Study of strain localizations in a polycrystalline medium in presence of a quasi-static crack (original) (raw)
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International Journal of Fracture, 2000
Three-dimensional Finite Element simulations of mode I crack tip fields in Compact Tension specimens are presented for elastic ideally-plastic F.C.C. single crystals. The computations are carried out within the framework of classical continuum crystal plasticity for three crack orientations: (001) [110], and (001) [100]. The attention is drawn on the strong differences between the plastic strain field obtained at the free surface and in the mid-section of the specimens. The results are compared, on the one hand, to analytical solutions for stationary cracks in single crystals under plane strain conditions and, on the other hand, to experimental tests on a single crystal nickel-based superalloy at room temperature. For this material, both octahedral and cube slip must be taken into account. A good agreement between experimental observations and numerical results is found in the structure of the strain localization bands observed at the free surface of (110)[001] cracked specimens. In particular, the evidence of kink banding near the crack tip is provided, confirmed by EBSD orientation mapping.
Computational Materials Science, 2016
Using crystal plasticity, finite element analyses were carried out to model cyclic deformation for a low solvus high refractory (LSHR) nickel superalloy at elevated temperature. The analyses were implemented using a representative volume element (RVE), consisting of realistic microstructure obtained from SEM images of the material. Monotonic, stress-relaxation and cyclic test data at 725°C were used to determine the model parameters from a fitting process and their sensitivity to RVE size and random grain orientation. In combination with extended finite element method (XFEM), the crystal plasticity model was further applied to predict surface crack growth, for which accumulated plastic strain was used as a fracture criterion. Again, realistic microstructure, taken from the cracking site on the surface of a plain fatigue specimen, was used to create the finite element model for crack growth analyses. The prediction was conducted for a pseudo-3D geometrical model, resembling the plane stress condition at specimen surface. The loading level at the cracking site was determined from a viscoplasticity finite element analysis of the fatigue specimen. The proposed model is capable of predicting the variation in growth rate in grains with different orientations.
JOM, 2019
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Modeling and Characterization of Near-Crack-Tip Plasticity from Micro-to Nano-Scales
2010
Methodologies for understanding the plastic deformation mechanisms related to crack propagation at the nano-, meso-and micro-length scales are being developed. These efforts include the development and application of several computational methods including atomistic simulation, discrete dislocation plasticity, strain gradient plasticity and crystal plasticity; and experimental methods including electron backscattered diffraction and video image correlation. Additionally, methodologies for multi-scale modeling and characterization that can be used to bridge the relevant length scales from nanometers to millimeters are being developed. The paper focuses on the discussion of newly developed methodologies in these areas and their application to understanding damage processes in aluminum and its alloys.
2012
This work presents two integrated experimental and modeling approaches for examining polycrystals at different length scales, which utilize different experimental techniques but the same elasto-crystal plasticity based finite element model (CPFEM). The goal of this work is to calibrate modeling approaches through experimental data, and then use the models to gain insight into the mechanics of deformation in nickel and nickel-base superalloy polycrystals. The first study utilized a micro-tensile test specimen of pure nickel with 259 grains, where the CPFEM simulations were initiated with the explicit 3D microstructure as measured with 3D-Electron Back Scattering Detection (EBSD) serial sectioning and compared with surface deformations measured with Digital Image Correlation (DIC). The second study utilized a larger polycrystalline nickel-base superalloy specimen with approximately 50,000 grains, where the CPFEM simulation results are compared with lattice strain data obtained through high energy x-ray diffraction utilizing a synchrotron x-ray source. In both cases the simulations are compared with different aspects of the experimental strain information (surface strain or lattice strain), and then the simulations are used to explore aspects of the heterogeneous nature of the deformation that are difficult or impossible to measure experimentally.
