The crack in a double cantilever beam is the most fundamental one-dimensional fracture problem. It has caused considerable confusions due to its in-depth subtleness and complex entanglement with different theories and numerical simulations. The present paper presents completely analytical theories based on Euler and Timoshenko beam theories using a brand new approach which reveals the hidden mechanics of the problem. Orthogonal pairs of pure modes are found and used to partition mixed modes. The developed theories are extensively validated against numerical simulations using finite element methods. Moreover, the fracture mode partition space is thoroughly investigated and crack tip running contact is found which results in a region of pure mode II. The theories are finally applied to general one-dimensional fracture in beams and axisymmetric plates.

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Developing a surface with low Secondary Electron Yield (SEY) is one of the main ways of mitigating electron cloud and beam-induced electron multipacting in high-energy charged particle accelerators. In our previous publications, a low SEY< 0.9 for as-received metal surfaces modified by a nanosecond pulsed laser was reported. In this paper, the SEY of laser-treated blackened copper has been investigated as a function of different laser irradiation parameters. We explore and study the influence of micro-and nano-structures induced by laser surface treatment in air of copper samples as a function of various laser irradiation parameters such as peak power, laser wavelength ( = 355 nm and 1064 nm), number of pulses per point (scan speed and repetition rate) and fluence, on the SEY. The surface chemical composition was determined by x-ray photoelectron spectroscopy (XPS) which revealed that heating resulted in diffusion of oxygen into the bulk and induced the transformation of CuO to sub-stoichiometric oxide. The surface topography was examined with high resolution scanning electron microscopy (HRSEM) which showed that the laser-treated surfaces are dominated by microstructure grooves and nanostructure features.