Bend Test – Yield Stress

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Bend test – Yield stress

General principles

Similar to the tensile test, the different deformation components in bend loading, which are time- and load-dependent, must be taken into account when evaluating the measurement results. Depending on the type of plastic, linear-elastic, linear-viscoelastic, nonlinear-viscoelastic, and plastic deformation components occur. The ratio of the deformation components in relation to the total deformation, depending on the respective loading conditions (temperature and time). Due to the load stress distributed linearly over the cross-section, the largest tensile or compressive stress [1, 2] always occurs in the outer peripheral fibre of the flexure test specimen. This results in a load level that varies over the specimen height or thickness, which means that the individual deformation components can occur simultaneously in terms of time and location. Since only individual symmetrically located layers in the specimen reach the yield stress, a pronounced yield point is not observed in the bend test in analogy to the tensile test.

Microscopic yield and macroscopic necking

Assuming a homogeneous and isotropic specimen condition without internal flaws (shrinkage cavities or agglomerations), when the material-dependent yield stress is reached in the tensile test, the most highly loaded specimen cross-section will enter the state of "cold yielding", which becomes visible macroscopically by a necking (Fig. 1).

Fig. 1:

Consequence of reaching yield stress in the tensile test

The stress level will subsequently remain constant, while the deformation will steadily increase. The energetic consumption in the test is essentially limited to the necking fronts in the flow area, so that the deformation stagnates in the still undeformed and already stretched areas. When the flow area, which is influenced by temperature and test speed, has exhausted its deformation capacity, a material-dependent hardening process is often subsequently observed. Since different stress levels occur in the flexure test, such a behaviour as in the tensile test is not observed (Fig. 2).

Fig. 2:

Consequence of reaching yield stress in the bend test

In contrast to the theoretical tensile–compressive behaviour, the effects on the stress and deformation field that actually occurs can be seen in particular in the peripheral fibre of the specimen when a yield point is reached. Due to this fact, especially when the yield point is reached, i.e. when plastic deformation sets in, the stress distribution over the cross-section deviates from linearity. The outer layers of the specimen will initially exhibit a constant stress. As the load stress increases, the yield zones in the interior shift towards the neutral fibre. This shift can be asymmetric if the yield stress in the tensile test σ_ty is different from the compressive yield stress (compressive yield point) σ_cy. Depending on whether strain hardening effects are observed in the un-tested material, further changes in stress distribution may occur in the flexural test.

Flow stresses in tensile and compression tests

The deformation effects listed in Fig. 3 show the effects when assuming different material behaviour. If the differing behaviour of plastics under tensile and compressive loading is taken into account, as already manifested in practice, for example, in different moduli in the tensile and compression test, then the assumption of symmetry of the neutral fibre is invalid for larger deformations (Fig. 3), as shown by the occurring displacement of the neutral fibre. The resulting bending stresses on the tensile and compression sides of the specimen are then different, in contrast to the calculation equation of the standard [3].

Fig. 3:

Influence of differing material behaviour and yield stresses in the tensile and compression test

See also

• Bend test
• Bend loading
• Bend test – Influences
• Bend test – Test influences
• Bend test – Specimen preparation
• Bend test – Shear stress
• Bend test – Specimen shapes

References

[1]	Bierögel, C.: Bend test on polymers. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3. Edition, p. 133–143 (ISBN 978-1-56990-806-8; ePub ISBN 978-1-56990-802-2; see AMK-Library under A 22)
[2]	Bierögel, C., Grellmann, W.: Bend loading. In: Grellmann, W., Seidler, S.: Mechanical and Thermomechanical Properties of Polymers. Landolt-Börnstein, Volume VIII/6A3, Springer Verlag, Berlin (2014) 164–191, (ISBN 978-3-642-55165-9; see AMK-Library under A 16)
[3]	ISO 178 (2019-04): Plastics – Determination of Flexural Properties