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Håkan Hallberg - One of the best experts on this subject based on the ideXlab platform.

  • Diagonally implicit Runge–Kutta (DIRK) integration applied to finite strain crystal Plasticity modeling
    Computational Mechanics, 2018
    Co-Authors: Sally Issa, Mathias Wallin, Matti Ristinmaa, Håkan Hallberg
    Abstract:

    Diagonally implicit Runge–Kutta methods (DIRK) are evaluated and compared to standard solution procedures for finite strain crystal Plasticity boundary value problems. The structure of the DIRK implementation is similar to that of a conventional implicit backward Euler scheme. It is shown that only very small modifications are required in order to transform the numerical scheme from one into the other. This similarity permits efficient adaption of the integration procedure to a particular problem. To enforce Plastic incompressibility, different projection techniques are evaluated. Rate dependent crystal Plasticity, using a single crystal is simulated under various load cases as well as a larger polycrystalline sample. It is shown that the two-stage DIRK scheme combined with a step size control and a time continuous projection technique for the update of the Plastic Deformation Gradient is in general more accurate than the implicit backward Euler and an update based on exponential mapping.

  • Diagonally implicit Runge–Kutta (DIRK) integration applied to finite strain crystal Plasticity modeling
    Computational Mechanics, 2018
    Co-Authors: Sally Issa, Mathias Wallin, Matti Ristinmaa, Håkan Hallberg
    Abstract:

    Diagonally implicit Runge–Kutta methods (DIRK) are evaluated and compared to standard solution procedures for finite strain crystal Plasticity boundary value problems. The structure of the DIRK implementation is similar to that of a conventional implicit backward Euler scheme. It is shown that only very small modifications are required in order to transform the numerical scheme from one into the other. This similarity permits efficient adaption of the integration procedure to a particular problem. To enforce Plastic incompressibility, different projection techniques are evaluated. Rate dependent crystal Plasticity, using a single crystal is simulated under various load cases as well as a larger polycrystalline sample. It is shown that the two-stage DIRK scheme combined with a step size control and a time continuous projection technique for the update of the Plastic Deformation Gradient is in general more accurate than the implicit backward Euler and an update based on exponential mapping.

Sally Issa - One of the best experts on this subject based on the ideXlab platform.

  • Diagonally implicit Runge–Kutta (DIRK) integration applied to finite strain crystal Plasticity modeling
    Computational Mechanics, 2018
    Co-Authors: Sally Issa, Mathias Wallin, Matti Ristinmaa, Håkan Hallberg
    Abstract:

    Diagonally implicit Runge–Kutta methods (DIRK) are evaluated and compared to standard solution procedures for finite strain crystal Plasticity boundary value problems. The structure of the DIRK implementation is similar to that of a conventional implicit backward Euler scheme. It is shown that only very small modifications are required in order to transform the numerical scheme from one into the other. This similarity permits efficient adaption of the integration procedure to a particular problem. To enforce Plastic incompressibility, different projection techniques are evaluated. Rate dependent crystal Plasticity, using a single crystal is simulated under various load cases as well as a larger polycrystalline sample. It is shown that the two-stage DIRK scheme combined with a step size control and a time continuous projection technique for the update of the Plastic Deformation Gradient is in general more accurate than the implicit backward Euler and an update based on exponential mapping.

  • Diagonally implicit Runge–Kutta (DIRK) integration applied to finite strain crystal Plasticity modeling
    Computational Mechanics, 2018
    Co-Authors: Sally Issa, Mathias Wallin, Matti Ristinmaa, Håkan Hallberg
    Abstract:

    Diagonally implicit Runge–Kutta methods (DIRK) are evaluated and compared to standard solution procedures for finite strain crystal Plasticity boundary value problems. The structure of the DIRK implementation is similar to that of a conventional implicit backward Euler scheme. It is shown that only very small modifications are required in order to transform the numerical scheme from one into the other. This similarity permits efficient adaption of the integration procedure to a particular problem. To enforce Plastic incompressibility, different projection techniques are evaluated. Rate dependent crystal Plasticity, using a single crystal is simulated under various load cases as well as a larger polycrystalline sample. It is shown that the two-stage DIRK scheme combined with a step size control and a time continuous projection technique for the update of the Plastic Deformation Gradient is in general more accurate than the implicit backward Euler and an update based on exponential mapping.

