How to Realize Volume Conservation During Finite Plastic Deformation

Volume conservation during plastic deformation is the most important feature and should be realized in elastoplastic theories. However, it is found in this paper that an elastoplastic theory is not volume conserved if it improperly sets an arbitrary plastic strain rate tensor to be deviatoric. We discuss how to rigorously realize volume conservation in finite strain regime, especially when the unloading stress free configuration is not adopted in the elastoplastic theories. An accurate condition of volume conservation is first clarified and used in this paper that the density of a volume element after the applied loads are completely removed should be identical to that of the initial stress free states. For the elastoplastic theories that adopt the unloading stress free configuration (i.e., the intermediate configuration), the accurate condition of volume conservation is satisfied only if specific definitions of the plastic strain rate are used among many other different definitions. For the elastoplastic theories that do not adopt the unloading stress free configuration, it is even more difficult to realize volume conservation as the information of the stress free configuration lacks. To find a universal approach of realizing volume conservation for elastoplastic theories whether or not adopt the unloading stress free configuration, we propose a single assumption that the density of material only depends on the trace of the Cauchy stress by using their objectivities. Two strategies are further discussed to satisfy the accurate condition of volume conservation: directly and slightly revising the tangential stiffness tensor or using a properly chosen stress/strain measure and elastic compliance tensor. They are implemented into existing elastoplastic theories, and the volume conservation is demonstrated by both theoretical proof and numerical examples. The potential application of the proposed theories is a better simulation of manufacture process such as metal forming.

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Multiscale modeling of plastic deformation of molybdenum and tungsten. III. Effects of temperature and plastic strain rate

Acta Materialia ◽

10.1016/j.actamat.2008.07.027 ◽

2008 ◽

Vol 56 (19) ◽

pp. 5426-5439 ◽

Cited By ~ 69

Author(s):

R. Gröger ◽

V. Vitek

Keyword(s):

Plastic Deformation ◽

Plastic Strain ◽

Strain Rate ◽

Multiscale Modeling ◽

Plastic Strain Rate ◽

Effects Of Temperature ◽

And Tungsten

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Evaluation of Associated and Non-Associated Flow Metal Plasticity; Application for DC06 Deep Drawing Steel

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.504-506.661 ◽

2012 ◽

Vol 504-506 ◽

pp. 661-666 ◽

Cited By ~ 1

Author(s):

Mohsen Safaei ◽

Wim De Waele ◽

Shun Lai Zang

Keyword(s):

Finite Element ◽

Plastic Strain ◽

Strain Rate ◽

Yield Stress ◽

Deep Drawing ◽

Kinematic Hardening ◽

Plastic Strain Rate ◽

Flow Rule ◽

Strain Rate Tensor ◽

Incremental Change

In this paper the capabilities of Associated Flow Rule (AFR) and non-AFR based finite element models for sheet metal forming simulations is investigated. In case of non-AFR, Hill’s quadratic function used as plastic potential function, makes use of plastic strain ratios to determine the direction of effective plastic strain rate. In addition, the yield function uses direction dependent yield stress data. Therefore more accurate predictions are expected in terms of both yield stress and strain ratios at different orientations. We implemented a modified version of the non-associative flow rule originally developed by Stoughton [1] into the commercial finite element code ABAQUS by means of a user material subroutine UMAT. The main algorithm developed includes combined effects of isotropic and kinematic hardening [2]. This paper assumes proportional loading cases and therefore only isotropic hardening effect is considered. In our model the incremental change of plastic strain rate tensor is not equal to the incremental change of the compliance factor. The validity of the model is demonstrated by comparing stresses and strain ratios obtained from finite element simulations with experimentally determined values for deep drawing steel DC06. A critical comparison is made between numerical results obtained from AFR and non-AFR based models

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Closed system of coupling effects in generalized thermo-elastoplasticity

International Journal of Applied Mechanics and Engineering ◽

10.1515/ijame-2016-0028 ◽

2016 ◽

Vol 21 (2) ◽

pp. 461-483 ◽

Cited By ~ 3

Author(s):

Z. Śloderbach

Keyword(s):

