PSI - Issue 13

Ekaterina Damaskinskaya et al. / Procedia Structural Integrity 13 (2018) 298–303 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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(2006), Kuksenko et al. (1996) have found that the accumulation of defects resulting from deformation of such heterogeneous materials as rocks, ceramics and various composite materials is characterized by the presence of several stages. At the initial stage of loading defects are formed randomly throughout the bulk of the material being deformed. Then defects are concentrated in a certain spatial region which can become a fracture nucleation site. To predict the development of the fracture process and to assess the degree of criticality of the state of deformed materials, it is necessary to understand the physical mechanisms responsible for a qualitative transition from the fracture stage at which defects are randomly distributed to the critical (or dangerous) stage at which a fault can develop and to find a criterion for this transition. However, the accumulation of defects in a certain region typically occurs on the background of disperse formation of defects in the entire bulk. For this reason, the main difficulty encountered in the search for an indicator of the state of a material is the absence of a pronounced transition from one stage of the fracture process to another. In spite of considerable research effort aimed at the search for criteria of transition from the stage of accumulation of random defects to the stage of formation of the fracture nucleation site [Hamie et al. (2006), Carpinteri et al. (2011), Ponomarev et al. (1977), Botvina (2011), Naimark (2003)], the physical mechanisms underlying this transition and the factors affecting it still remain unclear. For example, Kuksenko et al. (1996), Naimark (2003) and Panteleev et al. (2012) have theoretically shown that the transition from one stage to another occurs when the density of defects (cracks) in the deformed material reaches a critical value above which the defects begin to interact with each other by their local fields of elastic stresses. However, it is impossible to correctly determine the critical density of defects above which a transition to a "dangerous" stage occurs in the experiment (laboratory or full-scale). Another approach to finding a qualitative transition of the defect accumulation process from the first to the second stage is based on the concept of self-organized criticality suggested by Bak (1996) in which the set of defects is described in "simple-complex system" terms [Nicolis and Prigogine (1977)]. Nicolis and Prigogine (1977), and Malinetskii and Potapov (2002) have shown that "simple systems" are characterized by an exponential distribution of their parameters. In the general case, any "simple system" becomes "complicated" as a result of evolution. This means that such a system cannot be described by a sum of noninteracting "simple systems" and its properties differ from those of "simple systems". In the process of evolution the "complex system" passes into the state of self organized criticality [Malinetskii and Potapov (2002)] characterized by a power-law distribution of parameters [Bak (1996)]. Our analysis of the laboratory experiments on deformation of granite samples using the "simple-complex system" approach [Damaskinskaya et al. (2017)] revealed the stages at which the defect accumulation process developed in fundamentally different ways. As a system parameter, we used AE signal energies. It was found that at early stages of deformation, when the defects distributed randomly throughout the bulk were accumulated, the energy distribution of AE signals was approximated by an exponential function. The totality of such noninteracting defects could be regarded as a "simple system". As deformation proceeded, the accumulation of defects in a certain region to which a power-law energy distribution of the AE signals corresponded occurred. At this stage the totality of defects could be considered as a "complex system" in which the interaction between defects took place. This paper is concerned with our further studies of the laws governing fracture and the change in the functional form of the AE signal energy distribution. An important feature of our investigations is that defect accumulation is studied at different stages of deformation by means of two non-destructive methods, i.e., acoustic emission and X ray computer microtomography. The defect structure of rock samples before and after mechanical tests was investigated by X-ray microtomography (a ScyScan 1172 scanner, Bruker, Belgium). A specific feature of the X-ray computer microtomography method is that the spatial resolution correlates with the sample thickness [Tóth and Hudák (2013)]. Since the goal of the experiments was to investigate the laws of formation and accumulation of defects in the rock bulk, the sizes of the sample had to be large enough to distinguish between the sample regions from which AE signals were recorded. The samples which were optimal for mechanical tests and tomography were found to be 2. Experimental