Anisotrope plastische Formänderungen

Lehmann, Th.

doi:10.1007/bf02096162

Cited by 43 publications

(23 citation statements)

References 9 publications

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“…This value, according to [3,4,9,43], is likely to be small when compared to U p (plastic part of internal energy) or A p . To calculate anergy, the change in the yield point for austenitic steel 00H19N17Pr with the temperature, see expression (4.4), is required and the authors unfortunately do not have such data.…”

Section: Discussionmentioning

confidence: 99%

“…If the description is restricted to such changes in internal structure that are always accompanied by plastic deformation on a macroscopic scale, then the above quantity may also be termed "the reversible heat of plastic deformation," see [3,4,9,43]. The term Ts p is according to [3,4,9,43] likely to be small when compared to U p (plastic part of internal energy) or A p and the assumption s p ∼ = 0 may be regarded as considerably small from the point of view of applied thermoplasticity. In physical terms it means that entropy of elasto-plastic body is comparable to that of purely elastic body [3,4,9,43].…”

Section: Procedures Of Deriving the Thermodynamic Potentialmentioning

confidence: 99%

“…The term Ts p is according to [3,4,9,43] likely to be small when compared to U p (plastic part of internal energy) or A p and the assumption s p ∼ = 0 may be regarded as considerably small from the point of view of applied thermoplasticity. In physical terms it means that entropy of elasto-plastic body is comparable to that of purely elastic body [3,4,9,43]. In general, the higher the term Ts p , the higher is sensitivity of internal thermodynamic forces π to temperature, see (3.11).…”

Section: Procedures Of Deriving the Thermodynamic Potentialmentioning

confidence: 99%

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Thermodynamic potential of free energy for thermo-elastic-plastic body

Śloderbach

Pająk

2017

Continuum Mech. Thermodyn.

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The procedure of derivation of thermodynamic potential of free energy (Helmholtz free energy) for a thermo-elastic-plastic body is presented. This procedure concerns a special thermodynamic model of a thermo-elastic-plastic body with isotropic hardening characteristics. The classical thermodynamics of irreversible processes for material characterized by macroscopic internal parameters is used in the derivation. Thermodynamic potential of free energy may be used for practical determination of the level of stored energy accumulated in material during plastic processing applied, e.g., for industry components and other machinery parts received by plastic deformation processing. In this paper the stored energy for the simple stretching of austenitic steel will be presented. KeywordsFree energy · Thermo-elastic-plastic body · Enthalpy · Exergy · Stored energy of plastic deformations · Mechanical energy dissipation · Thermodynamic reference state

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Section: Discussionmentioning

confidence: 99%

Section: Procedures Of Deriving the Thermodynamic Potentialmentioning

confidence: 99%

Section: Procedures Of Deriving the Thermodynamic Potentialmentioning

confidence: 99%

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Thermodynamic potential of free energy for thermo-elastic-plastic body

Śloderbach

Pająk

2017

Continuum Mech. Thermodyn.

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“…This implies that the invariants of the stress tensor should be stationary, too. Applying this "stationary condition" 38 to the above introduced stress rates, Prager argued that the convected (non-corotational) rates presented with the Oldroyd rates (51) and (52) and the Truesdell rate (54) could not be recommended as these rates do not imply stationarity of the stress invariants.…”

Section: Wwwzamm-journalorgmentioning

confidence: 99%

“…However, the foundation of this classical theory was shaken by an unexpected discovery of spurious phenomena known as shear oscillations. It seems that Lehmann [38] 39 was the first to reveal that a rigid plastic J 2 -flow theory with kinematic hardening would predict an oscillating shear stress response to monotonically progressing simple shearing (refer to Fig. 3).…”

Section: Wwwzamm-journalorgmentioning

confidence: 99%

The Prandtl‐Reuss equations revisited

Bruhns

2013

Z Angew Math Mech

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At the beginning of the last century two different types of constitutive relations to describe the complex behavior of elastoplastic material were presented. These were the deformation theory originally developed by Hencky and the Prandtl-Reuss theory. Whereas the former provides a direct solid-like relation of stress as function of strain, the latter has been based on an additive composition of elastic and plastic parts of the increments of strains. These in turn were taken as a solid-and fluid-like combination of the de Saint-Venant/Lévy theory with an incremental form of Hookes law.Even nowadays this Prandtl-Reuss theory is still accepted within the restriction of small elastic deformations, i.e. it is generally stated in most textbooks on plasticity that this theory due to a number of defects can not be applied to large deformations. In the present article it is shown that this restrictive statement may be no longer true. Introducing a specific objective time derivative it could be shown that these defects disappear.

