Strain Rate Applications

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Strain rate applications

General information

In many applications, e.g. in automotive engineering, aerospace technology and sports, high strain rates of up to 500 s^-1 can occur in the material/component [1–3]. Table 1 provides an overview of the test methods used to determine material properties under the respective stress conditions with the achievable strain rates. Since the principle was introduced in 1914, the SPLIT-HOPKINSON Pressure Bar (SHPB) test has played a leading role in determining material behaviour under strain rates > 100 s^-1 due to its versatility and continuous development, in particular the feasibility of different types of loading [4].

Table 1: Test methods for material characterisation at high strain rates [3, 5, 6]

nominal strain rate (s-1)	type of loading	testing technique
<0.1	compression	electromechanical material testing machine
0.1–100		Servo-hydraulic testing machine
0.1–500		Cam plastometer, free-falling dart test
200–104		Split-HOPKINSON Bar (compression loading)
104–105		ballistics, projectiles
<0.1	tensile	electromechanical material testing machine
0.1–100 (300)		servo-hydraulic testing machine
100–104		Split-HOPKINSON Bar (tensile loading) explosive acceleration:
104		plate(flyer plate)
>105		ring (expanding ring)
<0.1	shear	electromechanical material testing machine
0.1–100 (300)		servo-hydraulic testing machine
10–103		impact test (torsional impact)
100–104		Split-HOPKINSON Bar (shear arrangement)
103–104		interlaminar shear test of a double-notched test specimen (double-notch shear test)
104–107		pressure-shear plate impact

In addition to the strain rates, the Figure also shows the characteristic test times and the deformation processes occurring in metals and plastics (using the example of isotactic and impact-modified polypropylene [7]). Modern servo-hydraulic testing machines can cover a strain rate range from 10^-3 to 10⁺³ [8], which is highlighted in grey in the Figure.

Figure:

Practically relevant, characteristic test times, strain rates and deformation mechanisms [9]

At strain rates greater than 1 s^-1, vibrations occur which reduce the information content of the stress–strain curves and make evaluation more complicated. These oscillations are due to the impact introduction of energy into the test specimen and are significantly influenced by the entire testing machine and the damping behaviour of the material [3, 10, 11] and cannot be avoided in high-speed tensile tests.

Reflected stress waves

These vibrations are attributable to the shock-like introduction of energy into the test specimen and are significantly influenced by the entire testing machine and the damping behaviour of the material [3, 10, 11]. In [3], the number of elastically reflected vibrations N (Eq. 1 and 2) is defined as the criterion for the evaluability of recorded curves in the average strain rate range of 1–100 s^-1.

$N\,=\,{\frac {\varepsilon _{y}\cdot c}{v_{T}}}$

(1)

with

εy		yield strain
c		velocity of the elastic stress wave
vT		crosshead speed

$c\,=\,{\sqrt {\frac {E_{t}}{\rho }}}$

(2)

with

ET		elastic modulus
$\rho$		density

The minimum number of oscillations for uniform stress distribution is specified as 10 in [12] and, based on the evaluation of SHPB tests (Split-HOPKINSON pressure bar) in [3], as three complete oscillations. If the number of oscillations is sufficiently high, uniform stress distribution in the test specimen can be assumed, although this condition is not comparable to the homogeneous stress distribution in a quasi-static tensile test.

Elastic modulus of plastics at high strain rates

The trend in automotive engineering is towards plastic components that are exposed to impacts and high dynamic loads, such as airbags, bumpers, instrument panels, etc.

To simulate the behaviour of materials under highly dynamic loads, characteristic values are required that enable the crash behaviour to be predicted. M. Keuerleber's dissertation [13] deals with a characteristic parameter that is relatively easy to determine using testing methods, namely the modulus of elasticity.

To determine the modulus of elasticity, uniaxial tensile tests were carried out on polypropylene at speeds ranging from 0.0001 m/s to 8 m/s and temperatures ranging from -10 °C to 40 °C.

See also

• Strain rate basics
• Deformation rate
• Deformation velocity
• Crosshead speed
• Test speed

References

[1]	Bardenheier, R.: Dynamic Impact Testing – VHS High Rate Testing Systems. Instron Ltd., High Wycombe, UK (2005)
[2]	Thoma, K.: Measurement of Mechanical Parameters in the Range of High and Highest Strain Rates – Examples of Practical Application for a Wide Spectrum of Materials. Report 17/02. Fraunhofer-Institut für Kurzzeitdynamic – Ernst-Mach-Institut EMI Freiburg (2002)
[3]	Xiao, X.: Dynamic Tensile Testing of Plastic Materials. Polymer Testing 27 (2008) 164–178 DOI: https://doi.org/10.1016/j.polymertesting.2007.09.010
[4]	Gray-III, G. T.: Classic Split-Hopkinson Pressure Bar Testing. In: ASM Handbook, Vol. 8, Mechanical Testing and Evaluation. ASM International (2000) pp. 462–476
[5]	Bardenheier, R., Rogers, G.: Dynamic Impact Testing. Instron Ltd., High Wycombe, UK (2003)
[6]	Hamouda, A. M. S., Hashmi, M. S. J.: Testing of composite materials at high rates of strain: Advances and challenges. Journal of Materials Processing Technology 77 (1998) 327–336 DOI: https://doi.org/10.1016/S0924-0136(97)00436-6
[7]	Gensler, R., Plummer, C. J. G., Grein, C., Kausch, H.-H.: Influence of the loading rate on the fracture resistance of isotactic polypropylene and impact modified isotactic polypropylene. Polymer 41 (2000) 3809–3819 DOI: https://doi.org/10.1016/S0032-3861(99)00593-5
[8]	Bardenheier, R., Borsutzki, M.: Anforderungen an Hochgeschwindigkeitsprüfsysteme zur Ermittlung von Kennwerten an Blechwerkstoffen. In: Buchholz, O.W., Geisler, S. (Eds.): Herausforderung durch den industriellen Fortschritt – Tagungsband Werkstoffprüfung (2003) 78–87 (ISBN 978-3-514-00703-1; ISBN 3-514-00703-9; see AMK-Library under M 11)
[9]	Schoßig, M.: Schädigungsmechanismen in faserverstärkten Kunststoffen – Quasistatische und dynamische Untersuchungen. Vieweg+Teubner / GWV Fachverlage GmbH, Wiesbaden (2010), (see AMK-Library under B 1-21) Content as pdf
[10]	Beguelin, P., Kausch, H. H.: The effect of the loading rate on the fracture toughness of poly(methyl methacrylate), polyacetal, polyetheretherketone and modified PVC. Journal Materials Science 29 (1994) 91–98 DOI: https://doi.org/10.1007/BF00356577
[11]	Karger-Kocsis, J., Benevolenski, O. I., Moskala, E. J.: Toward understanding the stress oscillation phenomenom in polymers due to tensile impact loading. Journal Materials Science 36 (2001) 3365–3371 DOI: https://doi.org/10.1023/A:1017935323058
[12]	Society of Automotive Engineers Japan (SAE J) 2749 (2008): High Strain Rate Testing of Polymers
[13]	Keuerleber, M.: Bestimmung des Elastizitätsmoduls von Kunststoffen bei hohen Dehnraten am Beispiel von Polypropylen (PP). Dissertation Universität Stuttgart, Institut für Kunststoffprüfung und Kunststoffkunde, Stuttgart, August (2006) (see AMK-Library under C 35), see see Deutsche Digitale Bibliothek