Flexural strength

[1] The transverse bending test is most frequently employed, in which a specimen having either a circular or rectangular cross-section is bent until fracture or yielding using a three-point flexural test technique.

The flexural strength represents the highest stress experienced within the material at its moment of yield.

When an object is formed of a single material, like a wooden beam or a steel rod, is bent (Fig.

1), it experiences a range of stresses across its depth (Fig.

At the outside of the bend (convex face) the stress will be at its maximum tensile value.

These inner and outer edges of the beam or rod are known as the 'extreme fibers'.

Most materials generally fail under tensile stress before they fail under compressive stress[citation needed] The flexural strength would be the same as the tensile strength if the material were homogeneous.

In fact, most materials have small or large defects in them which act to concentrate the stresses locally, effectively causing a localized weakness.

When a material is bent only the extreme fibers are at the largest stress so, if those fibers are free from defects, the flexural strength will be controlled by the strength of those intact 'fibers'.

However, if the same material was subjected to only tensile forces then all the fibers in the material are at the same stress and failure will initiate when the weakest fiber reaches its limiting tensile stress.

Both of these forces will induce the same failure stress, whose value depends on the strength of the material.

The resulting stress for a rectangular sample under a load in a three-point bending setup (Fig.

The equation of these two stresses (failure) yields:[2] Typically, L (length of the support span) is much larger than d, so the fraction

For a rectangular sample under a load in a three-point bending setup (Fig.

3), starting with the classical form of maximum bending stress:

(central axis to the outermost fiber of the rectangle)

Combining these terms together in the classical bending stress equation:

The flexural strength is stress at failure in bending. It is equal to or slightly larger than the failure stress in tension.
Fig. 3 - Beam under 3 point bending
Fig. 4 - Beam under 4 point bending