Th. Lehmann

Einige Bemerkungen zu einer allgemeinen Klasse von Stoffgesetzen für große elasto-plastische Formänderungen

ÜbersichtUnter den üblichen Voraussetzungen der phänomenologischen Plastizitätstheorie großer Formänderungen werden die Formulierungsbedingungen und einige spezielle Formulierungsmöglichkeiten für Fließbedingungen einer ziemlich allgemeinen Klasse erörtert, die isotrope und anisotrope Verfestigung umfaßt. Es schließen sich einige Bemerkungen zur Belastungsbedingung und zum zugehörigen Formänderungsgesetz an.SummaryThe restrictions for the formulation of yield conditions belonging to a rather general class comprehending isotropic and anisotropic hardening and some special cases are discussed under the usual assumptions of the phenomenological theory of plasticity at large deformations. Connected with this some remarks are following on the loading condition and the related stress-strain relations.

On the coupled thermo-mechanical process in the necking problem

Abstract The development of a neck in a uniaxial tension test with circular cross section is influenced by the heat production due to inelastic deformations. The theoretical investigation of this coupled thermomechanical process is based on a constitutive law defined within a general thermodynamical frame. For the numerical solution a finite element method is employed. Theoretical and experimental results are compared.

Some thermodynamical considerations on inelastic deformations including damage processes

SummaryA phenomenological theory of inelastic deformations including damage processes may be based on the fundamental assumption that the body can be considered as a classical continuum and that the principle of uniquely determined local thermodynamical state holds. Within this frame particular balance equations for energy and entropy can be stated describing the interaction between external energy supply and changes of the internal material structure. These balance equations are applied to elastic-plastic deformations including damage processes. The parameters describing the damage state can be considered either as thermodynamical state variables or merely as thermo-mechanical process variables. This distinction leads to different formulations.

Some theoretical considerations and experimental results concerning elastic-plastic stress-strain relations

SummaryWithin the frame of the classical phenomenological theory of plasticity the yield condition and the inelastic stress-strain relations are very restrictively correlated by the so-called normality rule. For certain classes of problems this leads to an unsatisfactory agreement with experimental results. It can be shown how the classical theory can be generalized in a suitable manner without violating the fundamental thermo-dynamical laws in order to obtain a better agreement between theoretical and experimental results in problems with non-proportional loading history.ÜbersichtIm Rahmen der klassischen phänomenologisehen Plastizitätstheorie ist das Formänderungsgesetz, d. h. die Beziehungen zwischen den Spannungs- und den Verzerrungsinkrementen durch die sog. Normalenregel, sehr eng mit der Fließbedingung verknüpft. Bei gewissen Problemen führt dies zu einer unbefriedigenden Übereinstimmung mit experimentellen Befunden. Es wird gezeigt, wie die klassische Theorie in geeigneter Weise verallgemeinert werden kann, ohne zu Widersprüchen im Rahmen der Thermodynamik zu führen. Auf diesem Wege läßt sich eine bessere Übereinstimmung zwischen theoretischen und experimentellen Ergebnissen bei nicht-proportionalen Belastungsprozessen erzielen.

On the description of transient cyclic hardening behaviour of mild steel CK 15

Abstract A series of strain-controlled experiments have been performed on thin-walled tubes made of mild steel CK 15. The experimental program includes uniaxial standard tests such as cyclic straining between fixed strain limits until cyclic stress amplitude saturation, as well as non-standard tests that include prestrain and cyclic mean stress relaxation. In addition, a tension-torsion test program has been designed. Nonradial strain paths of circular, rectangular, and triangular patterns have been examined, and significant extra hardening compared to the uniaxial case occurs. Specifically, the triangular pattern causes peak stresses exceeding the equivalent uniaxial stress amplitude by more than 50%. Furthermore, the v. Mises kinematic and isotropic parts of hardening are quantified by a reliable procedure involving nonlinear regression with the help of which the yield point is determined. On the basis of the experimental knowledge, a plasticity model has been developed that contains a new feature. This is represented by an isotropic memory surface that either expands or shrinks during plastic loading and thus allows for simulating hardening and softening due to high-low loading sequences.

Coupling Phenomena in Thermoplasticity

Abstract Based on classical continuum mechanics and thermodynamics, a general framework is developed for the formulation of a phenomenological theory of large inelastic nonisothermic deformations particularly of elastic-plastic and elastic-viscoplastic bodies. The framework allows also to take into account such phenomena as recrystallization, recovery, aging, and solid phase transformations. The considerations are focused on the interaction of thermic and mechanical processes. This interaction becomes particularly important in those processes which are very sensitive to material behaviour. Processes of this kind are bifurcation problems, e.g. the accumulation of second-order effects in cyclic processes, the generation of residual stresses in single or cyclic deformations, and many others.

Some theoretical considerations and experimental investigations on a constitutive law in thermoplasticity

Abstract Based on classical thermodynamics and restricted to classical continua, a general frame for the formulation of constitutive laws in thermoplasticity is sketched. Within this frame a more particular constitutive law is formulated taking into account large nonisothermal deformations with isotropic and anisotropic (kinematic) hardening, and allowing for certain deviations from the so-called normality rule. The material parameters and functions entering this law are determined for a mild carbon steel by isothermal tension-torsion tests on thin-walled tubes at different temperature levels. The separate knowledge of the influence of deformation rate is investigated since processes with large deformations at higher rates usually are nonisothermal. With respect to cyclic deformations, the given constitutive law has to be generalized.

On the concept of stress-strain relations in plasticity

SummaryIn some cases the plastic stress-strain relations based on the so-called normality rule lead to an unsatisfactory agreement with experimental results. This is particularly true in bifurcation problems or more generally in problems with non-proportional loading paths. Within the frame of a phenomenological theory of non-isothermic large deformations it is shown how plastic stress-strain relations can be modified in order to improve the agreement with the real material behaviour.

Einige Betrachtungen zur Thermodynamik großer elasto-plastischer Formänderungen

ZusammenfassungDer Beitrag bezieht sich auf die phänomenologische Theorie nicht-isothermer, elasto-plastischer Formänderungen unter Beschränkung auf quasistatische, homogene Vorgänge (Elementar-Prozesse). Üblicherweise werden diese Formänderungsvorgänge als thermo-mechanischer Prozeß beschrieben. Sie lassen sich aber auch als thermodynamische Zustandsänderungen darstellen. Der Beitrag behandelt die Unterschiede und die gegenseitigen Beziehungen dieser beiden Beschreibungsweisen.SummaryThis paper deals with the phenomenological theory of non-isothermic, elasto-plastic deformations under restriction to quasi-static, homogeneous processes (elementary processes). Generally such processes are described as thermo-mechanical processes. However they can also be described as variations of the thermodynamic state by means of thermodynamic state variables. This paper analyses the differences and the relations between these two descriptions.

On a generalized constitutive law in thermo-plasticity taking into account different yield mechanisms

SummaryThe classical theory of plasticity cannot explain some phenomena which can be observed in complex loading histories. Therefore it becomes necessary to introduce different yield mechanisms interacting in inelastic deformations. This is particularly true when nonisothermic processes shall be taken into account.In this paper a general mechanical and thermodynamical frame is scetched for the formulation of such generalized constitutive laws based on previous papers. Within this frame a fundamental scheme is developed for a constitutive law of an elastic-plastic body with two different yield mechanisms. A simplified version is applied in order to explain the appearence of concave yield surfaces which may be obtained after total unloading.