On an analytical estimation of characteristic lengths in pattern formation — application to fatigue

Abstract

A statistical treatment of a random experimental signal in the presence of additive white noise by means of a Taylor expansion around the mean is studied. As a result, an expansion of the original random signal in terms of an arbitrary white noise process where the appropriate “signal information” was included into the corresponding expansion coefficients by means of higher statistical properties of the experimental signal was derived. Such an expansion can give access to statistical properties of the original signal of any order. An implication of the method to material deformation stochastic modeling is also examined. Indeed, using TEM micrographs of the experimentally observed dislocation patterns of PSBs during cyclic plastic deformation, we produce a random spatial pulse according to the location of each phase. This pulse is the input spatial signal of the aforementioned formalism and the final outcome is the estimation of the corresponding characteristic length of the pattern using the analytically thus producing phase signal. This value is compared with previous estimation of the characteristic length derived by considering specific dislocation mechanisms during cyclic deformation in order to examine the validity and robustness of the proposed methodology.

Keywords and phrases:

• Pattern formation
• characteristic length
• random signal
• Taylor expansion
• correlation function
• cyclic deformation
• fatigue
• PSBs