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  • 1.
    Dahlberg, Carl
    Department of Solid Mechanics, KTH.
    The Functional Response of Mesenchymal Stem Cells to Electron-Beam Patterend Elastomeric Surfaces Presenting Micrometer to Nanoscale Heterogeneous Rigidity2017In: Advanced Materials, ISSN 0935-9648, E-ISSN 1521-4095Article in journal (Refereed)
  • 2.
    Dahlberg, Carl F. O.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Modeling of the mechanical behavior of interfaces by using strain gradient plasticity2009Licentiate thesis, comprehensive summary (Other academic)
  • 3.
    Dahlberg, Carl F. O.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    On the Role of Interfaces in Small Scale Plasticity2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The strong evidence for a size dependence of plastic deformation in polycrystalline metalsis the basis for the research presented in this thesis. The most important parameter for this, and arguably also the most well known, is the grain size. As the size of the grains in a microstructure is decreased the yield stress increases. This is known as the Hall–Petch relation and have been confirmed for a large number of materials and grain sizes. Other structural dimensions may also give rise to a similar strengthening effect, such as the thickness of films and surface coatings, the widths of ligaments and localization zones and the diameter of thin wires, to mention a few. The work presented in this thesis is shown to be able to model these effects.

    Size dependent plastic deformation have here been modeled in a continuum mechanical setting by an extension of the standard theory of solid mechanics. Specifically, the work in this thesis is formulated in terms of the higher order strain gradient plasticity (SGP) theory presented by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids, 52]. This allows size dependent plasticity phenomena to be modeled and a yield stress that is proportional to the inverse of the geometric dimension of the problem is predicted.

    The ability to model interfaces have been of specific importance to the work presented here. The state at internal interface is shown, via a physically motivated constitutive description, to be of great importance to capture size effects. The surface energy at grain boundaries is shown to influence both the local and the macroscopic behavior. At the smallest scales an additional deformation mechanism have been introduced at the internal boundaries. This allowed the strengthening trend associated with decreasing grains size to be halted, in qualitative agreement with reported experiments on the behavior of ultrafine and nanocrystalline polycrystals. In the later part of the thesis the focus is aimed at modeling grains structures to bring some insight into the different regions of deformation mechanisms in relation to grainsize and interface strength. A deformation mechanism map for polycrystals is suggested based on the results from structures with both hexagons and log-normal size distributed Voronoi tessellations, and the implication of a statistical variation in grain size have been explored.

    A finite element implementation of the theory have been developed that is a fully implicit backward-Euler algorithm with tangent operators consistent with the stress update scheme, which give excellent convergence properties and is numerically very stable. Higher order finite elements have been implemented for modeling of both bulk material and internal interfaces. A plane strain version have been used to model metal-matrix composites and explore the implication of some of the more exotic features of the theory.

  • 4.
    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.).
    An improved strain gradient plasticity formulation with energetic interfaces: theory and a fully implicit finite element formulation2013In: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 51, no 5, p. 641-659Article in journal (Refereed)
    Abstract [en]

    A fully implicit backward-Euler implementation of a higher order strain gradient plasticity theory is presented. A tangent operator consistent with the numerical update procedure is given. The implemented theory is a dissipative bulk formulation with energetic contribution from internal interface to model the behavior of material interfaces at small length scales. The implementation is tested by solving some examples that specifically highlight the numerics and the effect of using the energetic interfaces as higher order boundary conditions. Specifically, it is demonstrated that the energetic interface formulation is able to mimic a wide range of plastic strain conditions at internal boundaries. It is also shown that delayed micro-hard conditions may arise under certain circumstances such that an interface at first offers little constraints on plastic flow, but with increasing plastic deformation will develop and become a barrier to dislocation motion.

