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I have an HDPE pin, 2 mm high, 2 mm diameter, that I impress into a flat plaque of hot HDPE. It is not hot enough to melt the pin, but still hot enough that the material will shrink 4% in 24 hours.

How would I calculate the force required to remove the pin from this plaque? The coefficient of friction being used is 0.24, and an expected value for the force might be 3600 N.

It is possible that while the pin is pulled from the plaque, due to elongation the diameter toward the top of the pin becomes smaller.

My end goal is to figure out a formula that I can use to approximate the expected pull force of this pin given varying heights, diameters, and if the pin is hollow or solid on the inside. We cannot vary the shrinkage value.

Air
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William B.
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    You might need to approach this empirically; choose a few representative solid and hollow pin designs, perform tests, fit curves. Does the diameter of your pin change measurably after the plaque has shrunk around it? – Air Jun 02 '15 at 17:50
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    When saying "shrink 4%", are you talking about linear or volumetric shrinking? Because 4% linear shrinking, combined with a thermal expansion coefficient of around 120E-6 °C^-1, would result in a temperature difference of around 333°C which (if heated from room temperature) is way beyond the melting point of HDPE. Do you know the expected temperature difference? – Andrew Dec 09 '17 at 13:28

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