Living Hinge Design

 

      

 

 

 

 A living hinge is a thin flexible web of material that joins two rigid bodies together.  A properly designed hinge molded out of the correct material will never fail.  Long-life hinges are made from polypropylene or polyethylene.  If the hinge is not expected to last forever, engineering resins like nylon and acetal can be used. 

 

Physical Properties of Plastic as Applied to Living Hinge Design

          Before designing a living hinge, it is important to understand how the physical properties relate to the hinge design calculations.  There are three types of hinges: a fully elastic hinge, capable of flexing several thousand cycles, a fully plastic hinge, capable of flexing only a few cycles, and a combination of plastic elastic, capable of flexing hundreds of times. 

 

 

 

 

 

         

 

 

 

 

 

 

 

 

 

 

 

 

 

 

When a living hinge is flexed, the hinge's plastic fibers are stretched a certain amount, depending on its design.  The amount of stretch is the crucial factor determining hinge life.  Figure 1 shows a typical stress / strain curve for metals and some plastics (the shape of the curve will vary significantly depending on the type of plastic, and the testing speed). 

 

Yield Stress: The point on the stress / strain curve where an increase in strain does not require an increase in stress.  Not all plastics have a yield stress.

 

Elastic Limit: The maximum strain point at which the plastic will fully recover to its original shape.  Past this point, the plastic will permanently deform.  The yield stress and elastic limit do not necessarily occur at the same point.  For living hinge calculations, however, it will be assumed that they occur at the same point.  Also, when looking up material properties, yield stress is almost always reported; elastic limit is not.

 

Initial Modulus:  The initial slope of the stress / strain curve.  This is commonly called Young's Modulus, although it is usually impossible to find a Young's Modulus for a plastic because the stress / strain relationship is not generally linear.  Secant Modulus is a better measurement.

 

Secant Modulus:  The slope of the line joining the 0,0 point and the curve at some specified point.  Figure 1 shows the secant modulus at the yield point.  This value is relevant to the living hinge calculations.

 

Ultimate (Breaking) Strength:  The point on the stress / strain curve where the plastic fails. 

 

          To design a fully elastic hinge, the hinge's maximum strain must be in the elastic region of the curve; the plastic will fully recover its shape after a flex, and should last for many flexes.  A plastic hinge design will experience strain in the plastic region, will see permanent deformation, and will last only a few flexes.

 

Designing Fully Elastic Living Hinges for Polypropylene and Polyethylene 

          Hinges designed for polypropylene and polyethylene should follow dimensional guidelines to create a fully elastic hinge that will last forever.  Figure 2 shows some general dimensions for a properly designed living hinge.  Figure 3 shows dimensions for a right angle hinge.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

          The two major features of a living hinge are the recess on the top and the generous radius on the bottom.  Figures 4 and 5 show the purpose of the recess.  Many hinges are designed without a recess; as a result, when the hinge is bent 180°, a notch is formed.  This hinge design creates greater stress in the web, and the notch acts as a stress concentrator.  Hinges designed this way will not last long.  Figure 5 shows that with a recess, the notch is eliminated, and the web is able to fold over easier.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

          The large radius on the bottom of hinge helps orient the polymer molecules as they pass through the hinge.  Molecular orientation gives the hinge its strength and long life.  Commonly, immediately after a hinge part is molded, the operator or a machine will flex the hinge a few quick times to orient the molecules while the part is still warm. 

 

Designing Living Hinges for Other Resins 

 

          The hinge dimensions for polyethylene and polypropylene are based on the materials' properties, including modulus, yield stress, yield strain, ultimate stress, and ultimate strain. Because other resins' properties vary widely, living hinge dimensions must be calculated for each particular resin.  Figure 6 shows the dimensions that will be used in the calculations.  Basically, the calculations find the maximum strain in the hinge and compare it to the material properties.  If the strain is below the elastic limit, the hinge will survive.  If the strain is in the plastic region, the hinge will last a few cycles.  If the strain is the past the breaking point, the hinge will fail.

 

Hinge Design Calculations:

          Several simplifying assumptions are made, and tests have shown the assumptions are sound.  1) The hinge bends in a circle and the neutral axis coincides with the longitudinal hinge axis.  2) The outer fiber is under maximum tension; the inner fiber is under maximum compression.  3) When the tension stress reaches the yield point, the hinge will fail by the design criteria.

          Refer to Figure 6.

          1)      L₁ = pR (the perimeter of semicircle).

          2)      L₀ = p(R + t)

          The strain on the outer fibers can be calculated from the difference between L₁ and L₀.

