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Polymer Engineering DISCUSSION
A polypropylene cantilever bracket, 60 mm long with a 25 × 6 mm rectangular section, carries a steady 10 N load at its tip. Using the datasheet modulus of 1500 MPa I calculated a deflection of about 1 mm, and that is what I measured on the first day. After a few weeks the tip has dropped by roughly 3 mm and it is still moving slowly.
The stress is far below the yield strength, so why does it keep deforming, and how should the long-term deflection be calculated?
Polymers are viscoelastic: part of their response to load is immediate and elastic, and part is slow, time-dependent flow as chain segments gradually rearrange. Under a constant stress the strain therefore keeps increasing, quickly at first and then more slowly on a logarithmic time scale. This is creep, and it happens at any stress level, not only near yield.
Polypropylene is prone to it at room temperature because its glass transition is below 0 °C, so the amorphous regions between the crystals are already mobile. The datasheet modulus comes from a test lasting about a minute, and it describes only that first day of your bracket.
The standard design method is to replace Young's modulus with a creep modulus (also called apparent modulus): the stress divided by the total strain after a given time at a given temperature and stress level. It is read from the supplier's creep curves or isochronous stress-strain curves.
Your own measurement gives one point. Root stress is σ = M × c / I = (10 × 60) × 3 / 450 = 4 MPa, and the elastic formula δ = F × L³ / (3 × E × I) gave 1.07 mm with 1500 MPa. A deflection of 3 mm after a few weeks means the effective modulus has fallen to about 1500 × 1.07 / 3 = 530 MPa, roughly a third of the short-term value, which is a normal result for unfilled PP.
Decide the design life first, then use the creep modulus for that time and the highest sustained temperature. Creep in PP accelerates strongly with temperature, so a bracket that is acceptable at 23 °C may be far outside its limit at 50 °C inside an enclosure. If the supplier's data stop at 1,000 or 10,000 hours, extrapolating more than about one decade of time beyond the data is risky.
Check the stress as well as the deflection. Under sustained load, plastics can fail by creep rupture at stresses well below the short-term strength, so keep the long-term stress to a modest fraction of yield, using the supplier's long-term strength curves where they exist.
To reduce the sag, geometry is the cheapest lever because deflection goes with 1 / h³. Increasing the depth from 6 mm to 8 mm cuts deflection to (6 / 8)³ = 42 percent, and it lowers the stress, which also slows the creep. Better still, keep the wall thin and add a rib or turn the section into an L or U shape, which raises the second moment of area without creating thick sections that sink and cool slowly.
On material, a glass-fibre reinforced grade creeps much less than unfilled PP, and amorphous plastics used well below their glass transition, such as polycarbonate, are more stable under constant load, though they bring their own sensitivity to chemicals while stressed.
The same behaviour appears as stress relaxation when the deformation is fixed instead of the load. A plastic flange clamped by a screw, a press-fit or a permanently deflected snap hook slowly loses its force. For bolted joints through plastic, use metal compression limiters or shouldered inserts so the screw preload is carried by metal, and do not rely on a plastic thread to hold a gasket compressed for years.
Finally, most creep strain recovers slowly when the load is removed, but not all of it, so a part that has sagged for months will not return to its original shape by being unloaded.
