PSI - Issue 37

Fekete, Tamás et al. / Procedia Structural Integrity 37 (2022) 779–787 Fekete, T .: The Fundaments of Structural Integrity … / Structural Integrity Procedia 00 (2021) 000 – 000

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In the equations above, all physics and all variables depend on time;  means mass density, σ denotes stress, ext f is density of external forces, T means temperature, s is entropy density, i s is the irreversible part of the entropy density, q j denotes heat flux, s j represent entropy flux, n is outer normal to a surface area, t V denotes time dependent volume, t V  represents boundary of t V ; i α ( i = 1 … m ) symbolize inner variables describing short-scale processes in bulk resulting in dissipative reconfigurations, and i g ( i = 1 … m ) the thermodynamic driving forces conjugated to them, while k A ( k = 1 … n ) denote the inner variables representing macroscopic crack propagation, and each k G is the thermodynamic driving force – called generalized energy release rate – conjugated to the k -th crack variable. The bulk dissipation rate caused by the reconfiguration processes is i i  g α , and the dissipation accompanying crack propagation is k k G A  , – where the Einstein summation convention is used – . Given a domain of volume V , with surface area A , containing a crack having a front propagating at velocity V c in the reference frame, the crack front behaviour is described by the generalized ˆ and J J integrals as follows: ( ) ( ) ( ) 0 1 1 ˆ , lim 1 ˆ ( ) t c A A A A t ext i i A i V V V V J K dA J J G A J J K dV dV sT dV j dV A      → − = +  +  = =   = −  + −  + +            V σ v n f v g α (5) The crack-front stability is described by the time-dependent criterion, ( ) ( ) ..., ..., G R   = , which is formally looks like the classical J I = J Ic criterion used in today's SICs but is more deeply grounded. Summarizing the observations made so far, the model appears to be a promising approach to describe material ageing at the phenomenological level with a consistent account of bulk dissipation and paves the way for describing the behaviour of cracks in various dissipative ‘ environments ’ , even for multi-scale, multi-field problems. However, it must be noted here that the development of nonlinear field theories of fracture for multi-field and multi-scale problems is still in its infancy; an exciting and challenging research agenda for those working in the field. The development of industrially feasible models is also a challenging task for the medium-term future. 4. Summary, Conclusions At CER , research is underway to develop sound fundaments for future SICs of LSPSs . Many existing SIC methodologies have been revised. Despite the fact that many complex LSPSs have been built and operated over the decades based on the tried, standard-based engineering approaches, it has emerged that there are inherent problems even at the core of these methodologies. Generalised Conceptual Framework to SI seems to be a promising approach to lay solid fundaments for future SIC methodologies for LSPSs . Therefore, the paper outlined the structure of the Framework, showed how philosophical considerations can be used to pave the way for a sounder scientific approach to SI issues of LSPSs , and finally presented the essentials of an enhanced model, based on modern thermodynamics, more precisely on a variant of TIV . The enhanced model seems a promising approach to describe material ageing at phenomenological level and paves the way for describing behaviour of cracks in various dissipative ‘ environments ’ . References ASME 2021, 2021. Boiler and Pressure Vessel Code Complete Set . ASME New York. Cellucci, C., 2017. Rethinking Knowledge . The Heuristic View . Volume 4 of the series European Studies in Philosophy of Science, Springer International Publishing AG. https://doi.org/10.1007/978-3-319-53237-0 Chen, X.H., Mai, Y.W., 2013. Fracture Mechanics of Electromagnetic Materials . Nonlinear Field Theory and Applications . Imperial College Press, London. Cherepanov, G.P., 1967. The propagation of cracks in a continuous medium, Journal of Applied Mathematical Mechanics 31 3 503 – 512 Fekete, T., 2019. Towards a Generalized Methodology for Structural Integrity Calculations of Large-Scale Pressure Systems. In: ICSI 2019 The 3 rd International Conference on Structural Integrity, Procedia Structural Integrity 17 464 – 471.

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