PSI - Issue 23

I.A. Volkov et al. / Procedia Structural Integrity 23 (2019) 281–286 Author name / StructuralIntegrity Procedia 00 (2019) 000 – 000

282

2

1. Introduction In the course of their long service life, materials of structural elements of the equipment and systems of critical engineering objects (CEO) with service lives of several tens of years (atomic power plants, oil-processing equipment, reservoirs for gaseous and liquefied chemical products, new generation aviation gas-turbine engines (GTE) and plants (GTP), etc.), working in the conditions of nonstationary thermal-mechanical loading, accumulate microdefects leading to degradation of their initial strength characteristics, nucleation and growth of cracks. For a considerable time, such changes develop implicitly. Besides, the most hazardous zones, showing residual life of the elements, are, as a rule, inaccessible for nondestructive control means. To guarantee safe exploitati on of CEO’s and to prolong their life over normative time limits, it is required to control rates of development of damage levels in the most hazardous zones of structural elements (to evaluate spent life), as well as to forecast the development of such processes up to critical states (to evaluate residual life) by М itenkov et al (2007). As damage accumulation processes are closely connected with the stressed state kinetics, the accuracy of numerically evaluating strength and service life of structural elements will depend on how adequately the defining relations of MDM describe deformation processes in the hazardous zones of structural elements in the given exploitation conditions. Such parameters of the viscoplastic deformation process as length and type of the deformation trajectory, the stressed state type and history, etc., considerably affect the rates of damage accumulation processes by О hasi (1985) or Lemba and Sidebottom (1978) or McDowell (1985). In the present paper, in the framework of mechanics of damaged media, a mathematical model of MDM is developed, which describes damage accumulation processes in structural materials (metals and their alloys) due to degradation mechanisms determined by developing creep strains. Processes of ling-term strength of the VZh-159 heat-resistant alloy have been numerically analyzed; the obtained results have been compared with the data of full scale experiments. The MDM model consists of three interconnected parts:  Relations defining viscoplastic behavior of the material, accounting for its dependence on the failure process;  Equations defining damage accumulation kinetics;  A strength criterion of the damaged material. 2.1. Relations of thermal creep The relation between the stress tensor and elastic strain tensor are based on the equations of thermoelasticity: 2. Defining relations of mechanics of damaged media

)    ; К

 K e    3 Т

 ) ;

ij  

2 ; e ij Ge 

e ij ij e e e     c ij

,



e ij ij Ge G G   



2  

;

ij 

3         K e Т Т 

(1)

К

where  , e are spherical components, and ij   , ij e  are deviatoric components of stress ij  and strain ij e tensors, respectively; ( ) G T is shear modulus, ( ) K T is volumetric elasticity modulus, ( ) T  is thermal expansion coefficient – a function of temperature Т . To describe creep processes, a family of equipotential creep surfaces c F is introduced in the stress space, which have common center c ij  and different radii c C determined by the current stressed state:

( ) i F S S       c c c ij c c

0,1,2,...; i 

( ) i ij ij c F S S C    c c c

S

2 0;

;

c ij      ij

c

e

,

c ij

(2)

ij

ij

( ) i c F deftermining current stressed state c ij S .

where c  corresponds to current surface