PSI - Issue 59

Svitlana Fedorova et al. / Procedia Structural Integrity 59 (2024) 279–284 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

281

3

and the problem comes down to building this potential. Moreover, for boundary conditions (2) and (3) in normalized form

( 0) 0 (      

D D x

(5)

) 1

R

normalization conditions ( , 0) 0 ( , 1) 1 F L D F L D    

(6)

ensure the adequacy of the Kachanov model (4) and (6) to the experimental curve of evolutionary strength, regardless of the specific type of this potential. This decomposes the problem, allowing you to use the existing approximation exp R R ( ) x X L  and then worry about solving the other subproblems listed in the introduction. The implicit method involves choosing a prepotential from an unlimited set, which is given by the recursive algorithm of Fedorov (2023). The simplest prepotential 1 1 1 ( ; ) C F DC D  results in the damageability function of Chaboche and Lesne (1988). Taking into account the tradition of using a function with a divisor (1 ) D  , let us analyze in more detail the damageability function derived from the prepotential

1 2 2 1 2 ( ; , ) 1 (1 ) C C F DC C D    ,

(7)

2 C do not affect the normalization conditions (6). Assuming 1 1 C  and

1 C and

where the neutral parameters

2 ( ; ) С L   c , we obtain the normalized

converting another neutral parameter into a neutral load function 2 2

potential

2 D     c c . 2 ( ; ) L

2 2 ( , ; ) 1 (1 ) F L D

(8)

Here 2 c is a set of approximation parameters that influence the rupture moment only under unsteady loading of the material. These parameters should be found from the approximation of the corresponding experimental data. Most often these are tests with two-stage loading:

0

L for

x

     

s     ( ) 

1

s

( ) L L 

(9)

,

L forx

x



2

s

R

where s x is the moment of load jump.

3. Adequacy of the damageability function under unsteady loading L -criterion of the adequacy of the damageability function is expressed in the equality of the partial increment of the normalized potential over the lifespan of the material to the experimental value of the defect of the Palmgren Miner rule (PMR defect):     exp ( ) ( ), R L R F L O L x     . (10)

The left-hand side of this equality is the theoretical value of the PMR defect

th O . With two-stage loading (9)