Photon emission as a probe of chaotic processes accompanying fracture
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I. INTRODUCTION The fracture of many insulating materials is accompanied by the emission of photons, electrons, and other species during and following fracture.1"5 These emissions are collectively known as fracto-emission, and can be especially intense during fracture. In earlier work, we have shown that photon emission (phE) during the fracture of an epoxy sample may display rapid fluctuations well in excess of detector and amplifier noise.4 The amplitude of these fluctuations correlates well with the roughness of the resulting fracture surfaces, suggesting that these fluctuations reflect mechanical processes during crack growth. Since photon emission intensity measurements are readily made at time intervals as short as a few ns, they may yield detailed information on the progress and energetics of crack growth during catastrophic failure. In particular, phE fluctuations may shed light on the dynamics of possibly chaotic processes responsible for the fractal character of many fracture surfaces. Fractal dimension measurements have been made on the fracture surfaces of several metallic and ceramic materials.6"10 Since the underlying structure of many chaotic systems is fractal, this suggests that fracture is also to some degree chaotic, that is, deterministic, yet aperiodic and unpredictable. Recently, some simple models of the fracture process have been proposed which display chaos" or result in fractal surfaces.1213 However, to date little evidence for chaotic processes has appeared except in the fractal nature of the resulting surfaces. Recent developments in the analysis of time series data, such as that formed by a series of phE measurements, raise the possibility that such measurements may yield information about chaotic processes accompanying fracture. 1272
http://journals.cambridge.org
J. Mater. Res., Vol. 4, No. 5, Sep/Oct 1989
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In this work, we describe a preliminary analysis of phE accompanying the fracture of two materials, an epoxy and single crystal MgO. The intense phE accompanying the fracture of both these materials has been previously studied.3"5 The epoxy is readily formed into rather large, strong samples. Although the epoxy fracture is macroscopically brittle, the fracture surfaces show features associated with severe, local plastic deformation in the near surface region. Single crystal MgO undergoes brittle fracture, often with very high crack velocities, and has been the object of many studies of fracture and deformation. In this paper, we first describe autocorrelation and Fourier spectra computations which show that the faster fluctuations in phE are consistent with a nonstochastic, yet quasirandom origin. Then the fractal properties of the data are discussed. The fractal dimension of the phE data from the epoxy is also compared to fractal dimension measurements of the epoxy fracture surface. We then present correlation dimension calculations which show the phE data to be associated with a strange attractor of low dimension. Finally, an estimate of the largest Lyapu
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