Question $3$

Make an optimistic estimate for the same scenario like the problem in the module, m$3\mathrm{.}3$: bone fracture problems

During a soccer game, an opponent kicked your shin and created a $0\mathrm{.}01$ mm defect $($crack$)$ in your tibia as seen in Figure $1.$ You plan to run a marathon $\backslash ((42\mathrm{.}2\backslash$mathrm$\{$~km$\})\backslash )$ the next day. Should you be worried that your tibia will fracture if the maximum stress your tibia will experience is $11$ MPa $?$

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

m$=2\mathrm{.}5\backslash \backslash$

C$=2\mathrm{.}5\backslash$times $10^\{-6\}\backslash$mathrm$\{$~m$\}\backslash$left$(\backslash$mathrm$\{$MN$\}/\backslash$mathrm$\{$m$\}^\{3/2\}\backslash$right$)^\{-2\mathrm{.}5\}$

$\backslash$end$\{$array$\}$

$\backslash ]$

Tips:

$1.$ Calculate the maximum stress intensity factor your tibia will experience.

$2.$ Find the critical stress intensity factor in one of the tables in the module. Choose the value for an optimistic estimate.

$3.$ Determine what the critical crack length would be for fast fracture to occur.

figure $1$: Tibia defect for the fracture problem $([1],$ figure $9\mathrm{.}18)$

What is the difference between the critical crack lengths for the conservative and optimistic estimates?

Answer with an accuracy of $0\mathrm{.}001$ m $.$

Recall that the solution for the conservative estimate was shown in class on Wednesday, October $2,$ and is in the Chapter $6$ zybook lab.

You do not need to show the work for calculating the conservative estimate, but you do need to show the work for the optimistic estimate and then the difference in critical crack lengths.