View source for ICIT – Influence of Pendulum Hammer Velocity

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<span style="font-size:1.2em;font-weight:bold;">ICIT – Influence of Pendulum Hammer Velocity  </span>
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==ICIT: ratio of fracture load to the amplitude of the inertial load==

For the fracture mechanics analysis of impact force (F)-deflection (f) diagrams recorded in [[Instrumented Charpy Impact Test|instrumented Charpy impact tests]], in accordance with the criteria of [[Fracture Mechanics#Linear-elastic fracture mechanics|linear-elastic fracture mechanics (LEFM)]] and [[Fracture Mechanics#Elastic–plastic fracture mechanics (EPFM)|elastic‒plastic fracture mechanics]] (see: [[J-Integral Concept|J-integral concept]] and [[Crack Tip Opening Displacement Concept (CTOD)|crack tip opening displacement concept]]), the condition applies that the fracture load ''F''<sub>max</sub> must always be significantly greater than the amplitude of the inertial load ''F''<sub>1</sub> during unstable crack propagation (see: [[ICIT – Experimental Conditions|ICIT ‒ Experimental conditions]]) [1].

==Application of the low-blow method==

A tried-and-tested technique is to reduce the pendulum hammer velocity ''v''<sub>H</sub> (low-blow technique [2‒4]). To achieve this, it is simply necessary to reduce the fall height, which simultaneously reduces the work done by the pendulum (see also: [[Impact Loading Pendulum Impact Tester|impact loading pendulum impact tester]]).

The effects of a reduced pendulum hammer velocity are shown in '''Fig. 1''' using polypropylene ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PP) as an example, where a significant change in [[Material & Werkstoff|material]] behaviour can be observed. 

[[File:Hammer Velocity Fig-1-1.jpg]]

[[File:Hammer Velocity Fig-1-2.jpg]]
{| 
|- valign="top"
|width="50px"|'''Fig. 1''': 
|width="600px" |Effect of a reduced pendulum hammer velocity on the material behaviour of polypropylene ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PP) for ''s''/''W'' = 7, RT and ''a''/''W'' = 0.45 (a) and ''a''/''W'' = 0.2 (b)
|}

'''Figure 1''' shows that, at a pendulum hammer velocity ''v''<sub>H</sub> = 2.9 m/s and ''a''/''W'' = 0.45, the maximum impact load is significantly smaller than the amplitude of the [[Inertial Load|inertial load]] ''F''<sub>1</sub>; consequently, for [[Specimen|specimens]] with a [[Notching|notch]] positioned almost centrally, a fracture mechanics analysis based on fracture mechanics concepts is not possible. The increase in the amplitude of the [[Inertial Load|inertial load]] shown in the sub-figures is plotted against the decrease in the fracture load ''F''<sub>max</sub> for ''a''/''W'' = 0.2 and ''a''/''W'' = 0.45 in '''Fig. 2'''.

[[File:Hammer Velocity Fig-2.jpg]]
{| 
|- valign="top"
|width="50px"|'''Fig. 2''': 
|width="600px" |Dependence of the maximum impact load ''F''<sub>max</sub> and the inertial load ''F''<sub>1</sub> on the pendulum hammer velocity for polypropylene ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PP) at ''a''/''W'' = 0.2 and ''a''/''W'' = 0.45
|}

Whilst at ''a''/''W'' = 0.2 the inertial loads (see '''Fig. 1a''') remain smaller than the fracture loads even at the maximum possible hammer velocity of 2.9 m/s, this condition is no longer met for ''a''/''W'' = 0.45. For this a/W ratio, ''F''<sub>1</sub> and ''F''<sub>max</sub> are identical at 2.6 m/s, and at ''v''<sub>H</sub> > 2.6 m/s, ''F''<sub>1</sub> > ''F''<sub>max</sub>, meaning that the relationship ''F''<sub>max</sub> > ''F''<sub>1</sub> is not satisfied and no exact specification of fracture mechanical parameters is possible. The inertial loads lie in the range 8 N ≤ ''F''<sub>1</sub> ≤ 36 N and are virtually independent of the ''a''/''W'' ratio.

