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How do I compute the force required to pierce HDPE?

I have a $2\text{ mm}$ sheet of HDPE at $280-320^{\circ}\text{ F}$. I want to pierce the skin of this sheet with a $2\text{ mm}$-high pin with a surface area of $3.33\text{ mm}^2$. The pin is also made of HDPE and has cooled completely. With the Young's modulus of HDPE being $0.8\text{ GPa}$, how much force do I need to apply to have the cooled HDPE pin reach the molten layer of the HDPE sheet at $280-320\text{ F}$?

William B.
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