Reentrant corner

Figure 6.13 Effects of twinning reentrant corner (a) and particle interpenetrations (b) ( Elsevier 2003).

Figure 7 shows this effect for three particles close to the reentrant corner in the contraction geometry for P -C quadrilaterals. The closer the initial position of the particle to the separation line, the more difficult it is to turn around the corner. Low-order algorithms lead to particle trajectories that intersect impenetrable boundaries. 

Any material that transmits mechanical load from one place to another is susceptible to fracture. This susceptibility is enhanced if the geometry of the object includes reentrant corners, internal defects or other geometrical variations which serve as sites of stress concentration. At these sites, the local stress can be much larger than the nominal stress, which is loosely defined as the average stress transmitted at a cross-sectional area. As a consequence of stress concentration, the local stress can exceed the strength of the material and fracture ensues, even though the nominal stress is well below the fracture strength. 

Fig. 6.39. Images of dislocation nucleation in a bubble raft model of a single crystal subjected to surface indentation. In the case of the smallest surface roughness (a), dislocation nucleation occurs at the peaks of the asperities where they contact the indenter. At the intermediate scale (b), dislocation nucleation occurs at the reentrant corners at the bases of the asparities. Finally, for the largest scale asperity (c), the stress level near the stress concentrations has been reduced geometrically, and dislocations nucleated homogeneously at an interior point where the shear stress is the largest. Each bubble in this raft is 1 mm in diameter and it represents an atom which is approximately 0.3 nm in diameter. Reproduced with permission from Gouldstone et al. (2001).

Figure 3.20 Transmission electron micrograph of a polyoxymethylene crystal grown from 0.02% solntion in ortho-dichlo-robenzene at 114°C. Faster growth has farther sharpened the leading corners also seen are serrations that are the beginnings of secondary growth arms.The reentrant corners midway between the leading corners have also sharpened, and spiral growths are located near these featnres. Dark pleats indicate that the crystal had curvatnre before collapse. From Khoirry and Barnes [10] contribntion of the National Institute of Standards and Technology.

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