Abstract
In the paper the description of the postcritical behaviour of dissipative solids is presented. A simple model of an elastic-viscoplastic material with internal imperfections is proposed. This model is justified by physical mechanisms of polycrystalline matter flow in some regions of temperature and strain rate changes.
A model proposed satisfies the requirement that during the deformation process in which the effective strain rate is equal to the assumed static value the response of a material becomes elastic-plastic.
The identification procedure for all material functions and constants are based on available experimental data. Both the mechanical test data and physical, metallurgical observations are used. As an example of a quasi-static, isothermal flow process the boundary-initial-value problem describing the necking phenomenon is considered. The problem is formulated in such a way that enables discussion of the influence of strain rate effects, as well as of imperfection and diffusion effects on the onset of localization. Comparison of theoretical predictions with available experimental results is given.
Zusammenfassung
In der vorliegenden Arbeit wird das nachkritische Verhalten von Festkörpern mit innerer Reibung beschrieben. Ein einfaches Modell eines elastisch-viskoplastischen Materials mit Strukturfehlern wird vorgeschlagen. Dieses Modell ist gerechtfertigt durch die Fließmechanismen in polykristallinem Material, die in gewissen Bereichen von Temperatur und Dehnungsgeschwindigkeiten auftreten.
Das vorgeschlagene Modell erfüllt die Forderung, daß sich ein Material während eines Deformationsvorganges, bei dem die effektive Dehnungsgeschwindigkeit gleich dem statistischen Wert angenommen wird, elastisch-plastisch verhält.
Für die Materialfunktionen und -konstanten werden sowohl mechanische Experimente wie auch metallurgische Beobachtungen berücksichtigt. Als Beispiel für einen quasistatischen, isothermen Fließvorgang wird das Rand- und Anfangswertproblem benützt, welches die Einschnürung bei einem Zugversuch beschreibt. Das Problem ist in einer Art und Weise formuliert, die es erlaubt, den Einfluß von Dehnungsgeschwindigkeiten, Strukturfehlern und Diffusion auf den Beginn der Lokalisierung zu diskutieren. Die theoretischen Voraussagen werden mit vorhandenen Resultaten aus Experimenten verglichen.
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Perzyna, P. Stability of flow processes for dissipative solids with internal imperfections. Z. angew. Math. Phys. 35, 848–867 (1984). https://doi.org/10.1007/BF00945448
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DOI: https://doi.org/10.1007/BF00945448