Heung Nam Han - One of the best experts on this subject based on the ideXlab platform.

  • Crystal Plasticity finite element modeling of mechanically induced martensitic transformation (MIMT) in metastable austenite
    US, 2018
    Co-Authors: Mg Lee, Sj Kim, Heung Nam Han
    Abstract:

    A new crystal Plasticity model incorporating the mechanically induced martensitic transformation in metastable austenitic steel has been formulated and implemented into the finite element analysis. The kinetics of martensite transformation is modeled by taking into consideration of a nucleation-controlled phenomenon, where each potential martensitic variant based on Kurdjumov-Sachs (KS) relationship has different nucleation probability as a function of the interaction energy between externally applied stress and lattice Deformation. Therefore, the transformed volume fractions are determined following selective variants given by the crystallographic orientation of austenitic matrix and applied stress in the frame of the crystal Plasticity finite element. The developed finite element program is capable of considering the effect of volume change by the Bain Deformation and the lattice-invariant shear during the martensitic transformation by effectively modifying the evolution of Plastic Deformation Gradient of the conventional rate-dependent crystal Plasticity finite element. The validation of the proposed model has been carried out by comparing with the experimentally measured data under simple loading conditions. Good agreements with the measurements for the stress-strain responses, transformed martenstic volume fractions and the influence of strain rate on the Deformation behavior will enable the model to be promising for the future applications to the real forming process of the TRIP aided steel. (C) 2009 Elsevier Ltd. All rights reserved.X1555

  • crystal Plasticity finite element modeling of mechanically induced martensitic transformation mimt in metastable austenite
    International Journal of Plasticity, 2010
    Co-Authors: Myounggyu Lee, Sungjoon Kim, Heung Nam Han
    Abstract:

    Abstract A new crystal Plasticity model incorporating the mechanically induced martensitic transformation in metastable austenitic steel has been formulated and implemented into the finite element analysis. The kinetics of martensite transformation is modeled by taking into consideration of a nucleation-controlled phenomenon, where each potential martensitic variant based on Kurdjumov–Sachs (KS) relationship has different nucleation probability as a function of the interaction energy between externally applied stress and lattice Deformation. Therefore, the transformed volume fractions are determined following selective variants given by the crystallographic orientation of austenitic matrix and applied stress in the frame of the crystal Plasticity finite element. The developed finite element program is capable of considering the effect of volume change by the Bain Deformation and the lattice-invariant shear during the martensitic transformation by effectively modifying the evolution of Plastic Deformation Gradient of the conventional rate-dependent crystal Plasticity finite element. The validation of the proposed model has been carried out by comparing with the experimentally measured data under simple loading conditions. Good agreements with the measurements for the stress–strain responses, transformed martensitic volume fractions and the influence of strain rate on the Deformation behavior will enable the model to be promising for the future applications to the real forming process of the TRIP aided steel.

Andreas Menzel - One of the best experts on this subject based on the ideXlab platform.

