The adhesion between PE and steel will be very poor for two reasons. One is that the PE and steel have different thermal expansion coefficients so they shrink by different amounts during cooling. The effect is that there will be a stress at the interface that reduces bond strength. Luckily the modulus of a rubber is low so this stress will not be so high. To imagine this effect think of a spring, the force is the elongation x the modulus. Your elongation is due to the difference in thermal expansion coefficient and is relatively high but elastomers have low modulus so the force at the interface is not so high in the end.
The main problem is that PE is very non-polar and therefore will not interact with steel or other high energy surfaces. If your PE based elastomer is an ionomer (e.g. Surlyn or Iotek) then you have a chance because these contain ionic groups that should improve the bonding to metal. If your PE elastomer is not an ionomer then I would suggest you add something to improve the bonding. Things you could add to improve things are polymers compatible with PE but with some polar groups:
1. Ionomer e.g. Surlyn or Iotek
2. Polyethylenevinylacetate (EVA)
3. Polyethylene-co-acrylic acid (e.g. Polybond and others)
These would be added at 10 weight % as a first try.
