Fig. 4.

The pentagonal cross-section cantilever shares a similar feature of fracture with a 2D notched cantilever. (A) A 2D notched cantilever, whose dimensions are $\left\{a,H,L_0,L_1\right\}$, is loaded at its free end by a line force, $p$. The established solution to this problem, ${\mathrm{\Gamma }}_{2D}$, describes the stress intensity factor at the crack, $K_I$, for a given $p$. (B)${\mathrm{\Gamma }}_{2D}$ can also be used to predict the stress intensity factor for a rectangular cross-section cantilever (width $w$ and height $H$) under an external load, $P$. (C) The pentagonal cross-section falls in between two corresponding rectangular cross-sections: One is contained within the pentagon and the other itself contains the pentagon. It is postulated that the solution for the notched cantilever with pentagonal cross-section, ${\mathrm{\Gamma }}_{pent}$, is implicitly connected to its rectangular cross-section counterparts (described by ${\mathrm{\Gamma }}_{2D}$).