  • Finite-strain thermo-viscoPlasticity for case-hardening steels over a wide temperature range
    PAMM, 2019
    Co-Authors: Philip Oppermann, Ralf Denzer, Andreas Menzel
    Abstract:

    The aim of this work is the development of a thermodynamically consistent fully coupled thermo-viscoPlastic material model for metals undergoing finite Deformations. A multiplicative split of the Deformation Gradient into a thermal, an elastic and a Plastic part is introduced, where isotropic thermal expansion and isochoric Plastic Deformation are assumed. The model is based on a decomposition of the free energy into a thermo-elastic and a Plastic part and covers non-linear cold-work hardening and thermal softening. The model incorporates non-linear temperature dependent effects for the elastic moduli, thermal expansion, heat capacity, and heat conductivity. Furthermore, the temperature and strainrate dependency of the yield stress is realised using a Perzyna-type viscoPlastic model incorporating a von Mises yield function, both enhanced by thermal softening. Special care has been taken for the time integration of the Plastic Deformation Gradient to comply with the incompressibility constraint. Themodel and its parameters have been fitted against experimental data for case hardening steel 16MnCr5 (1.7131). We discuss the consistent linearisation of the proposed model and its implementation in a monolithic fully coupled finite element framework. Finally, we present results for selected boundary value problems. They show the localisation and regularization behaviour ofthe proposed model. (Less)

  • Thermo-ViscoPlasticity for Case Hardening Steels at Finite Deformations and Wide Temperature Ranges
    2019
    Co-Authors: Philip Oppermann, Ralf Denzer, Andreas Menzel
    Abstract:

    The aim of this work is the development of a thermodynamically consistent fully coupled thermo-viscoPlastic material model for metals undergoing finite Deformation and large temperature changes.The Deformation Gradient is supposed to be decomposable into a thermal, an elastic, and a Plastic part, where purely volumetric thermal expansion and isochoric Plastic distortion is assumed. The model is based on a split of the free energy into a thermo-elastic and a Plastic part. Where the first part is dependent on the elastic Deformation Gradient and the temperature, and the latter, covering non-linear cold-work hardening, shall only depend on the internal variables. Within this ansatz for the free energy and the kinematics, nonlinear temperature dependent effects are accounted for the elastic moduli, the thermal expansion, the heat capacity and the heat conductivity.Based on an associative flow rule, strain rate-dependency of the current yield stress is realised using a temperature dependent nonlinear Perzyna-type viscoPlastic model in combination with a von Mises yield function enhanced by non-linear thermal softening. The model and its parameters are fitted against experimental data for case hardening steel 16MnCr5 (1.7131).We discuss the consistent linearisation of the proposed model and its implementation in a monolithic fully coupled finite element framework. Special care has been taken on the implementation of the incompressibility constraint on the Plastic Deformation Gradient. Finally, we present results for selected boundary value problems demonstrating the performance of the model. (Less)

  • on the continuum formulation of higher Gradient Plasticity for single and polycrystals
    Journal of The Mechanics and Physics of Solids, 2000
    Co-Authors: Andreas Menzel, Paul Steinmann
    Abstract:

    This paper develops a geometrically linear formulation of higher Gradient Plasticity of single and polycrystalline material based on the continuum theory of dislocations and incompatibilities. As a result, a phenomenological but physically motivated description of hardening is obtained, which incorporates for single crystals second order spatial derivatives of the Plastic Deformation Gradient and for polycrystals fourth order spatial derivatives of the Plastic strains into the yield condition. Moreover, these modifications mimic the characteristic structure of kinematic hardening, whereby the backstress obeys a nonlocal evolution law. For the one-dimensional example of an infinite shear layer the relation between the characteristic length l and the width w of a localized elasto–Plastic shear band is examined in detail for both cases.

  • On the formulation of higher Gradient single and polycrystal Plasticity
    Journal De Physique Iv, 1998
    Co-Authors: Andreas Menzel, Paul Steinmann
    Abstract:

    This contribution aims in a geometrically linear formulation of higher Gradient Plasticity of single and polycrystalline material based on the continuum theory of dislocations and incompatibilities. Thereby, general continuum dislocation densities and incompatibilities are introduced from the viewpoint of continuum mechanics by considering the spatial closure failure of arbitrary line integrals of the displacement differential. Then these findings are translated to the Plastic parts of the displacement Gradient, the so called Plastic distorsion, and the Plastic strain, respectively, within an elasto-Plastic solid thus defining tensor fields of Plastic dislocation densities and Plastic incompatibilities. Next, in the case of single crystalline material the Plastic dislocation density and in the case of polycrystalline material the Plastic incompatibility are considered within the exploitation of the thermodynamical principle of positive dissipation. As a result, a phenomenological but physically motivated description of hardening is obtained, which incorporates for single crystals second spatial derivatives of the Plastic Deformation Gradient and for polycrystals fourth spatial derivatives of the Plastic strains into the yield condition. Moreover, these modifications mimic the characteristic structure of kinematic hardening, whereby the backstress obeys a nonlocal evolution law.

