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 $280-320\text{ F}$?
UPDATE: I've been told that the pin is supposed completely weld to the layer of HDPE. Based on the melt temp of the HDPE and the starting temp of the pin, I just don't think its possible in the 2 minutes before the material is quenched. I've attempted to figure out the rate of heat transfer, but can't find the thermal contact conductance coefficient, or the thermal contact resistance. Searching online turned up a tool "CoCoE.exe" but was having trouble running the program on my computer.