PSI - Issue 10

D. Mastrogiannis et al. / Procedia Structural Integrity 10 (2018) 319–325 D. Mastrogiannis et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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1. Introduction

The deformation process of solid materials is accompanied by numerous effects like the emission of acoustic (AE) and electromagnetic signals or the generation of pressure stimulated currents (PSC). This is well documented in numerous cases of laboratory experiments in the past years and it refers to different cases of materials, ranging from monocrystals to polycrystalline materials, piezoelectric and non-piezoelectric ones (Alexandridis et al. (2012); Hadji contis et al. (2004); Mastrogiannis et al. (2015); Mastrogiannis and Potirakis (2018); Nomikos and Vallianatos (1998); Vallianatos and Nomikos (1998); Vallianatos and Triantis (2013); Vallianatos and Tzanis, (1999, 1998)). The de formation and fracturing process of a material is a procedure with complex dynamics that define the aforementioned effects (Potirakis and Mastrogiannis (2017)). In the present paper, we focus on the study of AE and PSC detected during a recent bending experiment on an accurate copy of an authentic marble epistyle of the Parthenon Temple (Kourkoulis et al. (2017)). The purpose of this work is to investigate the AE and the PSC detected during the specific experiment within the frame of log-periodic power-law models (Anifrani et al. (1995); Sornette and Andersen (1998)). While acoustic and electromagnetic emissions detected during fracture experiments of well-defined and specially crafted specimens have already been successfully described by such models, it is interesting to investigate whether these models could also describe PSC as well as AE signals originating from complex structural setups. One should keep in mind that solid materials that are being deformed develop a complex network of damaged areas into their bulk volume, which eventually leads to the macroscopic rupture. The whole process is accompanied by various phenomena such as AE (Anastasiadis et al. (2004); Carpinteri et al. (2013); Hloupis et al. (2016); Potirakis and Mastrogiannis (2017); Stavrakas et al. (2004); Vallianatos et al. (2004); Zhang and Zhang (2017)) and PSC (Hadji contis et al. (2004); Kourkoulis et al. (2017)). Processes like dislocation movement, formation of dislocation pile ups and crack opening are associated with the generation of AE in most of the cases (Kietov et al. (2018); Strantza et al. (2017)). All these interactions that take place in this network of faults and microcracks exhibit a critical behavior with scale invariance characteristics (Mastrogiannis and Potirakis (2018); Potirakis and Mastrogiannis (2017)). This leads to the assumption that phenomena which accompany the deformation of a solid material could possibly be described by relevant power laws (Mastrogiannis et al. (2018)). Bearing this in mind the cumulative energy released through the acoustic signals can be described by a general log periodic power law given as (Sahimi and Arbabi (1996); Sornette (2002)):       ~ cos log Φ        m f f E t t 1+C ω t t (1) This mathematical expression reduces to a typical power law if C =0. The expression includes the power law exponent m and the period of log oscillations ω , which are both dimensionless. The amplitude of the oscillatory cor rection is denoted as C , the phase of the expression as Φ , while t f denotes the time point of the global rupture.The above model has been applied in cases of simple specimens of monocrystalline or granite samples (Mastrogiannis et al. (2011); Mastrogiannis and Potirakis (2018); Sahimi and Arbabi (1996)), describing both the energy released through electromagnetic and acoustic emissions. It hasn’t been applied though to more complex structural setups or to pressure stimulated currents. It should be mentioned that there is an extrapolated form of this equation (Moura et al. (2006, 2005); Yukalov et al. (2004)) that has been used in relevant experiments, providing reliable results (Mastrogiannis et al. (2018, 2011); Mastrogiannis and Potirakis (2018); Saltas et al. (2014)). Still Eq.(1), that is provided here, has been tested in many different experimental setups by various scientific groups, which means that is more consistent in the reliability of its results. Since this is the first time that such a model is being applied to PSC signals, it seemed a better choice in order to provide more solid results. In a future work we intend to use both expressions in order to detect any differences or similarities as it has been in a relevant work (Mastrogiannis et al. (2018)).

2. Experimental setup

As already mentioned, the mathematical model of Eq.(1) has been applied in various cases of simple standardized specimens and materials under controlled laboratory conditions. The main focus of this work is to examine whether the same model can be successfully applied to more complicated structures. The main idea is to test this on an accurate