# Avoiding and solving injection molding problems using shear rate calculations—Part 2

April 1, 2007

Part 1 of this article covered shear rate and some of its effects in actual case studies. Now that you know what it is, hereâ€™s how to make it work for you.

In the first part of this series last month (immnet.com/articles?article=3128) we talked about shear rates and introduced some typical problems that were solved by focusing on shear rates. This article shows how to go about calculating shear rates (g). These calculations were used in the case studies presented at the end of the first article.

How do you calculate shear rate?

Two formulas are generally used, one more commonly than the other, but there are many formulas available. They get more difficult as you try to include the resinâ€™s behavior over a greater range. Do you want to model the entire range of viscosity vs. shear rate, or are you interested only in the behavior representing actual molding conditions? The first formula promoted here captures a resinâ€™s behavior observed in the higher-shear regions generally found in injection molding.

This formula is called the true shear rate formula, the non-Newtonian shear rate formula, or the shear-thinning formula. It says that, as shear increases, the material flows easier. The shear rate for a round cross section is below (refer to â€œSymbols and Definitions,â€ to identify characters):

The character n is an index that describes the relationship between a materialâ€™s viscosity and its shear rate. It is different for different materials. We see this in practice because some materials donâ€™t flow much easier (lower viscosity) when you try to fill faster (higher shear). Polycarbonate is an example. If you want PC to flow better, you turn up the temperature. PC has an n of about .70, which means the curve is flatter (lower change in viscosity for a given change in shear rate). On the other hand, PP responds well to faster filling by flowing better. It is more shear sensitive. It has an n of about .32, much less than PC. (â€œTypical Values for nâ€ details how to find n of various materials.)

The viscosity vs. shear rate graph in Figure 1 shows how a plastic might behave over a large range of shear rates. Almost all molding happens in the region between the two vertical lines, especially the gates. The shear-thinning formula presented here is valid for this region. Other, more involved formulas may better represent a broader region.

For comparison, a formula that often appears in literature, sometimes referred to as the apparent shear rate, or Newtonian shear rate formula, is the formula for water (we are not using it):

It does not account for the material flowing easier (viscosity dropping) as the shear rate increases. If you plug in n = 1 for water in the shear thinning formula, you see it becomes the water formula. Shear rates for rectangular cross-sections (edge gates) are as follows:

where H is height and W is the width.

Shear rates for annular flow (hot drops with the spreader tip in the orifice or around valve gate pins) are far more involved to calculate. In select instances, the above formula will work for rectangular cross sections. H becomes the gate height measuring the distance between perimeters of the concentric circles. W becomes the average perimeter. In reality, this only works if the slit length is much longer than the slit height (more than 20:1), which it generally isnâ€™t. Because the spreader tips or valve gate pins are generally back far enough from the gate orifice, the formula for round cross-sections can be used.

How do different materials respond to shear?

Some materials are more shear sensitive than others. The molding community uses â€œshear sensitiveâ€ in a couple of contexts. Here it means a given change in shear rate for a shear-sensitive resin will cause a greater change in viscosity than for a less shear-sensitive resin. In Figure 2, this means the drop in viscosity for a resin sensitive to shear will be greater than that for a nonsensitive resin. For a given change in shear rate, the lower n will have a greater change in viscosity than a higher n. Lower n materials are more shear sensitive. â€œShear sensitiveâ€ also has been used to describe resins prone to overshearing, such as PVC and resins with flame retardants added.

The actual shape of the flow front can be affected by the power law. Figure 3 shows the effect of the power law index, n, on the flow front.

Note the flow front also is affected by the shear condition. Higher shear rates in plastics have more of a plug flow front. This is one reason that increasing fill rates when doing color changes helps clear things out. Reduce the fill rate with the followup material to flush out the previous color; then resume normal processing.

In Figure 4, we see the different flow front shapes of different fill speeds. You can see where the fast fill speed causes high shear. Also, the flow front starts looking more like a plug, or very similar to a low n material. But donâ€™t confuse a low power law index with a high-shear condition.

These formulas provide a relatively straightforward way to calculate shear rates, and can help avoid degradation and poor cosmetics. If you currently use flow analyses just to find minimum gate sizes based on shear rate, you can save money and time. In addition, these formulas, along with maximum allowable shear rates available from your resin supplier, offer you a way to figure out the minimum size of any flow channel.

Author Mike Miller ([email protected]) manages two business units for tool and diemaker Carlson Tool & Mfg. (Cedarburg, WI; www.carlsontool.com). He wrote this two-part article as part of a continuing effort to correlate what textbooks say to the issues he faces in practice.

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