Editor's note: Readers often tell us that truly useful design guidelines-those based on real engineering principles-can be worth their weight in gold. To that end, IMM presents an enriching series by Robert Cramer of Dow's Materials Engineering Center. In part one of this three-part series, Cramer conveys valuable insights into eliminating cracks around metal inserts by using sound design engineering principles. For this and other installments, he draws on actual projects conducted with customers during his years of experience as senior development scientist with Dow Plastics. |

Molded-in inserts have been used for many years, but the problem of cracking around the insert remains with us. What causes the cracking, and what can be done about it? Cracking is the result of exceeding the plastic material's strength under a given set of circumstances. If the crack spontaneously occurs under static loading, the tensile strength has been exceeded. Impact loads can cause stresses above the polymer's impact strength. If cracks take some time to appear, the culprit is creep rupture strength. To complicate matters, factors such as the presence of chemical agents can decrease material strength, while features such as sharp corners increase local stress. For a molded-in insert, however, material shrinkage is the primary cause of cracking.

As you may know, inserts are metal parts placed into the mold prior to mold close. During the injection cycle, molten plastic flows around the insert and locks it in place as the melt solidifies. Unfortunately, plastic shrinks as it cools and metal inserts, with their high modulus of elasticity, restrain that shrinkage around the insert. This sets up a residual stress in the plastic. If the stress exceeds material limitations, cracking occurs.

One way to get rid of the problem is to eliminate the insert, of course, but there are times when design requirements make this an unattractive option. For example, inserts provide close-tolerance metal threads capable of withstanding a continuous load and frequent disassembly. They can also be used to permanently attach load-bearing parts such as gears to a shaft. Finally, the metal insert functions as an electrically conductive path through a plastic part.

**Insert Design**

An important factor in preventing cracks around an insert is the design of the insert itself. Various grooves and knurling patterns are normally used to boost the pull-out or torque resistance, but these should not have sharp corners, or they will act as stress risers in the plastic part. Also, the inserts should be well-made, without machining marks or burrs that, again, can become stress risers.

Designers can follow various guidelines for bosses or housings around a molded-in insert. Unfortunately, these vary by source, and may cause confusion. For example:

- As a rule, the outside diameter of a boss should be 2 to 2 1/2 times the hole diameter to ensure adequate strength.
- Boss diameter is equal to twice the wall thickness of the part plus the diameter of the insert.

The first guideline ignores part thickness in favor of the hole or insert diameter, while the second relies only on part thickness. This can set up conflicting requirements-boss wall thickness must be great enough to endure residual stress from shrinkage around the insert and any external loads; it must also be thin enough to prevent sink marks in the wall to which it is attached.

Figure 1. Allowable interference vs. Dh/Ds. |

**Calculating Hoop Stresses**

Is there an engineering principle that can be used to guide the designer? Fortunately, there is-the equations used to calculate hoop stresses generated from an interference fit between two cylinders. For an inner cylinder of a highmodulus material and an outer cylinder of a lowermodulus material,

the equations reduce to:

where:

W = geometry factor

Ds = insert outside diameter, inches

Dh = boss outside diameter, inches

I = allowable diametral interference, inches

Sd = allowable stress, ft-lb/sq inch

Eh = modulus of elasticity for boss material, ft-lb/sq inch

µh = Poisson's ratio of boss material

If the allowable interference as a percentage of the insert diameter is calculated for a range of Dh/Ds and a given allowable stress, a curve like Figure 1, results. The curve indicates two conclusions:

- If the boss diameter is less than twice the insert diameter (Dh/Ds If the boss diameter is more than three times the insert diameter (Dh/Ds > 3), the slope of the curve is small. Increasing Dh in this region will not significantly increase the allowable interference.

These facts provide an engineering basis for design guidelines. First, a boss diameter less than twice the insert diameter permits a tiny interference, setting a practical lower limit for Dh/Ds. Secondly, a boss diameter greater than three times the insert diameter may result in large sink marks under the boss because it doesn't increase allowable interference. This sets a practical upper limit on Dh/Ds.

Figure 2. Handheld microphone with brass insert and ABS housing that cracked during storage or after use. |

**Applying the Principles**

Let's look at a real-world example. A manufacturer of handheld microphones was molding thin-wall ABS housings containing a brass insert (Figure 2). The housing outside diameter was 1.65 inch, while the insert had an outside diameter of 1.5 inch. A large number of housings were cracking either in storage or after a period of use. Was the problem residual stress around the insert, and if so, what could be done to correct the problem?

Assuming a mold shrinkage of .005 inch/inch, the "interference" between insert and housing is:

.005 inch/inch x 1.5 inch

= .0075 inch

The ABS material has a modulus of 321,000 psi. Using equations 1 and 2, the stress due to the shrinkage "interference" is 1553 psi, which is too high for long- term loading of ABS. If the housing wall thickness was doubled, to increase the OD to 1.8 inch, the stress would be reduced only to 1510 psi; even if tripled, the stress would decrease only to 1326 psi. It was readily apparent that simply making the housing thicker would have a minimal effect on stress.

Three other variables could be changed:

- Substitute a material with similar shrinkage but higher long-term stress resistance, such as PC, which can sustain 2000 psi.
- Reduce effective interference by preheating the insert before molding. As the insert cools, it will shrink with the plastic, reducing interference to the difference between mold shrinkage and shrinkage of the insert.
- Use a different inserting process, such as ultrasonic or heat inserting, which melts only a thin layer of plastic for greatly reduced residual stresses.

In this case, the manufacturer chose to change to ultrasonic inserts. While this required a small change to the core side of the tool, outside contours stayed the same. Substituting PC was considered too expensive, and maintaining temperature of a preheated insert would have been problematic.

This was a particularly severe example, with a large-diameter insert in a thin-wall housing. More common is a small-diameter insert in a boss. In those cases, Equations 1 and 2 can be used to establish the minimum outside diameter of the boss to prevent cracking. If the wall thickness of the boss is more than 75 percent of part thickness, then sink marks on the part surface are possible. Designers may then consider changing to a smaller diameter insert or different inserting process. If the minimum required wall thickness of the boss is less than 75 percent of the part thickness, the insert will not crack due to residual stresses and sink marks will not be a problem.

*Reference for equations:*

Engineering Considerations of Stress, Strain, and Strength, Robert C. Juvinall, pp. 128-130. 1967.

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