Mode I segmented crack model: Macro/symmetry, micro/ anti-symmetry and dislocation/skew-symmetry

Multiscale consideration is given to the stress and displacement field symmetry at the macro-, micro- and dislocation-scale level. Under Mode I loading, symmetry with reference to the macro-crack is preserved. However, anti-symmetry is allowed at the micro-scale to account for the irregular micro-crack path that need not be normal to the tensile applied stress at the macro-scale. Micro-normal and micro-shear tractions can prevail in the transitional region where micro- and dislocation-effects merge. For illustration, only edge dislocation emission from the micro-crack is considered. Estimates are made for the number of dislocation generated by changing the applied stress, material constant and length segments of the crack and dislocation. Optimum conditions are found for the maximum number of dislocations generated with reference to the length segment on which dislocations appear. These results are exhibited graphically. Discontinuities of the volume energy densities at the junctions of scaling crossing are caused by segmentation of the scale ranges in the model. This was done to allow the use of equilibrium mechanics in each of three scale ranges, including that of dislocation. Such an idealization is not completely unphysical since the occurrence of micro-cracking ahead of a macro-crack need not be a completely smooth process. The cracking of individual grains ahead of crack is a case in point. The spirit of developing multiscale models is to show that extended scale ranges can be made by connecting the results obtained from components scales. Nevertheless, it is essential to include coupling effects among the scales. This was made possible by using the scale multipliers in addition to the compatibility of the local displacement fields. The ways with which the results are affected by parameters at a higher or lower scale are assessed quantitatively. Restraining or material resistance can respond differently depending on the scale considered. This can be shown by the radial decay character of the volume energy density.