Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

ESEM observations of SCC initiation for 4340 high strength steel in distilled water

The stress corrosion cracking (SCC) initiation process for 4340 high strength steel in distilled water at room temperature was studied using a new kind of instrument: an environmental scanning electron microscope (ESEM). It was found that the applied stress accelerated oxide film formation which has an important influence on the subsequent SCC initiation. SCC was observed to initiate in the following circumstances: (1) cracking of a thick oxide film leading to SCC initiation along metal grain boundaries, (2) the initiation of pits initiating SCC in the metal and (3) SCC initiating from the edge of the specimen. All these three SCC initiation circumstances are consistent with the following model which couples SCC initiation with cracking of a surface protective oxide. There is a dynamic interaction between oxide formation, the applied stress, oxide cracking, pitting and the initiation of SCC. An aspect of the dynamic interaction is cracks forming in a protective surface oxide because of the applied stress, exposing to the water bare metal at the oxide crack tip, and oxidation of the bare metal causing crack healing. Oxide crack healing would be competing with the initiation of intergranular SCC if an oxide crack meets the metal surface at a grain boundary. If the intergranular SCC penetration is sufficiently fast along the metal grain boundary, then the crack yaws open preventing healing of the oxide crack. If intergranular SCC penetration is not sufficiently fast, then the oxidation process could produce sufficient oxide to fill both the stress corrosion crack and the oxide crack; in this case there would be initiation of SCC but only limited propagation of SCC. Stress-induced cracks in very thin oxide can induce pits which initiate SCC, and under some conditions such stress induced cracks in a thin oxide can directly initiate SCC.