PSI - Issue 20

D. Reznikov / Procedia Structural Integrity 20 (2019) 17–23 D. Reznikov / Structural Integrity Procedia 00 (2019) 000–000

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Table 1. Normative values of safety factors. Brach of industry, type of equipment

Range of values

Aviation and space industries

1.2 - 2.0 1.1 - 3.0 2.1 - 8.0 3.3 - 5.6 1.3 - 1.6 1.5 - 4.0

Equipment and pipelines of nuclear power plants

Metallurgic equipment Railroad transportation

Carrying and lifting equipment

Pressure vessels

The design value of safety factor n i at the moment t may be represented as the sum of three components:

n

i  

( ) t

n

( ) t   

( ) t

(0)



*

i (4) where n i (0) is the initial value of safety factor assigned in the process of the systems design by selection of the corresponding technical solutions and geometric and physical parameters of the system; Δ i ( t ) is the degradation function that describes the reduction of capacity parameters as a result of degradation processes (fatigue, corrosion, wear, etc.) in the technical system; * ( ) i t   is the maintenance function that characterizes an increase in capacity parameters (and/or reduction in operating loads) as a result of the implementation of a certain maintenance program ζ ( a m , a o , a r , a z ) which implies carrying out a series of protection measures (monitoring a m , maintenance a o , repair a r , and development of protection systems a z ). In engineering practice differential safety factors n 1 (0), n 2 (0), …, n k (0) are selected at the design stage. Apparently, the set of initial safety factors do not completely determine the system’s structural integrity at various stages of its operation. Due to degradation processes, extreme external impacts, errors of operators, etc., capacity parameters of TS components naturally tends to decrease. Therefore, the differential safety factors n i ( t ) are decreasing functions, which may fall below the allowed normative levels [ n i ] with the course of time. Therefore, a certain maintenance program ζ ( a m , a o , a r , a z ) that implies a set of specific protection measures which include monitoring of the technical state, maintenance, repairs, and introduction of protection systems should be implemented to secure the system's structural integrity during the whole system’s life cycle. Therefore initial safety factors n i (0) against the main ways of reaching TS limit states are to be assigned considering the expected intensity of degradation processes and in agreement with the accepted maintenance program ζ . Thus when the deterministic approach is applied, the system’s structural integrity may be characterized by the following parameters: (i) a set of initial differential margins n 1 (0), n 2 (0), …, n k (0); (ii) a family of so called degradation functions Δ 1 ( t ), Δ 2 ( t ), …, Δ k ( t ) that describe the reduction of the system’s capacity parameters as a result of degradation processes; (iii) the system maintenance program ζ ( a m , a o , a r , a z ) which is a complex parameter that determines the set of protection measures implemented in process of the TS operation. In this formulation the system’s structural integrity is characterized by the following functional:   , 1 2 * 1 2 ( ) (0) (0) (0), ( , , , ) ( ), ( ), , ( ), , , , Н n k mon TO rem SZ k Z t F a a a a t t t n n n         . (5) With the functional (5) taken into account, two strategies for securing structural integrity may be defined (Fig. 1): - Strategy 1 implies assignment of relatively small initial safety factors n 1 (0), n 2 (0), …, n k (0) and implementation of a significant set of protection measures that includes maintenance, routine repair, and overhaul at moments t 1 , t 2 , and t 3 respectively (the maintenance program ζ 1 ) . - Strategy 2 implies assignment of significant initial safety factors against the main ways of reaching the system’s limit states and the minimum amount of protection measures (the maintenance program ζ 2 ). The first strategy is applied to those TS whose components can be easily controlled in the process of operation and which may be replaced or repaired without the system shutdown. It is reasonable to use the second strategy for systems (or their components), access to which in the process of operation is complicated and they may not be repaired without significant material or time costs. i i ,