Strain Rate Basics
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Strain rate basics
Fundamentals of strain rate
The strain rate dε/dt indicates the velocity distribution of the strain according to the type of test in the volume of the test specimen, either infinitesimal or integral within a defined test specimen length. In materials testing, it is assumed that the applied test speed in quasi-static tests is distributed adequately across the test specimen cross-sectional area and length via the load linkage and the clamping device or the supports or bearings. If we consider only the tensile or compression test (Figs. 1a and b),
| Fig. 1: | Measurement of normative strain (a) in tensile testing, (b) in compression testing and (c) in three-point bending testing on plastics |
the nominal strain rate can be calculated directly from the crosshead speed if the clamping length or the pressure stamp distance L is known, using dε/dt = vT/L. However, since the load applied to the test specimen depends on the stiffness ratio between the testing machine and the test specimen, the quality of the clamping jaws and the linearity of the load line (bending effects), the quality of the drive and the surface of the test specimen (slippage) and its geometry, the actual strain rate sometimes deviates significantly from the calculated value. This can be remedied by performing strain-controlled tensile or compression tests, which are not standardised, however, and determining the integral normative strain and strain rate within the measuring length L0 of strain extensometers.
Influence of test specimen geometry on strain rate
A comparison of a tensile test on prismatic test specimens and multipurpose test specimens with shoulders for clamping shows how the test specimen geometry affects the velocity profile in the test specimen. Figure 2a shows that, assuming homogeneous and isotropic material behaviour and neglecting clamping effects in the prismatic test specimen, a constant distribution of strain rate is achieved (black curve in Fig. 2a). In the presence of shoulders in the upper and lower test specimen areas, the changed geometry A0 will result in a lower average strain rate, which is also not constant (red curve in Fig. 2a). If the tensile test is performed conventionally with a clamping length lE of 100 mm, a comparable constant crosshead speed vT and strain control, the diagrams shown in Fig. 2b are obtained. The green curves in Fig. 2b show the stress–strain behaviour (solid line in Fig. 2b) and the strain rate dε/dt (dashed line in Fig. 2b) for the conventional tensile test. Compared to the strain-controlled tensile test (red lines in Fig. 2b), there is a higher tensile strength and lower tensile strain at break, as the controlled test provides improved relaxation conditions for the plastic. However, it is essential that there is a constant strain rate between the strain extensometers in the controlled test, whereas in the conventional tensile test, a comparable nominal and normative strain rate only exists at approximately 2 % strain. Even in integrally controlled tensile tests, if one considers the local strain and speed distribution within the measuring length, there are considerable differences due to the heterogeneity of the test specimen morphology (see: laser extensometry), which can lead to increased interpretation problems when determining the true strain rate, especially in the case of constricting plastics.
| Fig. 2: | (a) (a) Schematic influence of the test specimen geometry and (b) effect of conventional and strain-controlled tensile tests on the strain rate of polyamide (abbreviation: PA) with 20 m.-% GF |
Strain rate of the peripheral fibre in the bending test
Similar problems exist when determining the peripheral fibre strain rate in the bending test (Fig. 1c), whereby differences between the three-point and four-point bending tests also occur here. Particularly in the case of significant differences in the tensile and compressive behaviour of plastics, displacement of the neutral fibres can occur in the bending test, and misleading measurement effects can arise from the crosshead path measurements [38].
Due to the impact loading in the presence of notches, a triaxial deformation state occurs in the impact or free-falling dart test, which also causes an inhomogeneous multi-axial distribution of the strain rate. Measurements of these velocity distributions are only possible on model materials under idealised conditions using complex testing techniques. In most cases, a theoretical analysis using FEM is used to evaluate the strain rates that occur in the load directions. However, due to the strong effects resulting from stress intensification at sharp notches during impact loading, a strong localisation and inhomogeneity in the strain rate distribution is caused, which has a very strong effect on the toughness properties of plastics.
Wiki explanations of terms relating to speed
The Wiki-lexicon "Polymer Testing & Diagnostics" from Polymer Service GmbH Merseburg (PSM) also explains the following terms in more detail under the heading ‘velocity’:
See also
References
| [1] | Bierögel, C.: Quasi-Static Test Methods. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 101–143 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-807-5; see AMK-Library under A 22) |
Weblink
- Wikipedia – The Free Encyclopedia: Deformation gradient; https://en.wikipedia.org/wiki/Finite_strain_theory (last accessed on January 4, 2026)