  • 5.
    Dahlberg, Carl F. O.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Faleskog, Jonas
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Energetic interfaces and boundary sliding in strain gradient plasticity; investigation using an adaptive implicit finite element methodArticle in journal (Refereed)
  • 6.
    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.).
    Strain gradient plasticity analysis of the influence of grain size and distribution on the yield strength in polycrystals2014In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 44, p. 1-16Article in journal (Refereed)
    Abstract [en]

    Plane strain models of polycrystalline microstructures are investigated using strain gradient plasticity (SGP) and a grain boundary (GB) deformation mechanism. The microstructures are constructed using a non-linear constrained Voronoi tessellation so that they conform to a log-normal distribution in grain size. The SGP framework is used to model the grain size dependent strengthening and the GB deformation results in a cut-off of this trend below a certain critical grain size. Plastic strain field localization is discussed in relation to the non-local effects introduced by SGP and a material length scale. A modification of the Hall-Petch relation that accounts for, not only the mean grain size, but also the statistical size variation in a population of grains is proposed.

  • 7.
    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.

  • 8.
    Dahlberg, Carl F. O.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Gudmundsson, Peter
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Hardening and softening mechanisms at decreasing microstructural length scales2008In: Philosophical Magazine, ISSN 1478-6435, E-ISSN 1478-6443, Vol. 88, no 30-32, p. 3513-3525Article in journal (Refereed)
    Abstract [en]

    A laminate structure with varying lamina thicknesses is used as a qualitative model of grain size dependence on yield behaviour in metallic materials. Both strain gradient plasticity and slip between layers are considered. It is shown that an inverse Hall-Petch effect can be generated in this way. For very small thicknesses, corresponding to very small grain sizes, sliding is the dominant mechanism and the strength then decreases with decreasing thickness. For larger thicknesses, strain gradient plasticity is controlling the deformation and the strength is, instead, increasing with decreasing thickness. Numerical examples are presented that demonstrate these mechanisms.

  • 9.
    Dahlberg, Carl F. O.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Mitchell-Thomas, R. C.
    Quevedo-Teruel, Oscar
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Reducing the Dispersion of Periodic Structures with Twist and Polar Glide Symmetries2017In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 7, article id 10136Article in journal (Refereed)
    Abstract [en]

    In this article, a number of guiding structures are proposed which take advantage of higher symmetries to vastly reduce the dispersion. These higher symmetries are obtained by executing additional geometrical operations to introduce more than one period into the unit cell of a periodic structure. The specific symmetry operations employed here are a combination of p-fold twist and polar glide. Our dispersion analysis shows that a mode in a structure possessing higher symmetries is less dispersive than in a conventional structure. It is also demonstrated that, similar to the previously studied Cartesian glide-symmetric structures, polar glide-symmetric structures also exhibit a frequency independent response. Promising applications of these structures are leaky-wave antennas which utilize the low frequency dependence.

  • 10.
    Dahlberg, Carl F.O.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Saito, Y.
    Öztop, M.S.
    Kysar, J. W.
    Geometrically necessary dislocation density measurements at a grain boundary due to wedge indentation into an aluminum bicrystal2017In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 105, p. 131-149Article in journal (Refereed)
    Abstract [en]

    An aluminum bicrystal with a symmetric tilt Σ43 (3 3 5)[1 1 0] coincident site lattice grain boundary was deformed plastically via wedge indentation under conditions that led to a plane strain deformation state. Plastic deformation is induced into both crystals and the initially straight grain boundary developed a significant curvature. The resulting lattice rotation field was measured via Electron Backscatter Diffraction (EBSD). The Nye dislocation density tensor and the associated Geometrically Necessary Dislocation (GND) densities introduced by the plastic deformation were calculated. The grain boundary served as an impediment to plastic deformation as quantified through a smaller lattice rotation magnitude and smaller GND density magnitudes in one of the crystals. There is evidence that the lattice rotations in one grain brought a slip system in that grain into alignment with a slip system in the other grain, upon which the impediment to dislocation transmission across the grain boundary was reduced. This allowed the two slip systems to rotate together in tandem at later stages of the deformation. Finite element crystal plasticity simulations using classical constitutive hardening relationship capture the general features observed in the experiments.

  • 11.
    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.

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