About

Material failure analysis often relies on determining the flexural strength, also known as the Modulus of Rupture (MOR). This mechanical parameter represents the highest stress experienced within the material at its moment of yield during a flexure test. Unlike direct tensile tests, which can be difficult to perform on brittle materials like ceramics or concrete, flexural tests provide a practical alternative by applying a transverse load to a beam specimen.

Engineers use this data to predict how beams will behave under load in construction and manufacturing. The accuracy of this calculation depends on the testing configuration. A 3-point bend test creates a peak stress at the exact center under the load, while a 4-point bend test distributes maximum stress over a larger region between the loading points, often revealing defects that a 3-point test might miss.

Formulas

The calculation for flexural stress σ depends on the beam geometry and the support configuration.

For 3-Point Bend Setup:

σ = 3FL2bd²

For 4-Point Bend Setup (Load span = L/3):

σ = FLbd²

Where:

F = Maximum Load (Force)
L = Length of support span
b = Width of specimen
d = Thickness/Depth of specimen

Reference Data

Material Class	Specific Material	Typical MOR (MPa)	Typical MOR (psi)
Concrete	Standard Cure (28 days)	3.0 - 5.0	435 - 725
Concrete	High Strength	6.0 - 10.0	870 - 1450
Wood	Pine (Southern Yellow)	50 - 85	7250 - 12300
Wood	Oak (Red)	90 - 110	13000 - 16000
Ceramics	Alumina (99%)	300 - 400	43500 - 58000
Ceramics	Silicon Carbide	400 - 600	58000 - 87000
Polymers	Nylon 6,6	80 - 100	11600 - 14500
Polymers	Polycarbonate	90 - 105	13000 - 15200
Composites	CFRP (Unidirectional)	1200 - 1800	174000 - 261000
Glass	Borosilicate	60 - 80	8700 - 11600

Frequently Asked Questions

In flexure tests, only the extreme fibers at the bottom of the beam experience the maximum tensile stress. The volume of material under high stress is smaller compared to a direct tensile test, reducing the probability of encountering a critical flaw. Consequently, MOR values often exceed direct tensile strength, especially in brittle materials.

Use a 4-point setup when testing materials containing heterogeneous defects (like composites or wood). The 4-point setup exposes a larger volume of material (between the two loading points) to the maximum stress, providing a more statistically representative measure of the material's structural integrity.

Yes. Due to the "size effect" in fracture mechanics, larger specimens often yield lower strength values because they are statistically more likely to contain a critical defect. Standardized dimensions (ASTM/ISO) are required for valid comparisons.

Consistency is mandatory. If using SI units, use Newtons (N) for Force and millimeters (mm) for dimensions to get MegaPascals (MPa). If using Imperial, use Pounds-force (lbf) and inches (in) to get PSI.