The aim of the research here is to prevent the propagation of the crack in the fabricated elastic medium with useful applications.
Theoretically, the study of the evolution of a crack system is performed on the level of the decrease of the total energy of the system with time (that is finite) and not on the stress level. Well, in this case the general way to proceed is to calculate G, the crack extension force (per unit length of the crack front) or energy release rate, for an arbitrary crack front configuration. The condition = 0 corresponds to the arrest of the crack ( is average G, averaged over all the positions on the crack front). The elastic constants Cij under stationary configuration (d/dCij =0) with =0 are those retained.
This is a difficult task: (1) use the most general crack-front configuration and (2) calculate the corresponding G under general loading. Well, use the laboratory reference frame, with tension or compression in the vertical Ox2-direction (the gravitational force direction), shears and induced normal Poisson stresses in the horizontal Ox1x3-plane in two perpendicular directions Ox1 and Ox3. Are we concerned with cubic crystals ...? We need to use the appropriate crystal structure.
By selecting an elastic-perfectly plastic material model stress singularity can be eliminated at the crack tip. But the strain at the crack tip will still be infinity. Hope this helps.
1) Your answer is on a purely assumption level.
2) Assuming no pre-existing crack, le material would deform plastically only.
3) In presence of a pre-existing crack, expansion of the latter would be observed on the elastic applied stress range first until the blunting of the crack (crack arrest), clearly in a two-dimensional crack scheme.
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