PSI - Issue 20

N.A. Makhutov et al. / Procedia Structural Integrity 20 (2019) 63–74 N.A. Makhutov and V.V. Zatsarinnyy / Structural Integrity Procedia 00 (2019) 000–000

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evaluate the uncertainty of non-conservatism. I.e. it is necessary to analyze qualitatively the manner in which the probabilistic safety factors will vary depending on the temperature. While analyzing the Fig. 4 and Table 4 a good match of experimental values for σ в, σ т , ψ k in temperature interval from -85 to +80 o C can be seen with the calculation values for these characteristics computed according to the formulas (2…6); which proves the possibility of using the calculation procedure given by Makhutov (2005, 2008). It is necessary to use the MMP characteristics at 20 o C as a basis for all strength and durability calculations inasmuch as all main basic properties are obtained at this temperature. Therefore, our prime interest lies in all MMP characteristics in the temperature range of -85…+80 o С including the v variation coefficients. For room temperature these characteristics are given in the Table 2. The values computed according to (9) amounted to ν Sk =0.0274 (for ν ψk =0.01). For the negative temperature of -85 o С the computed variations of mechanical properties determined according to (8) or (9) on the basis of which the functions of normal distribution were built constituted, correspondingly, ν σв =0.0333, ν т =0.0421, ν ψk =0.0922 and ν ψk =0.119. The variation coefficients for the temperature of -85 o С are higher than for the room temperature. If the σ т t , σ в t strength characteristics increase at negative temperatures, the S k value remains nearly constant and plasticity, ψ k , is decreasing, one may count out the changes of main characteristics towards overestimation in design calculations on a first approximation. In such cases, the data at room temperature can be used. At the temperature of +80 o С these characteristics will be reduced and the calculations will be made not in safety factor, i.e. the previous assumption will be non-conservative, and the lower characteristics are to be used during calculations. At negative temperatures the ψ k plasticity for 15H2NMFA, 3 steels drops, and, according to (1), the S k characteristic must also decrease; which does not contribute to the safety factor. Conventional basic strength calculations are performed based on deterministic estimation of the margins  n with reference to stresses in hazardous components, hazardous cross-sections and hazardous points Design code, 1989. where k  refers to critical stresses defined from set of experiments according to average values; э  - to working stresses defined on the basis of calculation according to operation loads preset by technical specifications. The yield stress σ т or the ultimate strength limit σ в , which are also specified by standards and technical conditions are usually used as k  . The calculations according to force criterions can be performed with the use of conventional (according to σ т , σ в ) or true (according to k S ) stresses. Then   т т т n    ;   в в в n    ;   S k S n S   . (11) When performing checking calculations for safety-related objects these margins are defined probabilistically for preset probability P of the parameters included into the formulas (10), (11). The probability Р = 50% corresponds with the deterministic calculation according to (10) and (11) at t = 20 o С. At pre-assigned values of э  the  n changes of margins towards their reduction take place in view of the data of Table 7 at reduced probabilities Р ( Р =1%). If during operation the value э  is varied (for the same probabilities Р – 50, 5, 1%), it is possible to allow the decrease of the  n safety factors by the formulas (10) and (11). At low ( t э <+20 o C) and elevated ( t э >+20 o C) t э operation temperatures the calculations based on temperatures are performed in addition to main and checking calculations by Makhutov (2008) and in Design code (1989) besides the э   k  n  (10)