Transfer distortions of acoustic emission signals - power relations between the signal parameters and normalized temporal shapes of avalanches

Abstract

Abstract Power law correlation between the rising time, $$\:R$$ , and amplitude, $$\:\:A$$ , of the detected acoustic emission, AE, signals is investigated in the framework of a driven damped harmonic oscillator model. It is shown, in contrast to the previous model calculation, that $$\:R\sim{A}^{1-{\varphi}_{AE}}$$ holds, similarly to the well-known enigma for acoustic emission; $$\:E\sim{A}^{3-{\varphi}_{AE}}\:$$ as well as $$\:S\sim{A}^{2-{\varphi}_{AE}}$$ , where E and A are the energy and area, and 3 and 2 are the expected exponents from the mean field theory, MFT. The same value $$\:{\varphi}_{AE}=1$$ was obtained for all the above exponents and transfer distortions cause mechanism independent changes. For the experimental value $$\:{\varphi}_{exp}={\varphi}_{AE}+{\varphi}_{o}$$ is fulfilled, where $$\:{\varphi}_{o}$$ is the exponent in the power relation between the amplitude and the rising time of the source function ( $$\:{\varphi}_{o}=-0.32$$ beyond the MFT and $$\:{\varphi}_{o}=0\:$$ in MFT). The calculated value of $$\:{\varphi}_{AE}=1$$ is in good agreement with experimental data obtained for different structural changes: $$\:{\varphi}_{exp}\:0.8\pm\:0.2$$ . Universal functions, well scaled together, can be obtained for the temporal avalanche shapes at fixed area normalizing the voltage by $$\:A$$ and the time by $$\:R\sim{A}^{1-{\varphi}_{exp}}$$ . The first part (around the peak) of it is not sensitive to transfer distortions, while the tail region can be heavily distorted.