A material’s stiffness and resistance to bending are determined by its flexural modulus. Design engineers must choose materials for structural durability and safety based on these values.
The propensity of a material to bend, or flexural deformation, which is the ratio of stress to strain, is the flexural modulus, sometimes referred to as the bending modulus.
In this article, we’ll explore what flexural modulus is, its formula and how it can be determined. We’ll also look at the relationship between structural modulus and tensile modulus.
Let’s drive in!
What is Flexural Modulus?
The ratio of stress to strain in flexural deformation, or a material’s propensity to resist bending, is the flexural modulus, also known as the bending modulus, an important characteristic in mechanics.
It employs units of force per area and is calculated from the slope of a stress-strain curve generated by a flexural test (such as the ASTM D790).
A linear stress-strain response is assumed by the flexural modulus determined by the 3-point bend test. Understanding a material’s stiffness or rigidity requires knowledge of its flexural modulus.
While certain material uses may require flexibility to avoid damage while bending, others may demand strength and rigidity for structural support.
Therefore, a few elements influence a material’s flexural modulus, and knowing these aspects helps with material development and selection.
The basic characteristics of the material dictate the base flexural modulus of the foundation material. For instance, flexibility in plastics depends on the kind of polymer, its molecular weight, thickness, and form.
Adding a fine mineral filler to the plastic, such as talc powder, is one method of adjusting its flexibility. These tiny mineral fillers usually stiffen the material and raise its flexural modulus.
The aspect ratio and particle size of a mineral filler also affect its capacity to adjust the flexural modulus. Particles with a higher aspect ratio raise the material’s flexural modulus more than those with a lower aspect ratio.
If the particle size aspect ratio rises while reducing the particle size of a mineral addition, the flexural modulus may rise as well.
It should be noted that flexural modulus is a helpful metric for materials that do not rupture or break when stress is applied. Flexural strength is a better way to assess brittle materials that shatter when subjected to a certain amount of force.
Related: What is Toughness, Hardness and Strength in a Material?
How Is the Flexural Modulus of a Material Determined?
A rectangular beam of the material with width w and height h is subjected to a 3-point analysis to determine its flexural modulus.
The distance between two support points positioned on the bottom of the beam is specified by the parameter L.
A displacement in the material, known as the deflection, d, is produced when a force, F, is applied to a point on the other side and between the two supports.
The following formula is used to get the flexural modulus, or Ebend, in units of force per area using these parameters:
(L3F) / (4wh3d) = Ebend
For engineers and architects, calculating flexural modulus is crucial since it indicates how much weight a material can hold when employed as structural support.
The Relationship Between Flexural Modulus and Tensile Modulus
Flexural modulus measurements work best with isotropic materials, or materials with consistent characteristics in all directions, since when the test sample bends, its top surface receives compression pressures while the opposing side experiences tensile deformation.
Since the flexural and tensile moduli of a material are both indicators of mechanical strain, they should be comparable under ideal elastic circumstances.
In other words, although the weights they are resisting are different, they both convey a material’s capacity to withstand deformation under stress.
According to elastic beam theory, when a concentrated load is applied to a simply supported beam:
D = L3F/48EI for deflection
When E is transposed, we get E = L3F/48Id.
I = 1/12 wh³ for a rectangular portion
E = L3F/4wh3d is obtained by substituting I for E in the equation.
Consequently, E = Ef
However, if measurements are made under less-than-ideal, non-elastic circumstances, these two characteristics can really be different.
Related: What is Residual Stress? Its Causes, Effect, and How to Measure
FAQs
What is the flexural modulus?
The propensity of a material to bend, or flexural deformation, which is the ratio of stress to strain, is the flexural modulus, sometimes referred to as the bending modulus.
Are flexural modulus and Young’s modulus the same?
Flexural modulus gauges a material’s stiffness or resistance to bending, while flexural strength is the highest stress a material can bear before breaking. Conversely, Young’s modulus is associated with the elastic characteristics of the material.
What is the difference between stiffness and flexural modulus?
The flexural modulus, or a material’s capacity to bend, is expressed in pounds per square inch (psi) and characterizes the stiffness of plastics. A material’s stiffness increases with its flexural modulus, while its flexibility increases with a lower flexural modulus.
What is the formula for flex modulus?
The ratio of stress (force) to strain (deformation), or flexible modulus, E, is a physical quantity that is connected to this one. E = L3F/4bd³D is the formula, with D standing for deflection.
What is the flexural formula?
The ratio of stress (force) to strain (deformation), or flexible modulus, E, is a physical quantity that is connected to this one. E = L3F/4bd³D is the formula, with D standing for deflection.