Paul Steinmann - One of the best experts on this subject based on the ideXlab platform.

  • on the continuum formulation of higher Gradient Plasticity for single and polycrystals
    Journal of The Mechanics and Physics of Solids, 2000
    Co-Authors: Andreas Menzel, Paul Steinmann
    Abstract:

    This paper develops a geometrically linear formulation of higher Gradient Plasticity of single and polycrystalline material based on the continuum theory of dislocations and incompatibilities. As a result, a phenomenological but physically motivated description of hardening is obtained, which incorporates for single crystals second order spatial derivatives of the Plastic Deformation Gradient and for polycrystals fourth order spatial derivatives of the Plastic strains into the yield condition. Moreover, these modifications mimic the characteristic structure of kinematic hardening, whereby the backstress obeys a nonlocal evolution law. For the one-dimensional example of an infinite shear layer the relation between the characteristic length l and the width w of a localized elasto–Plastic shear band is examined in detail for both cases.

  • On the formulation of higher Gradient single and polycrystal Plasticity
    Journal De Physique Iv, 1998
    Co-Authors: Andreas Menzel, Paul Steinmann
    Abstract:

    This contribution aims in a geometrically linear formulation of higher Gradient Plasticity of single and polycrystalline material based on the continuum theory of dislocations and incompatibilities. Thereby, general continuum dislocation densities and incompatibilities are introduced from the viewpoint of continuum mechanics by considering the spatial closure failure of arbitrary line integrals of the displacement differential. Then these findings are translated to the Plastic parts of the displacement Gradient, the so called Plastic distorsion, and the Plastic strain, respectively, within an elasto-Plastic solid thus defining tensor fields of Plastic dislocation densities and Plastic incompatibilities. Next, in the case of single crystalline material the Plastic dislocation density and in the case of polycrystalline material the Plastic incompatibility are considered within the exploitation of the thermodynamical principle of positive dissipation. As a result, a phenomenological but physically motivated description of hardening is obtained, which incorporates for single crystals second spatial derivatives of the Plastic Deformation Gradient and for polycrystals fourth spatial derivatives of the Plastic strains into the yield condition. Moreover, these modifications mimic the characteristic structure of kinematic hardening, whereby the backstress obeys a nonlocal evolution law.

  • Views on multiplicative elastoPlasticity and the continuum theory of dislocations
    International Journal of Engineering Science, 1996
    Co-Authors: Paul Steinmann
    Abstract:

    The objective of this contribution is a geometrically non-linear formulation of the continuum theory of dislocations within the framework of multiplicative elastoPlasticity at finite strains. Thereby, the continuum theory of dislocations is particularly motivated by the kinematic structure of single crystals. Two different views on the continuum theory of dislocations at finite inelastic strains are adopted. Firstly, different dislocation density tensors are introduced from the viewpoint of continuum mechanics as the incompatibility of the so-called Plastic intermediate configuration. Secondly, the continuum theory of dislocations is motivated as a Cartan differential geometry where the corresponding torsion tensor is associated to the dislocation density. Finally, as the main outcome of this contribution, the kinematically necessary dislocation density is considered within the exploitation of the thermodynamical principle of positive dissipation. As a result, a phenomenological description of hardening is obtained, which on the one hand incorporates second spatial derivatives of the Plastic Deformation Gradient into the yield condition and on the other hand mimics the characteristic structure of kinematic hardening.