developing the corresponding stochastic models for strength analysis were discussed in many papers (see, e.g., [1][2][3]). This problem is of utmost importance for creep strain, for which the spread of experimental values is as high as 50-70% and one has to consider these results as acceptable [3][4][5].Determining the strains and stresses of structural members subjected to nonlinear-creep conditions is a very difficult problem even in the deterministic formulation. The necessity of considering the microheterogeneities of the material leads to stochastic boundary-value problems, in which statistical nonlinearity should be taken into account in addition to the physical nonlinearity of the governing equations. Because of these difficulties, stochastic boundary-value creep problems admit analytical solutions only in the simplest cases [6-9].To solve stochastic boundary-value problems in elastic and creep regions, the small-parameter method is used [6-10]. However, owing to substantial difficulties that arise in calculating the second and higher order moments of a random function, this method provides solutions of the stochastic boundary-value problems of steady-state creep only in the first approximation [6,8].In the present paper, the analytical solution of the boundary-value problem of steady-state creep of a thickwalled tube loaded by internal pressure is constructed to the third approximation using the small-parameter method.We consider this problem in cylindrical coordinates for plane strain [ε z (r, t) = 0 orε z (r, t) = 0], assuming that the stochastic heterogeneities of the tube material are described by a function of one variable -the radius r. In this case, the components of the strain and stress tensors are random functions of the radius r.In accordance to the theory of viscous flow (steady-state creep), the creep strains ε r and ε ϕ are described by the following rheological relations in stochastic form [9]:Here σ r and σ ϕ are the radial and hoop stresses, respectively, U (r) is the random function governing the stochastic heterogeneity of the tube material, whose statistical characteristics are known: U = 0 and U 2 = 1, α is the

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