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Fließbedingung für Thermoplaste. Teil II: Isotrope Fließbedingung

Schlimmer

1980

Materialwissenschaft Werkst

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Ausgehend vom plastischen Potential fur anisotrope Werkstoffe. das im Teil I*" dieser Arbeit untersucht wurde, ist eine isotrope FlieRbedingung hergeleitet und mit experimentellen Ergebnissen vcrglichen. Yield criterion for thermoplastics part 11: Isotropic Yield CriterionUsing the plastic potential for anisotropic solids which have been investigated in the first part** of this paper, a isotropic yield criterion is derived and compared with experimental results. Plastisches Potential und FlieBbedingung bei lsotropieWenn der Anisotropietensor Alikl und der . , Bauschinger-Tensor" qj in ( 5 ) als isotrope Tensoren angesetzt werden, folgt als Sonderfall des anisotropen Werkstoffverhaltens ein plastisches Potential bei Isotropie. Dazu wird in Anlehnung an die lineare Elastizitatstheorie Aiikl als Linearkombination des Kugeltensors (Eins-oder Substitutionstensor) geschrieben [16]:Entsprechend folgt fur den Tensor zweiter Stufe: q, = as,,. (27) Mit (26) und (27) erhalt man aus (5) das plastische Potential bei Isotropie (28) 1 2Spannung a einen ,isotropen Bauschinger-Effekt", d. h. untcrschiedliche FlieRgrenzen gegeniiber Zugund Druckbeanspruchung be1 Isotropie reguhert. In (28) sind J l die lineare und J2 die quadratische Invariante des Spannungstensors: 1 Ji = ~q611, J2 = 2 (ffqoq -G~J . (29 a, b) Bei Isotropie kann das plastische Potentialdargestellt in den Invarianten des Spannungstensorsgetrennt nach gestaltund volumenandernden Anteilen angegeben werden. Mit dem Spannungsdeviator * Mitteilung aus dcm Institut fur Werkstoffkunde A der RWTH Aachen. 'Icil list erschienen in Heft 10/1980. * * und der quadratischen Invarianten des Spannungsdeviators folgt aus (2) und (28) die isotrope FlieBbedingung Ji = k i ( l -klJ1 + k,J:) (32) mit der SchubflieBgrenze k". Im Vergleich zu (28) und unter Berucksichtigung von (2), (30) sowie (32) ergeben sich die Idenditaten: k i ( l + 3 c a 2 B ) = const., kl = -a/3. k2 = -p/6; (33) G1. (32) stellt eine parabolische Abhangigkeit der quadratischen Invarianten J \ des Spannungsdeviators von der linearen Invarianten des Spannungstensors J1, d . h. voni hydrostatischen Spannungszustand dar, auf die Mises [14] allgemein hingewiesen und die Schleicher [23] in einer der G1. (32) ahnlichen FlieBbedingung berucksichtigt hat. Diese nichtlineare Abhangigkeit ergibt sich nun, wie die Herleitung von (32) aus dem plastischen Potential (3) zeigt. allein durch die bei Anisotropic und plastischer Kornpressibilitat zur Beschreibung des Bauschingeu-Effekts bzw. unterschiedlicher plastischer Verformungsmechanismen bei FlieRbeginn gegenuber Zugund Druckbeanspruchung eingefuhrten (fiktiven) Spannungen a,,. Aus der FlieUbedingung (32) geht unmittelbar hervor, daR fur plastisch inkompressibles Werkstoffverhalten kl = k2 E 0 (34) gelten muR. Danach kann bei Gultigkeit der getroffenen Voraussetzungen (Gl. 5) ein Werkstoff, dessen plastisches Volumen sich wahrend der Verformung nicht andert, kein unterschiedliches Verhalten gegenuber Zug-und Druckbeanspruchung zeigen. Mit (34) erhalt man aus (32) die quadratisc...

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Anisotrope plastische Formänderungen

Cited by 43 publications

References 9 publications

Thermodynamic potential of free energy for thermo-elastic-plastic body

Thermodynamic potential of free energy for thermo-elastic-plastic body

The Prandtl‐Reuss equations revisited

Fließbedingung für Thermoplaste. Teil II: Isotrope Fließbedingung

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