          3)     

Substitute for L₀ and L₁ in the strain equation and simplify.

          4)     

          5)     

          6)     

          Substitute

          7)     

            Solve for L₁

          8)     

          By definition, modulus equals stress over strain, .  For these calculations, we must use the secant modulus at yield.

          9)     

          Therefore,

          10)   

 

Elastic Hinge:

          In a fully elastic hinge design, s_bending must be less than s_yield and e_bending must be less than e_yield.  Failure occurs when e_{bending  =} e_yield and when s_bending=s_yield.  Either equation 8 or equation 10 can be used, depending on whether yield stress or strain is known.  To use the equations, find the yield strain (e_yield), or the yield stress (s_yield) and secant modulus at yield (E_{secant, yield}).  Substituting these values into the equations will result in the lowest value of L₁ that will yield an elastic hinge.  Either the hinge thickness or its length must be known as well.  Generally, a minimum processing thickness is selected, ranging from 0.008" to 0.015", and then a length is calculated. 

         

         

 

Plastic Hinge:

          A plastic hinge will only last a few cycles.  Cracks will probably start on the first flex.  Calculations for a plastic hinge are the same as those of for an elastic hinge, except s_ultimate and e_ultimate are used. 

         

               

 

Increasing Tear Resistance:

 

 

 

 

 

 

 

 

 

 

 

 

          Because the hinge is very thin, it is susceptible to tearing at its edges when any torque is applied.  There are a few techniques to help alleviate this problem. 

          1)  Increase the hinge thickness for a length of 0.020" to 0.040" at the ends.  For example, if the hinge thickness is 0.010", increase the ends to 0.020", and then blend the two thicknesses together.

          2)  Add radii to the ends of the hinge.

 

Processing Considerations:

          The key to living hinge life is to have the polymer chains oriented perpendicular to the hinge as they cross it.  As stated earlier, parts are generally flexed a few times immediately after molding to draw and further orient the hinge molecules.  Another important factor in determining orientation is gate location.  It is crucial to maintain a flow front as parallel to the living hinge as possible.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

          Figure 9 shows a poorly gated hinged part.  The plastic flows out of the center gate in a radial pattern.  As it approaches the center of the hinge, it hesitates because the hinge is very thin.  After the remainder of the gated side fills, plastic starts to cross over the hinge.  At this point, the plastic that first touched the center of the hinge is cold and possibly frozen. The resulting part will have air traps in the center of the back and along the hinge.  It will also have a weld line near the hinge.

          Figure 10 shows one example of a properly gated part.  A wide flash gate is placed on one end to create a flat flow front when the plastic reaches the hinge.  This results in even flow over the hinge, and provides proper orientation direction.  Locating a gate at the center of one end of the part would be another suitable gate location.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Example #1:

 

 

 

 

 

 

 

 

Material:  Hoechst Celanese Acetal Copolymer, Grade TX90 Unfilled High Impact

Tensile Strength at Yield:  45 MPa

Elongation at Yield:  15%

2t (hinge thickness) = 0.012"

l (hinge recess) = 0.010"

 

This is a 180° hinge.  Find the minimum hinge length for a fully elastic hinge.

NOTE:  This is all the mechanical data provided by the design manual.  You may have to run your own mechanical tests to find the necessary material properties.

 

For a fully plastic hinge, the minimum hinge length is calculated using

L₁ = (tp) / e_yield

L₁ = (0.006"*3.14159) / 0.15

L₁ = 0.126" for a fully elastic hinge

                                                                                                                                     

Example #2:

Material:  Dupont Zytel 101 NC010 Nylon 66, Unfilled

Tensile Strength at Yield:  83 MPa

Elongation at Yield:  5%

Elongation at Break:  60%

2t (hinge thickness) = 0.012"

l (hinge recess) = .010"

 

This hinge only has to bend 90°.  Find the minimum hinge length for a fully elastic design.

 

Since the bend is 90°, p can be substituted with p/2 (this can be found from the previous derivation).

          L₁ = (tp/2) / e_yield

            L₁ = (0.006"*3.14159*0.5) / 0.05

          L₁ = 0.188"

For a 180° bend, L₁ would need to be 0.376".  This is probably not moldable.  Even 0.188" may be difficult to mold.

 

( Figures 4, 5, 6, 7 as well as the figure in Example 1 all come from Paul A. Tres's book "Designing Plastic Parts for Assembly 2nd, Revised Edition." You can purchase his book at http://ets-corp.com/lectures/dppa/dppa.htm . )