PSI - Issue 39

Dmitry O. Reznikov / Procedia Structural Integrity 39 (2022) 236–246 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The governing parameters of fatigue crack growth processes are random in nature. The uncertainties in mechanical properties of structural materials, size of the defects, geometrical parameters of components should not be neglected and incorporated into crack growth models. That means that fatigue crack models should be probabilistic. Besides structural components in real operational conditions are subjected to variable amplitude loading. The traditional models based on the linear damage accumulation rule neglect effects of crack closure, residual stresses and often present over-conservative assessments of fatigue durability and probability of failures. The key parameters that determine the kinetics of fatigue damage accumulation and failure of structural components of technical systems are probabilistic. Therefore, the problem of assessing and ensuring the cyclic strength should be solved in a probabilistic formulation, taking into account the natural variability of the mechanical properties of structural materials, the scatter of the initial sizes of defects, the variability of loading modes, etc. It should be borne in mind that the parameters of loading cycles under real service conditions of structural components are not constant values: there are changes in the average stress levels, single and sequential overloads, and underloads, which cause acceleration or retardation of fatigue crack propagation. The history of in-service loads on structural components can be considered as a set of tensile and compressive loads, the effect of which on the crack growth rate is repeatedly superimposed on each other. This superposition of the effects of overloads and underloads is called the effect of the load history and sequence of loads or the interaction of amplitudes (Schijve, 2009).

Nomenclature a

crack depth

initial crack depth

a 0 a C a i

critical value of the crack depth

crack depth at the i -th loading cycle a ( j ) ( N ) sampled j-th crack growth curve a maes a tr ( N ) true crack growth curve C parameter of Paris equation E { x } mean of the random variable x a OL

crack depth measured during the in-service inspection crack depth at the instant of the overload application

E' { x } mean of prior probabilistic distribution of x E'' { x } mean of prior probabilistic distribution of x i number of loafing cycle K I mode I stress intensity factor K I c fracture toughness k OL overload factor L likelihood function M n number of crack growth curves in the sample m exponent of the Paris equation N number of constant amplitude loading cycle s F P  prior probability of failure F P  posterior probability of failure p internal pressure R stress ratio under constant amplitude loading R p,OL size of the plastic zone induce by the overload r p minimum value of hoop stress in the CA loading cycle maximum value of hoop stress in the CA loading cycle yield strength S { x } standard deviation of the random variable x S' { x } standard deviation of prior probabilistic distribution of x S y r 0 radius of the tube S min S max

size of the plastic zone induce by constant amplitude loading cycle