Plastic Strain ◽

Strain Rate ◽

Plastic Flow ◽

Yield Surface ◽

Plastic Strain Rate ◽

Generalized Function ◽

Strain Rate Tensor ◽

Field Equations ◽

Coupling Effects ◽

Thermodynamic Forces

Abstract In this paper, the field equations of the generalized coupled thermoplasticity theory are derived using the postulates of classical thermodynamics of irreversible processses. Using the Legendre transformations two new thermodynamics potentials P and S depending upon internal thermodynamic forces Π are introduced. The most general form for all the thermodynamics potentials are assumed instead of the usually used additive form. Due to this assumption, it is possible to describe all the effects of thermomechanical couples and also the elastic-plastic coupling effects observed in such materials as rocks, soils, concretes and in some metalic materials. In this paper not only the usual postulate of existence of a dissipation qupotential (the Gyarmati postulate) is used to derive the velocity equation. The plastic flow constitutive equations have the character of non-associated flow laws even when the Gyarmati postulate is assumed. In general formulation, the plastic strain rate tensor is normal to the surface of the generalized function of plastic flow defined in the the space of internal thermodynamic forces Π but is not normal to the yield surface. However, in general formulation and after the use the Gyarmati postulate, the direction of the sum of the plastic strain rate tensor and the coupled elastic strain rate tensor is normal to the yield surface.

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Slow plastic strain rate compressive flow in binary CoAl intermetallics

Materials Science and Engineering ◽

10.1016/0025-5416(85)90298-8 ◽

1985 ◽

Vol 73 ◽

pp. 87-96 ◽

Cited By ~ 30

Author(s):

J. Daniel Whittenberger

Keyword(s):

Plastic Strain ◽

Strain Rate ◽

Plastic Strain Rate ◽

Compressive Flow

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An Experimental Study on the Effect of Prior Plastic Straining on Creep Behavior of 304 Stainless Steel

Journal of Engineering Materials and Technology ◽

10.1115/1.2904207 ◽

1993 ◽

Vol 115 (2) ◽

pp. 200-203 ◽

Cited By ~ 11

Author(s):

Z. Xia ◽

F. Ellyin

Keyword(s):

Stainless Steel ◽

Plastic Strain ◽

Strain Rate ◽

Creep Behavior ◽

Test Procedure ◽

Constant Strain Rate ◽

304 Stainless Steel ◽

Creep Model ◽

Plastic Strain Rate ◽

Creep Tests

Constant strain-rate plastic straining followed by creep tests were conducted to investigate the effect of prior plastic straining on the subsequent creep behavior of 304 stainless steel at room temperature. The effects of plastic strain and plastic strain-rate were delineated by a specially designed test procedure, and it is found that both factors have a strong influence on the subsequent creep deformation. A creep model combining the two factors is then developed. The predictions of the model are in good agreement with the test results.

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An Assessment of the Method Used to Determine Activation Parameters in L12 Alloys

MRS Proceedings ◽

10.1557/proc-552-kk9.12.1 ◽

1998 ◽

Vol 552 ◽

Cited By ~ 2

Author(s):

B. Matterstock ◽

G. Saada ◽

J. Bonneville ◽

J. L Martin

Keyword(s):

Mechanical Properties ◽

Theoretical Analysis ◽

Plastic Strain ◽

Strain Rate ◽

Characteristic Time ◽

Constant Strain Rate ◽

Activation Parameters ◽

Plastic Strain Rate ◽

Clear Indication ◽

Load Relaxation

ABSTRACTThe characterisation of dislocation mechanisms in connection with macroscopic mechanical properties are usually performed through transient tests, such as strain-rate jumps, load relaxations or creep experiments. The present paper includes a careful and complete theoretical analysis of the relaxation and the creep kinetics. We experimentally show that the plastic strain-rate is continuous at the transition between constant strain-rate conditions and both load relaxation and creep test. The product of the plastic strain-rate at the onset of the transient test () with the characteristic time (tk) of the transient is found to be independent of , as theoretically expected. This is a clear indication that the assumptions underlying the theoretical analysis are relevant.

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Calculation of Material Flow in Orthogonal Cutting by Using Streamline Model

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.407-408.490 ◽

2009 ◽

Vol 407-408 ◽

pp. 490-493 ◽

Cited By ~ 2

Author(s):

Xue Feng Bi ◽

Gautier List ◽

Yong Xian Liu

Keyword(s):

Plastic Strain ◽

Strain Rate ◽

Line Shape ◽

Material Flow ◽

General Equation ◽

Flow Line ◽

Orthogonal Cutting ◽

Plastic Strain Rate ◽

Complex Variation ◽

Streamline Method

The streamline method was used to investigate the plastic strain rate in machining. The streamline function presented in this paper is a general equation with three parameters controlling the complex variation of flow line shape. Velocity and deformation field were obtained by streamline analysis. The validation of this model was conducted by comparing with other experimental results published. It shows that the streamline model presented in the paper can be applied to the evaluation of strain rate in machining.

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