PSI - Issue 39

Dmitry O. Reznikov / Procedia Structural Integrity 39 (2022) 256–265 Reznikov D.O./ Structural Integrity Procedia 00 (2019) 000–000

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kinetics of crack growth. The presence of these uncertainties necessitates the probabilistic description of the processes of damage accumulation and fracture of structural components of pipeline systems (Makhutov,2008; Matvienko et al.2021).

Nomenclature a

crack depth

initial crack depth

a 0 a C

critical value of the crack depth

crack depth after N r constant amplitude loading cycles

r N a

crack depth after N r constant amplitude loading cycles and N k overloads

r k N N a 

parameter of Paris equation

C D

diameter of the tube E { x } mean of the random variable x K I mode I stress intensity factor K I c fracture toughness k OL overload factor m exponent of the Paris equation N k number of overloads N r

number of cycles of constant amplitude loading

failure probability

P F p Σ p s R r R Σ

internal pressure under overloads

internal pressure under constant amplitude loading stress ratio under constant amplitude loading minimum value of hoop stress in the CA loading cycle maximum value of hoop stress in the CA loading cycle stress ratio under overload cycle

S min S max

S { x } standard deviation of the random variable x v Nk parameter of the extreme value distribution Y ( a ) correction function β Nk parameter of the extreme value distribution Δ K I stress intensity factor range Δ S stress range under constant amplitude loading ΔΣ stress range under overload cycles Σ i peak value of i -th overload Σ max

maximum value of peak hoop stress in the serious of overloads

wall thickness

δ

ν x

coefficient of variation of x

In real service conditions, the structural components of pipeline systems, in addition to regular loading modes, which can be considered as loading by internal pressure with cycles with a constant amplitude, are subjected to repeated random impacts of increased amplitude (overloads), for example, during hydraulic tests, hydraulic shocks, etc. The intensity of such impacts is unknown in advance. Therefore, the magnitudes of the overload effects are assumed to be independent, equally distributed according to the normal law, random variables. The presence of the extended axial surface crack is postulated on the inner surface of the pipeline component under consideration. It is assumed that the crack length significantly exceeds its depth. The initial crack depth and the parameters of the kinetic equation describing the cyclic crack growth are assumed to be random values. Due to the fact that only limited amount of information regarding the size of the crack and the mechanical characteristics of the structural material is available, the initial size of the crack and the parameters of the Paris equation are assumed to be distributed according to the law of uniform density. If additional information is obtained about the actual size of pipeline defects and the mechanical properties of the structural material, the type and parameters of the probabilistic