Mode II segmented crack model: Macro/skew-symmetry micro/anti-symmetry and dislocation/skew-symmetry
Material non-homogeneity can vary with different degrees of severity depending on the size scale at which the observation is being made. For a polycrystalline material, the state of affairs within a grain can differ widely from those in a cluster of grains. The situation is further complicated by the presence of defects and imperfections which may grow under load while the stress symmetry conditions with reference to the defects in the form of a line or area can also change with size scale. Macro/symmetry for a line defect or crack dominated by applied load may no longer prevail when viewed at the microscopic scale where the material structure can influence the symmetric. In the work to follow, in-plane macro-shear load is considered such that the corresponding macro-stress field would be skew-symmetric with reference to a line defect if the grain size is small in comparison with the continuum element. When the grain structure comes into play, the line defect may no longer be in a state of pure in-plane shear. Micro-normal and micro-shear stresses may both be present on the micro-crack rendering a state of mixed mode micro-crack extension. This effect will be considered in addition to the generation of edge dislocations from the end of a micro-crack. According to the classical theory of dislocations, edge dislocations pertain only to the skew-symmetric stress field. The transitions from mode II macro/ skew-symmetry to mixed mode micro/anti-symmetry and finally to dislocation/skew-symmetry is considered in a line defect model using the continuum mechanics approach while realizing the physical process from macro to atomic is one of non-equilibrium in addition to the effect of material non-homogeneity where the properties of the bulk and those of the local region can differ. Segmentation of the scale range is made to alleviate the use of non-equilibrium behavior, the complexities of which would be beyond the scope of this investigation. Discontinuities of the volume energy densities are thus introduced at the scale crossing junctions. Their severity can be adjusted by the prevailing material and geometric parameters that are also affected by the applied macroscopic load. The presented analytical model is useful for making sensitivity analyses involving the influence of atomic and microscopic effects on the macroscopic behavior. As it is to be expected, the results depend on a combination of load, geometry and material at the different scales.
KeywordsIntensity Factor Energy Release Rate Edge Dislocation Line Defect Applied Shear Stress
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