The expected linear relationship between the amplitude of the inertial loads and the pendulum hammer velocity can be confirmed for both ''a''/''W'' ratios [1]. For ''v''<sub>H</sub> > 1.5 ms<sup>-1</sup>, a material-specific increase of 15 Ns/m is determined for polypropylene ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PP), and for ''v''<sub>H</sub> < 1.5 ms<sup>-1</sup>, a different increase has been observed experimentally, which makes sense given the condition ''F''<sub>1</sub> → 0 as ''v''<sub>H</sub> → 0. The difference in the fracture load ''F''<sub>max</sub> for ''a''/''W'' = 0.2 and ''a''/''W'' = 0.45 results from the change in the residual cross-sectional area (ligament × specimen thickness).

==Recording diagrams suitable for fracture mechanics analysis==

It is evident from this that evaluable ''F''-''f'' diagrams ‒ i.e. those satisfying the control conditions ''F''<sub>max</sub> > ''F''<sub>1</sub> and ''t''<sub>B</sub> > 2.3…3τ (see: [[ICIT – Experimental Conditions|ICIT ‒ Experimental conditions]]) ‒ for determining fracture mechanical [[Material Value|characteristic values]] at high hammer velocities can only be expected for small ''a''/''W'' ratios. As the [[Velocity|velocity]] decreases, the relationship between load and deflection becomes increasingly non-linear. Due to the increasing material embrittlement associated with decreasing test temperature, which is linked to a reduction in fracture times ''t''<sub>B</sub>, the control condition ''F''<sub>max</sub> > ''F''<sub>1</sub> cannot be met at low temperatures and high ''a''/''W'' ratios.

A check of the [[Energy Balance ICIT|energy balance]] – which stipulates that the impact energy absorbed by the specimen must be less than one third of the total energy of the pendulum impactor – showed that these conditions are adequately met even at a hammer velocity of 1 ms<sup>-1</sup> (~40° hammer falling angle) [1].

Whilst the fracture forces do not change significantly for ''v''<sub>H</sub> > 1.5 … 2 ms<sup>-1</sup> (see '''Fig. 2'''), it is demonstrated in [1] that the specimen deflection decreases as expected with increasing pendulum hammer velocity and can therefore be regarded as an indicator of the increasing embrittlement that occurs with rising velocity [5].

==See also==

* [[Instrumented Charpy Impact Test|Instrumented Charpy impact test]]
* [[ICIT – Experimental Conditions|ICIT – Experimental conditions]]
* [[Impact Loading Plastics|Impact loading plastics]]

==References==

{|
|-valign="top"
|[1]
|[[Grellmann,_Wolfgang|Grellmann, W.]]: Beurteilung der Zähigkeitseigenschaften von Polymerwerkstoffen durch bruchmechanische Kennwerte. Habilitation (1986), [https://de.wikipedia.org/wiki/Technische_Hochschule_Leuna-Merseburg Technische Hochschule Leuna-Merseburg], Wiss. Zeitschrift TH Merseburg 28 (1986), No. 6, pp. 787–788 ([https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Habil_Grellmann_Inhaltsverzeichnis.pdf Content], [https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Habil_Grellmann_Kurzfassung.pdf Summary]) 
|-valign="top"
|[2]
|Retting, W.: Untersuchung des Verhaltens von Kunststoff-Folien bei biaxialer Stoßbeanspruchung. Materialprüfung 8 (1966) 2, pp. 55‒60; [https://doi.org/10.1515/mt-1966-080202 https://doi.org/10.1515/mt-1966-080202]
|-valign="top"
|[3]
|Ortmann, R.; Man, J.: Wiss. Zeitschrift TH Magdeburg 24 (1980) 1, p. 101 
|-valign="top"
|[4]
|Holzmann, M., Man, J.: Dynamika Lomova Houzevnatost (Dynamische Bruchzähigkeit), Zvaranie (1977) 5‒9 pp. 1‒43 
|-valign="top"
|[5]
|[https://www.researchgate.net/profile/Wolfgang-Grellmann Grellmann, W.], [[Seidler,_Sabine|Seidler, S.]] (Eds.): Kunststoffprüfung. Carl Hanser, Munich (2025) 4th Edition (ISBN 978-3-446-44718-9; E-Book: ISBN 978-3-446-48105-3; see [[AMK-Library]] under A 23) 
|}

[[Category:Fracture Mechanics]]
[[Category:Instrumented Impact Test]]