PSI - Issue 28

L.A. Igumnov et al. / Procedia Structural Integrity 28 (2020) 2086–2098 L.A. Igumnov, I.A. Volkov/ Structural Integrity Procedia 00 (2019) 000–000

2087

2

residual life of existing structures in the process of operation. Particularly relevant these tasks for structures and apparatus service life which is several tens of years (nuclear power plants, petrochemical equipment, aviation gas turbine engines (GTE) and installation (GTU), a new generation, etc.). The classical methods of prediction of longevity by using semiempirical formulas require a large amount of experimental information and is valid only for a narrow range of loading conditions. In recent years for solving such problems successfully develops new scientific direction mechanics of a damaged medium (Volkov I.A., Korotkikh Y.G. (2008), Volkov I.A., Igumnov L.A. (2017)). The current practice of using MDM equations for different mechanisms of resource exhaustion suggests that this approach is efficient enough for practical applications, it is sufficient to evaluate correctly the process of resource exhaustion of structural elements and components of load-bearing structures. In the present work developed a mathematical model of the mechanics of a damaged medium used to assess the durability of materials and structures in fatigue and creep. Laws of damage accumulation in structural alloys affected by fatigue and creep are analyzed, using numerical modeling and by comparing the obtained results with experimental data. 2. Determine the ratio of MDM Model damaged environment, developed in (Volkov I.A., Korotkikh Y.G. (2008), Volkov I.A., Igumnov L.A. (2017)) consists of three interrelated parts:  equations describing the viscoplastic behavior of the material taking into account the dependence of the failure process (Volkov I.A. et al. (2015));  evolutionary equations describing the kinetics of damage accumulation;  criterion of the strength of the damaged material. In elastic region the relationship between the spherical and deviatoric components of the tensors of stresses and strains by using Hooke's law:







),   

' 2 , e G е e e e e     e p

ij   G G

(1)

3 (  

, 3 [           c К е T T 

)]    

' К K G е   , 2

К е Т



'   е



ij

ij

ij

ij

ij

ij

ij

ij

here is , , , е е     – ball, and

, , , ij ij ij ij e e         – the deviatoric components of the stress tensor

ij  , deformations ij e their

velocities ij   , ij е  respectively; Т – the temperature; 0 Т – the initial temperature; ( ) К Т – is the bulk modulus; ( ) G Т – shear modulus; ( ) Т  – is the coefficient of linear expansion of the material. Effects of monotonous and cyclic deformation in the stress space are accounted for using a Mises form of the yield surface:

(2)

2 ij ij р F S S C    , 0 s

'     . p

S

ij

ij

ij

To describe complex cyclic deformation modes in the stress space, a cyclic ‘memory’ surface is introduced:

(3)

0

F 

2 max       p p ij ij

where

max  – is the maximum in the history of the loading module variable p ij  . For the yield surface radius, the following evolutionary equation is assumed (Volkov I.A. et al. (2015)):       3 р s p С q H F a Q C Г F q T                , (4)