PSI - Issue 65

Maslov S.V. et al. / Procedia Structural Integrity 65 (2024) 139–146 Author name / Structural Integrity Procedia 00 (2024) 000–000

141

3

               0 e

     

Cr e

(2)

0

where, instead of a constant deformation  acting over time  the function is used that describes the change in deformation over time  . In this case,   Cr e    is the creep functionality depending on the nature of the change in function   e  over time  ;   0   is the output signal of the strain gauge, which would occur under the instantaneous effect of deformation  which acts on the strain gauge at the end of the time interval  . Since the creep of strain gauges Cr , determined by formulas (1) and (2) has a different interpretation due to different patterns of deformation change  , the set-ups for its determination may also be different. The work (Klymov M.V. et al, 2020) proposes to determine the value   , Cr   , based on formula (1) using a beam with 4 supports loaded with a fixed deformation const   and heated by a flowing electric current. This method is based on the classical approach to determining creep and gives acceptable results if it is possible to keep the deformation value unchanged based on a strain gauge. If the set temperature and deformation lead to creep of the material, this condition is not fulfilled due to a change in the shape of the beam longitudinal axis over time and a corresponding decrease in deformation based on the strain gauge. Therefore, using this classical approach to determine the creep of strain gauges at temperatures above 450 °C for exposure times equal to several dozen hours may be difficult, and for longer exposure times (several hundred hours), it may be practically impossible. To determine the creep of strain gauges   , Cr   in the range of strain values and exposure time, for which experimental data can be obtained using a 4-support beam, one can partially use the theoretical approach developed in the classical paper (Klokova, N.P., 1990; Daychik M.L. et al, 1989). According to this approach, the creep of a strain gauge under prolonged strain is determined by the following formula.

 

   

 









  ,  

Cr

Cr e

e

(3)

1

1  



1

2





    

e

where e Cr is the steady-state creep value at   ; α 1 and α 2 are the creep rate indicators. The first term in formula (3) is determined by the so-called short-term creep associated with the behavior of a carrier that does not exhibit plastic properties. The second term characterizes the change in the plastic properties of the carrier during long exposures. The analysis of the strain gauge creep at a constant deformation of 0.15% and a temperature of 490 °C allowed finding that the second term in formula (3) for strain gauges with a sensitive element made of nickel molybdenum alloy with an organosilicate carrier was no more than 10–15% of the total creep   , Cr   at a holding time of up to 600 s. Some experimental data obtained for these conditions are shown in Table 1.

Table 1. Creeps of strain gauges at 0.15% deformation and a temperature of 490 °C for a holding time of up to 600 s. Time, s 50 100 250 400 500 600 Creep, experimental data -0.6% -1.2% -2.6% -3.6% -4.3% -4.90% Creep, calculation of the first term. Cr = 7%, α1 = 600 -0.56% -1.07% -2.38% -3.40% -3.95% -4.40%

Creep, calculation of the second term. α2 = 8.5x10 4

-0.06%

-0.12%

-0.29%

-0.47%

-0.58%

-0.76%

The analysis of Table 1 shows that the second term of formula (3) has a small effect on the total creep of strain gauges under the above conditions. Therefore, to simplify further analysis of the error of field study findings, the creep of strain gauges caused by constant deformation is proposed to be determined using a simplified formula: