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  • 1. Balieu, R.
    et al.
    Lauro, F.
    Bennani, B.
    Delille, R.
    Matsumoto, T.
    Mottola, E.
    A fully coupled elastoviscoplastic damage model at finite strains for mineral filled semi-crystalline polymer2013In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 51, p. 241-270Article in journal (Refereed)
  • 2.
    Balieu, Romain
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering.
    Kringos, Niki
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering.
    A new thermodynamical framework for finite strain multiplicative elastoplasticity coupled to anisotropic damage2015In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 70, p. 126-150Article in journal (Refereed)
    Abstract [en]

    The thermodynamical framework of an elastoplastic model coupled to anisotropic damage is presented in this paper. In the finite strain context, the proposed model is based on the multiplicative decomposition of the strain gradient into elastic and plastic parts. The anisotropic degradation is introduced by means of a second order tensor and another intermediate configuration is introduced by fictitiously removing this degradation from the plastic intermediate configuration. To enhance the physical meaning of the Mandel-like stress measure work conjugated to the inelastic flow stated in this fictitious configuration, i.e. the "effective stress", a new damage rate tensor is defined with its associated push-forward and pull-back operations. The emphasis in this paper is placed on the description of the interesting properties of the novel definitions of the push-forward and pull-back operations which are discussed through a thermodynamical framework. Furthermore, a specific constitutive model with the plastic and damage flow rules deduced from the restrictions imposed by the second law of thermodynamics is discussed with an application on an asphalt concrete material where the anisotropic evolution of the damage is highlighted.

  • 3. Dahlberg, Carl F. O.
    Spatial distribution of the net Burgers vector density in a deformed single crystal2016In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 85, p. 110-129Article in journal (Refereed)
    Abstract [en]

    A two-dimensional deformation field on an indented single crystal, where the only nonzero lattice rotation occurs in the plane of deformation and only three effective in-plane slip systems are activated, is investigated both experimentally and numerically. ElectronBackscatter Diffraction (EBSD) is utilized to probe the lattice rotation field on the sample. The lattice rotation field is utilized to calculate the two non-zero components of Nye'sdislocation density tensor, which serves as a link between plastic and elastic deformation states. The enhanced accuracy of EBSD enabled measurements of the net Burgers vector density, and a new quantity β, which monitors the activity of slip systems in the deformed zone. The β-field is compared to the slip system activity obtained by analytical solution and also by crystal plasticity simulations. A qualitative comparison of the three methods confirms that the β-field obtained experimentally agrees with the slip system activity obtained analytically and by numerical methods.

  • 4.
    Dahlberg, Carl F. O.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Boåsen, Magnus
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Evolution of the length scale in strain gradient plasticity2019In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 112, p. 220-241Article in journal (Refereed)
    Abstract [en]

    An equivalence is assumed between a microstructural length scale related to dislocation density and the constitutive length scale parameter in phenomenological strain gradient plasticity. An evolution law is formed on an incremental basis for the constitutive length scale parameter. Specific evolution equations are established through interpretations of the relation between changes in dislocation densities and increments in plastic strain and strain gradient. The length scale evolution has been implemented in a 2D-plane strain finite element method (FEM) code, which has been used to study a beam in pure bending. The main effect of the length scale evolution on the response of the beam is a decreased strain hardening, which in cases of small beam thicknesses even leads to a strain softening behavior. An intense plastic strain gradient may develop close to the neutral axis and can be interpreted as a pile-up of dislocations. The effects of the length scale evolution on the mechanical fields are compared with respect to the choice of length evolution equation.

  • 5.
    Dahlberg, Carl F. O.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Faleskog, Jonas
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Niordson, Christian F.
    Legarth, Brian Nyvang
    A deformation mechanism map for polycrystals modeled using strain gradient plasticity and interfaces that slide and separate2013In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 43, p. 177-195Article in journal (Refereed)
    Abstract [en]

    Small scale strain gradient plasticity is coupled with a model of grain boundaries that take into account the energetic state of a plastically strained boundary and the slip and separation between neighboring grains. A microstructure of hexagonal grains is investigated using a plane strain finite element model. The results show that three different microstructural deformation mechanisms can be identified. The standard plasticity case in which the material behaves as expected from coarse grained experiments, the nonlocal plasticity region where size of the microstructure compared to some intrinsic length scale enhances the yield stress and a third mechanism, active only in very fine grained microstructures, where the grains deform mainly in relative sliding and separation.

  • 6.
    Dahlberg, Carl
    et al.
    Columbia University.
    Saito, Yuki
    Columbia University.
    Öztop, Muin S.
    Columbia University.
    Kysar, Jeffrey W.
    Columbia University.
    Geometrically necessary dislocation density measurements associated with different angles of indentations2014In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 54, p. 81-95Article in journal (Refereed)
    Abstract [en]

    Experiments and numerical simulations of various angles of wedge indenters into face-centered cubic single crystal were performed under plane strain conditions. In the experiments, the included angles of indenters are chosen to be 60 degrees, 90 degrees and 120 degrees and they are indented into nickel single crystal into the < 00 (1) over bar > direction with its tip parallel to < 1 1 0 > direction, so that there are three effective in-plane slip systems on (1 1 0) plane. Indenters are applied 200 mu m in depth. The midsection of the specimens is exposed with a wire Electrical Discharge Machining (EDM) and the in-plane lattice rotations of the region around the indented area are calculated from the crystallographic orientation maps obtained from electron backscatter diffraction (EBSD) measurement. No matter which angles of indenters are applied, the rotation fields are very similar. There is a strong lattice rotation discontinuity on the line below the indenter tip. The magnitude of the lattice rotation ranges from -20 degrees to 20 degrees. Lower bounds on the Geometrically Necessary Dislocation (GND) densities are also calculated and plotted. The numerical simulations of the same experimental setup are performed. The simulation results of lattice rotation and slip rates are plotted and compared with the experimental result. There is high correlation between the experimental result and the numerical result.

  • 7.
    Dong, Zhihua
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Schönecker, Stephan
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Applied Material Physics.
    Li, Wei
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Applied Material Physics.
    Kwon, Se Kyun
    Pohang Univ Sci & Technol, Grad Inst Ferrous Technol, Pohang 37673, South Korea..
    Vitos, Levente
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Applied Material Physics. Uppsala Univ, Div Mat Theory, Dept Phys & Astron, SE-75121 Uppsala, Sweden.;Wigner Res Ctr Phys, Res Inst Solid State Phys & Opt, POB 49, H-1525 Budapest, Hungary..
    Plastic deformation modes in paramagnetic gamma-Fe from longitudinal spin fluctuation theory2018In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 109, p. 43-53Article in journal (Refereed)
    Abstract [en]

    Using an efficient first-principles computational scheme, we calculate the intrinsic stacking fault energy (gamma(isf) ) and the unstable stacking fault energy (gamma(usf)) of paramagnetic gamma-Fe as a function of temperature. The formation energies are derived from free energies accounting for thermal longitudinal spin fluctuations (LSFs). LSFs are demonstrated to be important for the accurate description of the temperature-dependent magnetism, intrinsic and unstable stacking fault energies, and have a comparatively large effect on gamma(isf) of gamma-Fe. Dominated by the magneto-volume coupling at thermal excitations, gamma(isf) of gamma-Fe exhibits a positive correlation with temperature, while gamma(usf )declines with increasing temperature. The predicted stacking fault energy of gamma-Fe is negative at static condition, crosses zero around 540 K, and reaches 71.0 mJ m(-2) at 1373 K, which is in good agreement with the experimental value. According to the plasticity theory formulated in terms of the intrinsic and unstable stacking fault energies, twinning remains a possible deformation mode even at elevated temperatures. Both the large positive temperature slope of gamma(usf) and the predicted high-temperature twinning are observed in the case of austenitic stainless steels.

  • 8.
    Fredriksson, Per
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Gudmundson, Peter
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Size-dependent yield strength of thin films2005In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 21, no 9, p. 1834-1854Article in journal (Refereed)
    Abstract [en]

    Biaxial strain and pure shear of a thin film are analysed using a strain gradient plasticity theory presented by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379-1406]. Constitutive equations are formulated based on the assumption that the free energy only depends on the elastic strain and that the dissipation is influenced by the plastic strain gradients. The three material length scale parameters controlling the gradient effects in a general case are here represented by a single one. Boundary conditions for plastic strains are formulated in terms of a surface energy that represents dislocation buildup at an elastic/plastic interface. This implies constrained plastic flow at the interface and it enables the simulation of interfaces with different constitutive properties. The surface energy is also controlled by a single length scale parameter, which together with the material length scale defines a particular material. Numerical results reveal that a boundary layer is developed in the film for both biaxial and shear loading, giving rise to size effects. The size effects are strongly connected to the buildup of surface energy at the interface. If the interface length scale is small, the size effect vanishes. For a stiffer interface, corresponding to a non-vanishing surface energy at the interface, the yield strength is found to scale with the inverse of film thickness.

  • 9.
    Gudmundson, Peter
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Dahlberg, Carl F. O.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Isotropic strain gradient plasticity model based on self-energies of dislocations and the Taylor model for plastic dissipation2019In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 121, p. 1-20Article in journal (Refereed)
    Abstract [en]

    A dislocation mechanics based isotropic strain gradient plasticity model is developed. The model is derived from self-energies of dislocations and the Taylor model for plastic dissipation. It is shown that the same microstructural length scale emerges for both the energetic and the dissipative parts of the model. Apart from a non-dimensional factor of the order of unity, the length scale is defined as the Burgers vector divided by the strain for initiation of plastic deformation. When the structural length scale approaches this microstructural length scale, strengthening effects result. The present model predicts an increased initial yield stress that is controlled by the energetic contribution. For larger plastic strains, the hardening is governed by the dissipative part of the model. The theory is specialized to the simple load cases of tension with a passivation layer that prohibits plastic deformation on the surfaces as well as pure bending with free and fixed boundary conditions for plastic strain. Simulations of initial yield stress for varying thicknesses are compared to experimental observations reported in the literature. It is shown that the model in a good way can capture the length scale dependencies. Also upper bound solutions are presented for a spherical void in an infinite volume as well as torsion of a cylindrical rod. The model is as well applied to derive a prediction for the Hall-Petch effect.

  • 10.
    Hård af Segerstad, P.
    et al.
    Department of Applied Mechanics, Chalmers University of Technology.
    Larsson, R.
    Department of Applied Mechanics, Chalmers University of Technology.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    A constitutive equation for open-cell cellular solids, including viscoplasticity, damage and deformation induced anisotropy2008In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, ISSN 0749-6419, Vol. 24, no 5, p. 896-914Article in journal (Refereed)
    Abstract [en]

    A thermodynamically consistent approach is developed for modelling the response of an open-cell cellular solid at finite compressive strains. The cellular solid is considered as a network of struts, where each strut connects two vertex points. A hypothesis is proposed that the vertex points move affinely in the finite strain regime, where the struts buckle plastically. The strut deformation is assumed to be 1-dimensional and depend directly on the macroscopic deformation; thus the description of the strut response requires only a scalar valued response function. Owing to this simple ansatz it is possible to include multiple nonlinear mechanisms, such as hyperelasto-viscoplasticity and damage. The macrostress is obtained by averaging over a statistical ensemble of struts. The model has been implemented in the context of finite strains and damage coupled to viscoplastic Perzyna type behaviour. All model parameters may be determined by performing tests in simple compression. The model is well capable of reproducing data from compression experiments on various open-cell aluminium foams.

  • 11. Hård af Segerstad, P.
    et al.
    Toll, Staffan
    Chalmers University of Technology.
    Larsson, R.
    Computational modelling of dissipative open-cell cellular solids at finite deformations2009In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, ISSN 0749-6419, Vol. 25, no 5, p. 802-821Article in journal (Refereed)
    Abstract [en]

    This study concerns the constitutive modelling of dissipative open-cell structural cellular solids under primarily finite compressive deformations and the corresponding non-linear finite element implementation. A thermodynamically consistent, mechanistic approach presented in Hard of Segerstad et al. [Hard of Segerstad, P., Larsson, R., Toll, S., 2008. A constitutive equation for open-cell cellular solids, including viscoplasticity, damage and deformation induced anisotropy. International Journal of Plasticity. 24, 896-914.] is adopted for modelling the initial linear-elastic response and the subsequent plateau behaviour. In these regions the cellular solid is considered as a network of struts, where each strut connects two vertex points. A hypothesis is proposed that the vertex points move affinely in the finite strain regime, where the struts buckle plastically. The strut deformation is further assumed to be one-dimensional and depend directly on the macroscopic deformation; thus the description of the strut response requires only a scalar valued response function. Owing to this simple ansatz, the introduction of multiple non-linear mechanisms, such as hyperelasto-viscoplasticity and damage becomes feasible for large scale computations. An additional hyperelastic volumetric response, activated near the point-of-compaction, is introduced for two reasons, (i) to capture the stiffness recovery at high compressive volumetric deformations, where the struts come into contact, and (ii) to prevent numerical instability. The model is implemented as a user defined constitutive driver in the implicit version of the finite element code ABAQUS and tested experimentally for an open-cell aluminium alloy foam (Duocel 6101-0,40 ppi). All material parameters are determined by a simple compression test, and subsequently used to simulate the indentation of a rigid sphere into a foam cylinder. The model accurately captures the experimental load-displacement relation and the deformed geometry.

  • 12.
    Österlöf, Rickard
    et al.
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL. Scania CV AB, Sweden.
    Wentzel, Henrik
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.). Scania CV AB, Sweden.
    Kari, Leif
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.
    A finite strain viscoplastic constitutive model for rubber with reinforcing fillers2016In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 87, p. 1-14Article in journal (Refereed)
    Abstract [en]

    A three dimensional viscoplastic constitutive model for finite strains in a co-rotational explicit scheme is developed and implemented using finite elements that captures the amplitude dependency, commonly referred to as the Fletcher-Gent effect, and frequency dependency of rubber with reinforcing fillers. The multiplicative split of the deformation gradient is utilized and the plastic flow rule stems from an extension to finite strains of a boundary surface model with a vanishing elastic region. The storage and loss modulus for a 50 phr carbon black filled natural rubber are captured over a large range of strain amplitudes, 0.2-50% shear strain, and frequencies, 0.2-20 Hz. In addition, bimodal excitation is replicated accurately, even though this measurement data is not included when obtaining material parameters. This capability is essential when non-sinusoidal loading conditions are to be replicated. By separating the material and geometrical influence on the properties of a component, the design engineers have the capability to evaluate more concepts early in the design phase. This also reduces the need of complex prototypes for physical testing, thereby saving both time and money.

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