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Mechanisms and Theory of Indentation of Ice Plates

  • B. Michel (a1) and N. Toussaint (a1)

Abstract

This study gives the results and interpretation of tests made in a cold room on ice plates held vertically in a press and indented at various speeds with a rectangular indentor. These plates, 81 cm square, were held and frozen solid to a steel frame to represent semi-infinite ice sheets. The tests were carried out at — 10°C with indentation speeds varying from 6 × 10 -5 cm/s to 3 cm/s.

It was found that the nominal pressure of indentation varies as a function of loading rates in a manner similar to that of the strength of S2 ice in uniaxial compression. The pressure increases rapidly with loading rates up to its maximum value at a strain-rate of 5 × 10-4 S-1. From there on, the pressure decreases. In the ductile range and up to the point of maximum pressure, a theoretical model was proposed where the theory of Hill (1950) of indentation of an ideal plastic body can be applied to predict an indentation pressure close to three times that of the uniaxial crushing strength.

The tests did not show any so-called “ratio effect” caused by the ratio of the indentor width to the plane thickness. This effect could be explained by the influence of the geometry of the indentor on the strain-rate.

Résumé

Mécanismes et théorie de l’indentation de plaques de glace. L’étude donne les résultats et l’interprétation d’essais effectués en chambre froide sur des plaques de glace maintenues verticallement dans une presse d’essai et indentés, à différentes vitesses, par un indenteur rectangulaire. Ces plaques carrées de 81 cm de coté étaient congelées et maintenues dans un cadre rigide d’acier de façon à représenter des plaques de glace semi-infinies. Les essais furent effectués à — 10°C avec des taux d’indentation variant de 6 × 10-5 cm/s à 3 cm/s.

La pression nominale d’indentation varie, en fonction des taux de chargement, d’une façon semblable à celle de la résistance ultime de la glace S2 en compression uniaxiale. La pression croit rapidement avec les taux de chargement jusqu’à un maximum correspondant à un taux de déformation de 5 × 10-4 S-1. A partir de ce point, la pression diminue. Dans le domaine ductile et jusqu’à ce maximum, un modèle théorique est proposé où la théorie de Hill (1950) de l’indentation d’un plastique ideal peut s’appliquer pour prédire une pression d’indentation égale à près de trois fois la résistance en compression uniaxiale de la glace.

Les essais n’ont pas montré d’effet géométrique causé par le rapport de la largeur de l’indenteur à l’épaisseur de la glace. Cet effet peut être explique indirectement par l’influence de la géometrie de l’indenteur sur le taux de déformation.

Zusammenfassung

Mechanismus und Theorie der Prägebelastung von Eisplatten. Diese Arbeit enthält die Ergebnisse und die Interpretation von Versuchen in einer Kältekammer an Eisplattcn, die senkrecht in einer Presse gehalten und mit einem rechtwinkligen Stempel unter verschiedenen Geschwindigkeiten eingeprägt wurden. Die quadratischen Platten mit 81 cm Seitenlänge wurden in einem Stahlrahmen gehalten und fest gefroren; sie konnten somit als halb-infinite Eistafeln betrachtet werden. Die Versuche liefen bei — 10°C mit Prägegeschwindigkeiten zwischen 6 × 10-5 cm/s und 3 cm/s.

Es zeigte sich, dass der nominale Prägedruck sich in Abhängigkeit von der Belastungsgeschwindigkeit ändert, und zwar auf eine Weise, die dem Festigkeilsverhalten von S2-Eis bei einachsiger Kompression ähnelt. Der Druck wächst schnell mit der Belastungsgeschwindigkeit an, bis er sein Maximum bei einer Geschwindigkeit von 5 × 10-1 S-1 erreicht. Von da an nimmt der Druck ab. Für den Dehnungsbereich und bis zum Punkt maximalen Druckes wurde ein theoretisches Modell entworfen, in dem die Anwendung der Theorie von Hill (1950) für die Prägung eines ideal plastischen Körpers zur Vorhersage eines Prägedruckes von nahezu der dreifachen Quetschfestigkeit führt.

Die Versuche zeigten keinen sog. “Verhältnis-Effekt”, hervorgerufen durch das Verhältnis zwischen Breite des Prägers und Plattendicke. Dieser Effekt könnte mit dem Einfluss der Form des Prägers auf die Verformungsrate erklärt werden.

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References

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Mechanisms and Theory of Indentation of Ice Plates

  • B. Michel (a1) and N. Toussaint (a1)

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