Relationship between Linear and Volumetric Shrinkages

Shrinkage is inherent in the injection molding process. Shrinkage occurs because the density of polymer varies from the processing temperature to the ambient temperature
There are linear and volumetric shrinkages. Both methods are difficult to measure accurately.

Volumetric shrinkage

To understand shrinkage it is first necessary to appreciate just how large the volumetric shrinkage of plastics is.

All plastic materials have high volumetric shrinkages as they cool from the melt to the solid. Without pressure, this is typically about 25%. Plastics parts cannot be made without, in some way, offsetting this large volumetric shrinkage. In injection molding, the application of high pressure can reduce this volumetric shrinkage, but by no means eliminate it.

Relation between Liner and Volumetric Shrinkage

Linear shrinkage is driven by volumetric shrinkage, but there is not a one to one relationship. If the plastic were free to shrink in all directions the linear shrinkage Si would be approximately one third of the volumetric shrinkage Su. In fact the exact relationship is:
Si = 1 – (1 – Su)s

Volumetric shrinkage for a given pressure, temperature and level of crystallinity will always be the same. However, the way volumetric shrinkage is divided into the three linear shrinkage components, (in the thickness direction, parallel and perpendicular to flow), will vary.

The relationship between volumetric and linear shrinkages depends on stress relaxation and orientation.

Stress Relaxation
In practice, the two linear shrinkage components in the plane of the molding will have values much less than one third the volumetric shrinkage value. This is because the material is constrained in this own plane while within the cavity. Look at graph below, sringkage of plastic will smaller when pressure injection going up.