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Title: A finite strain isotropic/kinematic hardening model for springback simulation of sheet metals

Abstract

Crucial for the accurate prediction of the blank springback is the use of an appropriate material model, which is capable of modelling the typical cyclic hardening behaviour of metals (e.g. Bauschinger effect, ratchetting). The proposed material model combines both nonlinear isotropic hardening and nonlinear kinematic hardening, and is defined in the finite strain regime. The kinematic hardening component represents a continuum extension of the classsical rheological model of Armstrong-Frederick kinematic hardening. The evolution equations of the model are integrated by a new form of the exponential map algorithm, which preserves the plastic volume and the symmetry of the internal variables. Finally, the applicability of the model for springback prediction has been demonstrated by performing simulations of the draw-bending process.

Authors:
;  [1]
  1. Institute of Solid Mechanics, Braunschweig University of Technology, D-38106 Braunschweig (Germany)
Publication Date:
OSTI Identifier:
21056996
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 907; Journal Issue: 1; Conference: 10. ESAFORM conference on material forming, Zaragoza (Spain), 18-20 Apr 2007; Other Information: DOI: 10.1063/1.2729501; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ALLOYS; BENDING; COMPUTERIZED SIMULATION; HARDENING; METALS; NONLINEAR PROBLEMS; NUMERICAL ANALYSIS; PLASTICITY; STRAINS; SYMMETRY

Citation Formats

Vladimirov, Ivaylo N., and Reese, Stefanie. A finite strain isotropic/kinematic hardening model for springback simulation of sheet metals. United States: N. p., 2007. Web. doi:10.1063/1.2729501.
Vladimirov, Ivaylo N., & Reese, Stefanie. A finite strain isotropic/kinematic hardening model for springback simulation of sheet metals. United States. doi:10.1063/1.2729501.
Vladimirov, Ivaylo N., and Reese, Stefanie. Sat . "A finite strain isotropic/kinematic hardening model for springback simulation of sheet metals". United States. doi:10.1063/1.2729501.
@article{osti_21056996,
title = {A finite strain isotropic/kinematic hardening model for springback simulation of sheet metals},
author = {Vladimirov, Ivaylo N. and Reese, Stefanie},
abstractNote = {Crucial for the accurate prediction of the blank springback is the use of an appropriate material model, which is capable of modelling the typical cyclic hardening behaviour of metals (e.g. Bauschinger effect, ratchetting). The proposed material model combines both nonlinear isotropic hardening and nonlinear kinematic hardening, and is defined in the finite strain regime. The kinematic hardening component represents a continuum extension of the classsical rheological model of Armstrong-Frederick kinematic hardening. The evolution equations of the model are integrated by a new form of the exponential map algorithm, which preserves the plastic volume and the symmetry of the internal variables. Finally, the applicability of the model for springback prediction has been demonstrated by performing simulations of the draw-bending process.},
doi = {10.1063/1.2729501},
journal = {AIP Conference Proceedings},
number = 1,
volume = 907,
place = {United States},
year = {Sat Apr 07 00:00:00 EDT 2007},
month = {Sat Apr 07 00:00:00 EDT 2007}
}
  • Sheet metal forming processes invariably involve non-proportional loading and changes in deformation/loading direction, resulting in a very complex material and structural behaviour. Much of this complexity can be traced back to the reaction of the material microstructure to such loading. In the case of hardening behaviour, for example, the interplay between the direction of inelastic deformation, the orientation of dislocation structures, and the current deformation/loading direction, plays an important role. The purpose of the current work is the formulation, numerical implementation and application of a thermodynamically-consistent material model for anisotropic hardening in such materials taking this interplay into account. Direction-more » and orientation-dependent quantities are represented in the model with the help of evolving structure tensors. These include the strength of dislocation structures, dislocation polarization, and kinematic hardening. Together with the initial texture-based inelastic flow anisotropy, these govern the evolving anisotropic response of the model to changes in loading direction. To exemplify this, the behaviour of the model subject to typical two-stage loading histories involving monotonic, reversing and orthogonal changes in loading/deformation direction are investigated for various parameter values. These simulations demonstrate clearly the effect of severe and abrupt changes in deformation/loading direction on the hardening behaviour and so on the resulting springback process.« less
  • In this paper, we discuss the application of a newly developed coupled material model of finite anisotropic multiplicative plasticity and continuum damage to the numerical prediction of the forming limit diagram at fracture (FLDF). The model incorporates Hill-type plastic anisotropy, nonlinear Armstrong-Frederick kinematic hardening and nonlinear isotropic hardening. The numerical examples examine the simulation of forming limit diagrams at fracture by means of the so-called Nakajima stretching test. Comparisons with experimental data for aluminium sheets show a good agreement with the finite element results.
  • In this paper the application of a crystal plasticity model for body-centered cubic crystals in the simulation of a sheet metal forming process is discussed. The material model parameters are identified by a combination of a texture approximation procedure and a conventional parameter identification scheme. In the application of a cup drawing process the model shows an improvement of the strain and earing prediction as well as the qualitative springback results in comparison with a conventional phenomenological model.
  • Characterization of material hardening behavior has been investigated by many researchers in the past decades. Experimental investigation of thin sheet metals under cyclic loading has become a challenging issue. A new test fixture has been developed to use with a regular tensile-compression machine (for example, MTS machine). Experimental results of tension-compression tests are presented followed by a review of existing testing methods. Numerical modeling of the tested data is presented using a new kinematic hardening model.
  • The constitutive modeling of the materials' mechanical behavior, usually carried out using a phenomenological constitutive model, i.e., a yield criterion associated to the isotropic and kinematic hardening laws, is of paramount importance in the FEM simulation of the sheet metal forming processes, as well as in the springback prediction. Among others, the kinematic behavior of the yield surface plays an essential role, since it is indispensable to describe the Bauschinger effect, i.e., the materials' answer to the multiple tension-compression cycles to which material points are submitted during the forming process. Several laws are usually used to model and describe themore » kinematic hardening, namely: a) the Prager's law, which describes a linear evolution of the kinematic hardening with the plastic strain rate tensor b) the Frederick-Armstrong non-linear kinematic hardening, basically a non-linear law with saturation; and c) a more advanced physically-based law, similar to the previous one but sensitive to the strain path changes. In the present paper a mixed kinematic hardening law (linear + non-linear behavior) is proposed and its implementation into a static fully-implicit FE code is described. The material parameters identification for sheet metals using different strategies, and the classical Bauschinger loading tests (i.e. in-plane forward and reverse monotonic loading), are addressed, and their impact on springback prediction evaluated. Some numerical results concerning the springback prediction of the Numisheet'05 Benchmark no. 3 are briefly presented to emphasize the importance of a correct modeling and identification of the kinematic hardening behavior.« less