= Three-point flexural test
= Three-point bending test
{synonym}
A \b[three-point flexural test] loads a specimen through one central contact while two separated supports carry the reactions. In a small-deflection <simply supported beam> model, an incremental central <force> and the resulting midspan <displacement> determine the <midspan compliance of a simply supported beam>. With a known <second moment of area>, that response yields a flexural modulus.<Beam Displacements by David Roylance>[Introduction; Example1 and equation7]{ref}
The apparatus must distinguish specimen deflection from machine travel. The manufacturer's fixture description uses adjustable lower anvils and a central loading member; a direct midspan plunger can transmit deflection to an <extensometer>. A <load cell> supplies the force record.<Three Point Bend Test Fixtures by Instron>[Principle of Operation; direct deflection measurement]{ref} The <crosshead displacement> can also contain deformation of the frame and contacts.
For an original readout example, stipulate span $L=0.120\,\mathrm m$, width $b=12\,\mathrm{mm}$ and thickness $h=4\,\mathrm{mm}$, so $I=6.4\times10^{-11}\,\mathrm{m^4}$. Suppose a linear loading interval gives direct midspan compliance $C_s=0.020\,\mathrm{mm/N}$, while machine travel gives $C_m=0.025\,\mathrm{mm/N}$. Applying the same beam relation to the two readouts gives
$$
E_s=\frac{L^3}{48IC_s}=28.125\,\mathrm{GPa},\qquad
E_{\rm apparent}=\frac{L^3}{48IC_m}=22.5\,\mathrm{GPa}.
$$
The apparent modulus is twenty percent lower. The numbers are chosen to isolate the displacement-channel effect; they do not characterize a particular fixture. Inferring a material <Young's modulus> further assumes the beam's linear, homogeneous bending model is adequate. Contact indentation, support motion and transverse <shear strain> can otherwise alter the measured compliance. The parent <simply supported beam> supplies the deflection derivation and support-comparison figure.
Back to article page
