Why is the bending strength of a material about 1.5 times greater than its tensile strength?

When looking at a resin material data sheet, you might ask: ‘What does it mean that the tensile strength is 50 MPa, but the flexural strength is 75 MPa?’ Many people have asked themselves this question. In fact, for many materials the flexural strength tends to be higher than the tensile strength. Especially for brittle materials such as ceramics, it is not unusual for flexural strength to be 1.5 to 2 times higher than tensile strength.

So why do these differences occur? This article explains the reasons from a mechanical and material perspective.

What is the difference between flexural and tensile strength?

First, let's briefly summarise the definitions of the two.

Tensile Strength: the maximum stress a material can withstand under a uniform tensile load up to rupture.

Flexural Strength: Maximum bending stress at which a specimen fails in a three- or four-point bending test.

Typical formula for flexural strength (3-point bending):

Bending stresses are concentrated in one part of the material.

In bending tests, tensile and compressive stresses occur simultaneously at the top and bottom of the material. Bounded by the neutral axis of the cross-section, the upper side is subject to compression and the lower side to tensile stress.

Particularly noteworthy:

Maximum stress is only applied in the surface layer The closer to the neutral axis, the lower the stress becomes, and at the centre it is zero

This means that only a small surface area of the material can trigger fracture.

In contrast, internal defects (bubbles and microcracks) are more likely to trigger fracture in tensile tests, as the stress is applied uniformly over the entire surface.

This is why the same material can be “stressed all over” in a tensile test, whereas in a flexural test it is “highly stressed in parts but helped by other parts”.

Differences between the effect of defects and fracture behaviour.

This difference is particularly significant in brittle materials.

Tensile test: internal defects are pulled in the direction of opening, accelerating fracture

Flexural test: defects are confined to the surface and do not lead to total collapse

This difference in defect susceptibility is the main reason why flexural strength is higher than tensile strength.

Theoretical support: Mohr-Coulomb's point of view

Failure of a material is considered to occur on the basis of maximum principal or shear stress; in Mohr-Coulomb's failure criterion, the conditions under which failure occurs are:

According to this theory of fracture, the combined state of shear and principal stresses produced by bending is more likely to satisfy the **delayed fracture (i.e. higher strength)** condition than pure tension.

**√3 times? Upper limit in ideal brittle bodies

In some literature, in ideal brittle bodies:

An approximate formula has been introduced which states that

This is a theoretical upper limit assuming that fracture occurs in a combined tensile and shear stress state. In actual materials it is often lower than this, often by a factor of 1.2 to 1.5.

Material-specific examples.

material	Tensile strength (MPa)	Flexural strength (MPa)	Ratio
ABS	45	55～60	1.2～1.3
POM	70	90	1.29
PC	60	90	1.50
PPS	95	145	1.53

Thus, a ratio of around 1.5 times is common for plastics and other materials.

Practical applications.

In the early stages of design or during material selection, when flexural strength data are not available, it is practically useful to approximate the tensile strength by multiplying it by a factor.

Of course, accurate data based on actual measurements and CAE analysis is recommended for the final design.

Summary.

-Bending tests are stress localised → fracture is less likely to occur than in tensile tests

-The influence of defects on fracture is smaller in bending

-Theoretical bending strength may be up to √3 times higher in ideal brittle materials

-Bending strengths of around 1.2 to 1.5 times higher are observed in many materials.

The phenomenon of flexural strength being higher than tensile strength stems from intrinsic properties of material mechanics, such as stress distribution, mechanisms of fracture initiation and the influence of defects.