Inertial Load

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Initial load, impact impulse or inertial force

Causes of inertial load

The occurrence of an inertial load (also referred to as inertial force) caused by mass inertia, which is superimposed on the actual deformation behaviour, represents a measurement and evaluation problem in materials testing under dynamic loads. Due to the large differences in damping behaviour, the vibration problem is even more pronounced for plastics than for metals.

When the stress is applied suddenly during dynamic (impact) tests, a complex reaction occurs in the entire coupled system, which consists of the following components:

• Reaction forces of the test specimen,
• Acceleration forces,
• Signal vibrations caused by spring-mass forces,
• Signal vibrations caused by reflected body sound waves,
• High-frequency signal vibrations caused by downstream measuring electronics.

Relationship between inertial load and maximum load in ICIT

In an electronically recorded load–time or load–deflection diagram in the instrumented Charpy impact test (ICIT), the mass inertia causes a reaction force to occur in the test specimen, the amplitude of which must always be considered in relation to the maximum load (force at the onset of unstable crack propagation). The vibration that occurs is referred to as inertial vibration. The inertial load is independent of the a/W ratio (a – notch depth, W – specimen width) of the test specimen, but depends on stress parameters such as velocity and temperature.

Criteria for determining the start of unstable crack propagation

The decisive factor in determining the point at which unstable crack propagation begins is that the maximum impact load F_max

$F_{max}\;>\;F_{1}$

must be greater than the inertial load F₁. To check this equation, the amplitude of the inertial force can be estimated using the equation

$F_{1}\approx {\frac {Z_{1}\,\cdot \,Z_{2}}{Z_{1}+Z_{2}}}\cdot v_{I}$

must be greater than the inertial load F₁. To check this equation, the amplitude of the inertial force can be estimated using the equation

$Z_{1{,}2}\,=\,c_{1{,}2}\cdot \rho _{1{,}2}$

where

Z1,2		spezific sound impedance of specimen and/or pendulum
ρ1,2		Density of specimen and/or pendulum hammer material
c1,2		sound velocity of specimen and/or pendulum hammer
vI		impact velocity according to ISO 13802

If the maximum impact load is greater than the inertial load, the fracture mechanics parameters can be determined using static evaluation formulas.

See also

• ICIT– Influence of pendulum hammer velocity
• ICIT– Experimental conditions
• ICIT– Limits of fracture mechanics evaluation
• ICIT– Nonlinear material behaviour

References

• Grellmann, W.: Bewertung der Zähigkeitseigenschaften durch bruchmechanische Kennwerte, In: Schmiedel, H. (Ed.): Handbuch der Kunststoffprüfung. Carl Hanser, Munich Vienna (1992), pp. 139–183, (ISBN 3-446-16336-0; see AMK-Library under A 3)
• Grellmann, W., Seidler, S. (eng.): Kunststoffprüfung. Carl Hanser, Munich (2025) 4th Edition, pp. 256–261 (ISBN 978-3-446-44718-9; E-Book: ISBN 978-3-446-48105-3; see AMK-Library under A 23)
• ISO 13802 (2025-08): Plastics – Verification of Pendulum Impact-testing Machines – Charpy, Izod and Tensile Impact-testing