0 Critical Ruptures

The fracture of materials is a catastrophic phenomenon of considerable technological and scientific importance. Here, we analysed experiments designed for industrial applications in order to test the concept that, in heterogeneous materials such as fiber composites, rocks, concrete under compression and materials with large distributed residual stresses, rupture is a genuine critical point, i.e., the culmination of a self-organization of damage and cracking characterized by power law signatures. Specifically, we analyse the acoustic emissions recorded during the pressurisation of spherical tanks of kevlar or carbon fibers pre-impregnated in a resin matrix wrapped up around a thin metallic liner (steel or titanium) fabricated and instrumented by Aérospatiale-Matra Inc. These experiments are performed as part of a routine industrial procedure which tests the quality of the tanks prior to shipment and varies in nature. We find that the seven acoustic emission recordings of seven pressure tanks which was brought to rupture exhibit clear acceleration in agreement with a power law " divergence " expected from the critical point theory. In addition, we find strong evidence of log-periodic corrections that quantify the intermittent succession of accelerating bursts and quiescent phases of the acoustic emissions on the approach to rupture. An improved model accounting for the cross-over from the non-critical to the critical region close to the rupture point exhibits interesting predictive potential. 1 Plan of the study In this paper, we first present in section 2 a brief review of the " critical rupture " concept with an emphasis on the role of heterogeneity. Section 3 describes the experimental systems and the properties of the acoustic emission time series that we analyse with three theoretical formulas derived from the critical rupture concept. We present a brief justification for these three power laws. Section 4 gives the results obtained on the acoustic emission energy release rate on seven systems. Section 5 analyses the cumulative energy releases of these seven systems. Section 6 describes the relative merits of the three power law formulas for the prediction of the critical pressure of rupture and section 7 concludes. The damage and fracture of materials is of enormous technological interest due to their economic and human cost. They cover a wide range of phenomena like, e.g., cracking of glass, aging of concrete, the failure of fiber networks in the formation of paper and the breaking of a metal bar subject to an external load. Failure of composite systems …