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

71

9

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(9)

where the experimental characteristics of yield stress, ultimate strength and cross-sectional narrowing limits at room temperature are additionally introduced. By doing so, the value of specified characteristics can be calculated with the distributions built according this procedure, for example, for the probability of Р=0.01, and compared quantitatively with the value determined earlier according to the formulas (2…6) . Similar computations were performed for steel 3 (C-0,14-0,22%; Fe-97%) at the same temperatures. Comparison of the precision (uncertainty) Δ of determining these values is given in Table 6. Here, positive signs before numbers show that the numerical value of mechanical property characteristic, defined according to the abovementioned distribution curves is higher than the value computed according to formulas, and vice versa. For the purpose of refining the uncertainties in calculating the values of specified characteristics σ т , σ в , ψ k and Sk (taking into account temperature dispersal during trials) and their repeatability (stability) two additional variable temperatures, -83 and -88 o С, were introduced into calculation. The uncertainty for ψ k marked as ±Δ 2 means that the variation coefficient for characteristic was computed according to (9), Δ 1 – according to (8).

Table 6. Summary table of errors (in%) of the MMP values calculated from the normal distribution curves and formulas (2-6).

Sk t , MPa

Steel

t 0 ,C

ψ

t , %

t , MPa

σ t , MPa -1.95 В

σ

k

Т

15Х2НМФА

- 85

-2,8

Δ 1= +2 Δ 2= -6,1 Δ 1= -3,88 Δ 2= -9,97

Δ 1== +1,2 Δ 2=- +4,65 Δ 1= +0,06 Δ 2= -2,96

3

-85

-3,5

+0,44

It is important to note that for 15H2NMFA steel and for characteristics σ т t and σ В t the errors are mostly negative (within the limits from -2 to -2.8%); which indicates the conservatism of evaluating these characteristics (contributing to the safety factor) in comparison with the calculation evaluation based on the formulas. For the ψ k t and Sk t characteristics the errors are observed to be both positive and negative and amount up to  4,6%. This indicates the need of a refined definition of these calculation characteristics and coefficients of their variation. It should be noted that the Δ 1 and Δ 2 errors for the S k characteristic were determined (Table 6) at negative temperatures as the difference between the S k value (Table 6) computed according to formulas (2…6) and the values computed according to formula (1), where the σ В0,01 value (at probability Р=0.01) was determined with a variation coefficient according to (8), and the ψ k value was determined according to both (8) and (9). The σ В0,01 and ψ k0,01 values were taken from the theoretical curve of normal distribution for σ в and ψ k , correspondingly. 4. Probabilistic characteristics of safety factors It is understood that while analyzing the results of the researches performed in the general case it is necessary to build engineering designs contributing to safety factors. If the calculation MMP characteristics in the range of negative or positive temperatures were found to be lower in comparison with the experiment, the coefficients of the safety factor are determined with conservatism. While further analyzing the calculations it is possible to go for the refinement of the margins and back out of conservatism based on refinement of calculations and calculation characteristics. However, if the calculation characteristics do not contribute to the safety factor, it is desirable to