The bottom figure shows a polymer matrix composite that is loaded in the fiber direction. Ef$=200$GPa,Em$=5$GPa, the volume fraction $($V$\_($f$))$ is $0\mathrm{.}6.$ The interfacial shear strength is tau$=30$ MPa $,$ and the radius of the fiber is r$=5$mum. When the composite is loaded to $600$ MPa $,$ one fiber

breaks as shown in the figure. $($a$)$ Plot quantitatively the stress profile in the broken fiber as a function of x$,$ where $\text{'}$ x $\text{'}$ is the distance from the fiber break. $($b$)$ When the composite stress is increased to $650$ MPa $,$ the same fiber breaks at a distance of $75$ mm to the right of the first break.

Plot the stress profile in the fiber between the two breaks.