Flexural Strength

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Flexural strength

Determination methods

The flexural strength σ_fM is determined in a three-point or four-point bending test [1, 5] on plastics or short fibre-reinforced plastic composites. The test on rigid and semi-rigid plastics, i.e. thermoplastic moulding compounds, extrusion compounds and casting compounds, is carried out in accordance with ISO 178 [1–4] in a three-point bending test. For fibre-reinforced plastics, the three-point or four-point bending test (method A or B) in accordance with ISO 14125 [5] can be used.

Definition of flexural strength

The definition of flexural strength is identical in both standards and states that flexural strength corresponds to the maximum bending stress that is withstood by the test specimen (see also: test piece) during a bend test [1–5].

In contrast to ISO 14125, where primarily only the deflection at the point of flexural strength s_M or the deflection at flexural strength is determined as the deflection at the force at which flexural strength is achieved, ISO 178 requires the flexural strain ε_fM at flexural strength to be determined. The flexural strength is determined in the three-point bending test according to Eq. (1) [1–4].

$\sigma _{fM}\ ={\frac {3F_{M}\cdot L}{2b\cdot h^{2}}}$

(1)

In the four-point bending test, the flexural strength is calculated according to Eq. (2) [5], where L is the support span in both equations and b and h represent the cross-sectional dimensions of the test specimens.

$\sigma _{fM}\ ={\frac {F_{M}\cdot L}{b\cdot h^{2}}}$

(2)

In the case of three-point bending according to ISO 178, the dimensionless flexural strain for flexural strength is calculated using Eq. (3) or, when multiplied by 100, as flexural strain in percent. Based on the simplified bending theory of the undeformed test specimen, this flexural strain corresponds to the symmetrical peripheral fibre strain on the tension (strain) or compression (contraction) side of the test specimen (Fig. 1).

$\varepsilon _{fM}\ ={\frac {6s_{M}\cdot h}{L^{2}}}$

(3)

The corresponding bending strain ε_fM can be calculated as an approximate peripheral fibre strain according to ISO 14125 as a dimensionless parameter using Eq. (4) and the geometric boundary conditions of the four-point bending test from the measured deflection s_M [5].

$\varepsilon _{fM}\ ={\frac {4,7s_{M}\cdot h}{L^{2}}}$

(4)

In this case, too, the bending strain can be expressed as a percentage value by multiplying it by a factor of 100.

Evaluation of bend tests

According to [1], bending strength can only be determined if the maximum of the flexural stress-flexural strain curve lies within the deflection interval of 0 ≤ s ≤ s_C or the strain interval 0 ≤ ε_f ≤ 3.5 % which corresponds to a standard deflection s_C of 6 mm for test specimens with a thickness of 4 mm. For larger deflections of up to approx. 9 mm and when a deflection of 6 mm is reached without a maximum occurring, the standard flexural stress σ_fC must then be determined (Fig. 1), which is not comparable with the flexural strength.

Fig. 1:

Determination of characteristic values for plastics in bending tests according to ISO 178 [1]

The limit value of 6 mm no longer exists in the latest edition of ISO 178 [3], meaning that this regulation no longer applies. The ISO 14125 standard does not specify such a deflection limit (Fig. 2), but all stress and bending strain values must be evaluated using correction equations in order to approximately compensate for the influence of excessive deflections in comparison with bending theory. As a result of support spacing reductions, support friction, and horizontal forces, the measured peripheral fibre strains are too large, and the bending strengths are generally too small [6].

Fig. 2:

Determination of characteristic values for plastics in bending tests according to ISO 14125 [5]

See also

• Bend test
• Bend test – Yield stress
• Bend test – Test influences
• Bend loading
• Strength

References

[1]	ISO 178 (2010-12): Plastics – Determination of Flexural Properties
[2]	ISO 178 (2013-04): Plastics – Determination of Flexural Properties
[3]	ISO 178 (2019-04): Plastics – Determination of Flexural Properties
[4]	ISO/DIS 178 (2026-03: Plastics – Determination of Flexural Properties
[5]	ISO 14125 (1998-03): Fibre-reinforced Plastic Composites – Determination of Flexural Properties (Technical Corrigendum Corrigendum1:2001-07 + AMD 1:2011-02)
[6]	Bierögel, C.: Bend Test on Polymers. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 133–143 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-807-5; see AMK-Library under A 22)