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Polymer Engineering DISCUSSION
For an isotropic elastic material, bending and tension should give the same Young's modulus, and for steel they do. But the datasheet for a glass-filled nylon I am using lists a tensile modulus and a flexural modulus that differ by more than 10 percent, and for some unfilled plastics the two are not equal either.
Where does the difference come from, how is the flexural value actually calculated from the test, and which of the two should go into a deflection calculation or an FEA model?
The flexural modulus is not measured directly; it is calculated from a three-point bend test using simple beam theory: E_f = L³ × m / (4 × b × h³), where L is the support span, b and h the width and thickness of the bar, and m the slope of the load-deflection line.
With the common 80 × 10 × 4 mm bar on a 64 mm span and a slope of 25 N/mm: E_f = 64³ × 25 / (4 × 10 × 4³) = 6,553,600 / 2,560 = 2560 MPa. The formula assumes a homogeneous, linear material that behaves the same in tension and compression, with no shear deflection. Plastics break each of those assumptions a little, so the number that comes out differs from the tensile result.
The biggest reason in moulded bars is that the material is not uniform through the thickness. Injection moulding produces a skin where the chains, and any fibres, are aligned along the flow direction, and a core where they are more random or lie across it. Bending stresses are highest at the surfaces and zero at the mid-plane, so a bend test mostly measures the stiff, oriented skin. A tensile test loads the whole cross-section equally and gives the average.
In short-glass-fibre grades this effect is strong, and it also means that both datasheet values describe a test bar with favourable orientation. A real part with fibres running in other directions is usually less stiff than either figure.
There are test-related reasons too. Polymers are nonlinear even at small strains, so the modulus depends on the strain range over which the slope is taken, and the tension and bending standards do not define the same range or strain rate. Many polymers are also somewhat stiffer in compression than in tension, which shifts the neutral axis in bending.
Shear deflection adds to the measured deflection and lowers the apparent modulus; the standard span of 16 times the thickness keeps that small for unfilled plastics, but it grows for short spans and for highly anisotropic materials. None of this makes either value wrong. They are different measurements.
For design, match the modulus to the loading. If the part is a wall or rib in bending, as most plastic parts are, the flexural modulus is a reasonable choice for hand calculations. For FEA with solid or shell elements, the solver wants a material modulus, and the tensile value is the normal input because the elements work out the bending behaviour themselves.
Whichever you pick, the larger errors come from elsewhere: temperature, moisture in nylons, time under load and fibre orientation can each change stiffness by far more than the 10 percent gap between the two datasheet numbers. For long-term loads use the creep modulus for the expected time and temperature rather than either short-term value.
