Udo Gamer

Elastic-plastic deformation of the rotating solid disk

SummaryThe plane state of stress in a rotating circular disk of elastic-plastic material with linear strain hardening is studied based on Trescas yield condition and its associated flow rule. The plastic core consists of two parts with different forms of the yield condition. By specializing the results to perfectly plastic material, the usual statically determinate stress distribution is recovered but, since the plastic strain at the axis becomes infinite, these stresses are not meaningful.ÜbersichtDer ebene Spannungszustand in einer rotierenden Kreisscheibe aus elastisch-plastischem Werkstoff mit linearer Verfestigung wird berechnet unter Zugrundelegung der Trescaschen Fließbedingung und der zugehörigen Fließregel. Der plastische Kern setzt sich zusammen aus zwei Teilen, in denen die Mießbedingung verschiedene Formen annimmt. Durch Grenzwertbildung werden die Ergebnisse auf idealplastisches Verhalten spezialisiert; man findet die übliche statisch bestimmte Spannungsverteilung. Da diese aber mit unbeschränkten plastischen Dehnungen an der Scheibenachse verbunden ist, können die Spannungen nicht sinnvoll sein.

Rotating elastic-plastic solid shaft with fixed ends

Abstract Based on Trescas yield condition and the flow rule associated with it, the distribution of stress, strain, and displacement in a rotating elastic-perfectly plastic solid cylinder with fixed ends is discussed. Special attention is paid to the behavior in the fully plastic state.

The shrink fit with elastic-plastic hub exhibiting constant yield stress followed by hardening

Abstract The subject of the investigation is the distribution of stress, displacement and plastic strain in a rotating shrink fit, the hub material of which undergoes plastic deformation with constant stress up to a certain plastic strain and linear hardening for larger strain.

A theory of rotating elasto-plastic shrink fits

SummaryThe paper gives a rigorous theory of rotating elasto-plastic shrink fits under the assumptions of infinitesimal strain, ideal plasticity and validity of Trescas yield condition. The plastic strain increments are computed by the associated flow rule. Furthermore, it is assumed that the shaft remains purely elastic during the entire loading history. It is shown that, below a limit speed, the plastic deformation is governed by one side of the Tresca hexagon only. Beyond this speed, a second face of Trescas hexagon becomes involved. In this case plastic prestrains accumulated below the limit speed have to be considered. For both speed regimes, solutions comprising stresses and radial displacement are obtained. Finally a numerical example is given.übersichtDer Aufsatz gibt eine exakte Theorie des rotierenden elasto-plastischen Preßverbandes unter den Voraussetzungen infinitesimaler Verzerrungen, idealer Plastizität und der Gültigkeit der Trescaschen Fließbedingung. Die plastischen Dehnungsinkremente werden nach der zugeordneten Fließregel berechnet. Ferner wird vorausgesetzt, daß die Welle während der vollständigen Belastungsgeschichte rein elastisch bleibt. Es wird gezeigt, daß unterhalb einer Grenzdrehzahl die plastische Deformation von nur einer Seite des Trescaschen Sechsecks bestimmt wird. Oberhalb dieser Drehzahl wird eine zweite Seite des Trescaschen Sechsecks beteiligt. In diesem Fall müssen plastische Vordehnungen berücksichtigt werden, die unterhalb der Grenzdrehzahl entstanden. Für beide Drehzahlbereiche werden Lösungen abgeleitet, welche Spannungen und Radialverschiebung umfassen. Schließlich wird ein numerisches Beispiel angegeben.

A concise treatment of the shrink fit with elastic-plastic hub

Abstract Based on Trescas yield criterion and the associated flow rule, the distribution of stress and displacement in a shrink fit consisting of a solid elastic shaft and an elastic-plastic hub with nonlinear isotropic hardening is derived. Since the stresses are expressed in terms of the equivalent plastic strain, the distinction between plastic and elastic regions of the hub lapses.

Dynamic stress concentration in an elastic half space with a semi-circular cavity excited by SH waves

Abstract Subject of the investigation is the stress distribution and the dynamic stress concentration factor at the surface of a semi-circular cavity in a half space excited by plane harmonic SH waves. Using wave function expansion for the incident wave and the reflected waves, a closed form solution is obtained. Numerical results are represented graphically.

STRESS DISTRIBUTION IN AN ELASTIC PLASTIC DISK SUBJECTED TO A CIRCULAR HEAT SOURCE

Abstract Stress distribution in a perfectly plastic disk caused by a circular heat source of constant output is investigated. It is shown that, dependent on the ratio of the radius of the disk to the radius of the heat source, Trescas yield condition assumes different forms. In certain cases, the plastic zone is composed of two parts associated with different branches of the yield condition. The critical time for avoiding secondary plastic flow is discussed.

Ein Beitrag zur Spannungsermittlung in Querpreßverbänden

ÜbersichtDer ebene Spannungszustand in einem Kreisring aus elastisch-plastischem Material mit linearer Verfestigung unter Außendruck wird untersucht. Die Anwendung der Ergebnisse auf den Querpreßverband schließt sich an.SummaryThe plane state of stress in a circular ring of elastic plastic material with linear hardening due to external pressure is studied. There follows the application of the results to a shrink fit.

Der elastisch-plastische Querpreßverband bei verschiedenen Fließgrenzen von Innen-und Außenteil

ZusammenfassungGegenstand der Untersuchung sind die Bedingungen für die Plastizierung des Innenteils eines idealplastischen Preßverbands. Dieses unerwünschte Ereignis kann eintreten, wenn die Fließgrenze des Innenteils kleiner als diejenige des Außenteils ist.

Elastic-plastic deformation of a centrally heated disk

The subject of this investigation is stress, displacement, and plastic strain in a centrally heated elastic‐plastic disk. The material is assumed to obey Trescas yield criterion and its associated flow rule and to exhibit linear strain hardening. Due to the loading under consideration, plastic flow sets in at the center of the disk in a “corner-regime” of Trescas hexagon, and, as in related cases, the plastic core is composed of two parts, the outer lying in a “side-regime.” For a special hardening parameter, explicit expressions for stress, displacement, and plastic strain are derived. With increasing core temperature, a second plastic zone forms at the edge of the disk.