Fractal pattern formation at elastic-plastic transition in heterogeneous materials

Fractal patterns are observed in computational mechanics of elastic-plastic transitions in two models of linear elastic/perfectly-plastic random heterogeneous materials: (1) a composite made of locally isotropic grains with weak random fluctuations in elastic moduli and/or yield limits; and (2) a polycrystal made of randomly oriented anisotropic grains. In each case, the spatial assignment of material randomness is a non-fractal, strict-white-noise field on a 256 x 256 square lattice of homogeneous, square-shaped grains; the flow rule in each grain follows associated plasticity. These lattices are subjected to simple shear loading increasing through either one of three macroscopically uniform boundary conditions (kinematic, mixed-orthogonal or traction), admitted by the Hill-Mandel condition. Upon following the evolution of a set of grains that become plastic, we find that it has a fractal dimension increasing from 0 towards 2 as the material transitions from elastic to perfectly-plastic. While the grains possess sharp elastic-plastic stress-strain curves, the overall stress-strain responses are smooth and asymptote toward perfectly-plastic flows; these responses and the fractal dimension-strain curves are almost identical for three different loadings. The randomness in elastic moduli alone is sufficient to generate fractal patterns at the transition, but has a weaker effect than the randomness in yield limits. In the model with isotropic grains, as the random fluctuations vanish (i.e. the composite becomes a homogeneous body), a sharp elastic-plastic transition is recovered.Comment: paper is in pres

Analysis of the Mechanism of Destruction of Aircraft Components

A shock absorber cylinder of aircraft landing gear leg was used as object of investigation. In process of testing the fatigue crack was grew during action of periodic loading which imitates full cycle including take-off landing and running at the ground. This testing was finished by destruction of the piston rod of shock absorber. Different acoustic emission (AE) parameters have been measured during object loading. It was noted great irregular changes of AE parameters in the different stages of loading. Correlation of AE signal and crack growth development was set by fractal analysis, which carried out by electron-scan microscope and X-ray spectrum analyzer. The relief changes and spectral characteristics of material are researched. It was that fatigue destruction was begun from international surface and an intra-grain crack has been initiated destruction of the material. It is shown that cumulative AE may be used for determination of initiation of fatigue crack and principal stages of their development