The k-Factor: Why Missing Fillets Will Destroy Your Plastic Parts Under Load

You've designed a plastic bracket. It holds a static load of 500 N, and based on the cross-sectional area, the nominal stress (σ_Nominal) is only 15 MPa. Your material's yield strength is 45 MPa. It should be perfectly safe, right?

Not if there is a sharp 90° corner.

In plastic part design, sharp corners don't just create poor flow dynamics for molten polymer; they act as severe stress multipliers. The actual maximum stress your part experiences is dictated by the Stress Concentration Factor (k).

The Equation:

σ_Max = k · σ_Nominal

Where σ_Nominal = F / A

💡 The Example

Let's look at a stepped flat bar loaded in tension. The thick section (D) is 10 mm, and the thin section (d) is 5 mm, making the ratio d/D = 0.5.

If you machine a sharp corner, the localized stress approaches infinity. But let's say you add a tiny 0.5 mm transition radius (r), making your r/d ratio 0.1.

Looking at standard k-factor charts for this geometry, an r/d of 0.1 gives a k-factor of 2.0.

The Math:
σ_Max = 2.0 · 15 MPa = 30 MPa

The Result: By having too small of a transition fillet, your local stress just doubled from 15 MPa to 30 MPa. If the part is exposed to cold temperatures (packing the molecules closer together and making the polymer more brittle), that localized 30 MPa stress will initiate a crack and easily tear the part in half.

🛠️ The Solution

1. Increase the Radius: Pushing the r/d ratio to 0.3 (a 1.5 mm radius in this specific example) drops the k-factor from 2.0 down to approximately 1.2, drastically improving the mechanical integrity of the joint.
2. Beware the Shrinkage Trap: While larger radii theoretically reduce the local stress concentration, you cannot blindly increase them. Excessively large radii create thick, non-uniform wall sections that lead to shrinkage stresses and shrinkage voids, which will adversely affect your dimensional tolerances.
3. The Sweet Spot: To balance stress relief with proper injection molding flow, maintain uniform wall thickness through the transition by ensuring the outside radius is exactly equal to the inside radius plus the wall thickness.

Great design isn't just about the bulk material properties; it's about managing the localized geometry where the forces actually concentrate.