PSI - Issue 30

Dmitry O. Reznikov et al. / Procedia Structural Integrity 30 (2020) 128–135 Dmitry O. Reznikov/ Structural Integrity Procedia 00 (2020) 000–000

131

4

The matrix equation (2) gives an assessment of economic risk induced by the engineering facility. It includes the vector of loading regimes { L }, describing probabilities of various normal and abnormal regimes of thermo mechanical loading, influence of aggressive environment etc.); a vulnerability matrix [ V ] whose components provide conditional probabilities that the system will reach various damaged end states if different loading regimes occur; and the vector of consequences that determine expected losses that correspond to different damaged end states of the system. The vulnerability assessment is a key element of comprehensive risk estimation procedures. It summarizes the results of the system scenario assessment and reveals the system’s weaknesses and inability to

withstand various impacts and loading regimes. 3. Multilevel vulnerability assessment model

Structurally complex systems require a more detailed scenario assessment be carried out. Such assessment should take into account that the processes of damage accumulation and fracture develop at various scale levels ranging from nano to macro scales. In other words, if a structurally complex technical system is being considered the scenario tree describing the multivariant processes of damage accumulation and fracture should be multilevel and include subtrees describing damage accumulation and fracture at the levels of material, structural components and the system as a whole. At the current level of the development of basic science and methods for technical diagnostics, it is practically feasible to analyze fracture processes at four scale levels: (1) the mesoscale level related to material degradation, and two macro scale levels: (2) the scale level of structural components describing development of macro-defects and fracture of the system components, (3) the structural scale level describing the scenarios of subsequent component failures leading to total collapse of the system, and (4) the upper level of the system environment describing failure processes beyond the system boundaries. Bearing this in mind one may consider the system vulnerability as an integral property of the system that could be split up to differential properties that characterize: - Material vulnerability as the inability of the structural material to sustain imperfections and high stresses; - Component vulnerability as the weakness of structural components to sustain local damage and macro defects; - Structural vulnerability as the inability of a system to withstand loads throughout its service life in the presence of a local defects and fracture of its constitutive components Due to the high level of uncertainty related to variability of the system parameters (mechanical characteristics of structural materials, geometrical dimensions) and loading regimes, the assessment of CTS vulnerability should be carried out in a probabilistic formulation. Taking into account the multiscale character of damage accumulation and fracture processes, the probabilistic complex event “system destruction” can be considered as a sequence of coupled random events [1,5]: (1) < L > the system is subjected to loading regime L; (2) < MD | L > the occurrence of a specific material damage given the system was subjected to L; (3) < LD | L,MD > the achievement by a structural component of the local limit state LD , provided events L and MD occur; (4) < F| L , MD, LD > a system collapse if the events L, MD and LD happen. Then the probability of the system destruction can be evaluated as:

(3)

( ) , ) P F P L P MD | L LD | L MD F L MD LD     ( ) ( ) P( , ) P( | ,

where P ( MD|L ) is the material vulnerability; P ( LD|L,MD ) is the component vulnerability, P ( F | L,MD,LD ) is the system vulnerability. Then risk generated by the system can be estimated as:

( ) F F R P F U P L LD| L MD P MD| L U       . ( ) P( , ) ( )

(4)

For structurally complex engineering systems that are subjected to multiple loading regimes and multiple failure scenarios as shown by Makhutov and Reznikov (2008, 2019), Makhutov (2009), vulnerability assessment implies assessment of a multilevel scenario tree (see Fig. 2). As a result of action of various thermomechanical loads, some of the material mesovolumes located in stress concentration zones can be transferred from the intact to some damaged state through scenario s i (m) (see Fig. 2a). From this perspective material damage may be considered as an initiating event of component failure scenario s j (c) ending in the structural component failure. Due to the material