Grain scale simulation of local deformation behavior
Asia Pacific Journal on Computational Engineering, 2014
In this work, a full-field finite element simulation of a heterogeneous DC04 steel microstructure identified from two-dimensional (2D) electron backscatter diffraction (EBSD) data is performed under a macroscopic tensile deformation. After discretization procedure by finite elements, the EBSD microstructure is subjected to homogeneous displacement boundary conditions approximately describing a large strain uniaxial tensile test. A crystal plasticity model applied on integration points of FE method is used to simulate the deformation behavior and the grain orientation evolution. The simulated grain orientation fields are compared to experimental measurements of the specimen after the tensile test at different deformation levels.
Crack-tip parameters in polycrystalline plates with soft grain boundaries
2008
Two micromechanical models are used to calculate the statistical distributions of the stress intensity factor of a crack in a polycrystalline plate containing stiff grains and soft grain boundaries. The first is a finite-element method based Monte Carlo procedure where the microstructure is represented by a Poisson-Voronoi tessellation. The effective elastic moduli of the uncracked plate and the stress intensity factor of the cracked plate are calculated for selected values of the parameters that quantify the level of elastic mismatch between the grains and grain boundaries. It is shown that the stress intensity factor is independent of the expected number of grains, and that it can be estimated using an analytical model involving a long crack whose tip is contained within a circular inhomogeneity surrounded by an infinitely extended homogenized material. The stress intensity factor distributions of this auxiliary problem, obtained using the method of continuously distributed dislocations, are in excellent agreement with those corresponding to the polycrystalline microstructure, and are very sensitive to the position within the inhomogeneity of the crack tip. These results suggest that fracture toughness experiments on polycrystalline plates can be considered experiments on the single grain containing the crack tip, and in turn reflect the a / w effects typical of finite-geometry specimens.
Computational description of nanocrystalline deformation based on crystal plasticity
Acta Materialia, 2004
The effect of grain size on the mechanical response of polycrystalline metals was investigated computationally and applied to the nanocrystalline domain. A phenomenological constitutive description is adopted to build the computational crystal model. Two approaches are implemented. In the first, the material is envisaged as a composite; the grain interior is modeled as a monocrystalline core surrounded by a mantle (grain boundary) with a lower yield stress and higher work hardening rate response. Both a quasiisotropic and crystal plasticity approaches are used to simulate the grain interiors. The grain boundary is modeled either by an isotropic Voce equation (Model I) or by crystal plasticity (Model II). Elastic and plastic anisotropy are incorporated into this simulation. An implicit Eulerian finite element formulation with von Mises plasticity or rate dependent crystal plasticity is used to study the nonuniform deformation and localized plastic flow. The computational predictions are compared with the experimentally determined mechanical response of copper with grain sizes of 1 lm and 26 nm. Shear localization is observed during work hardening in view of the inhomogeneous mechanical response. In the second approach, the use of a continuous change in mechanical response, expressed by the magnitude of the maximum shear stress orientation gradient, is introduced. It is shown that the magnitude of the gradient is directly dependent on grain size. This gradient term is inserted into a constitutive equation that predicts the local stressstrain evolution.
Nanostructurally small cracks (NSC): a review on atomistic modeling of fatigue
Fatigue is one of the most damaging mechanisms in structural components. With the development of structural nanomaterials, it is imperative to investigate the fatigue damage phenomena at the atomic scale. To study fatigue behavior at the nanoscale, one must apply non-continuum modeling frameworks, such as molecular statics (MS), molecular dynamics (MD), and Monte Carlo (MC) methods. To date, only MD and MS simulations using embedded atom method (EAM) and modified embedded atom method (MEAM) potentials have been conducted, and this paper reviews these simulations of the nanoscale fatigue-crack growth in nickel and copper including single crystals, bicrystals, and polycrystals. A nanoscale size middle tension (MT) specimen with the lateral side applied periodic boundary conditions was used to investigate the fatigue behavior in nickel and copper single crystals. Simulation results revealed that the cyclic plastic deformation at the crack tip was the main influencing factor for fatigue-crack growth. Two main nanoscale mechanisms of crack propagation were observed: (1) the main cracks linked with the voids nucleated in front of crack tip due to high dislocation density generated by the cyclic loading; and (2) the main cracks broke the atomic bonds in the crack plane without much plasticity. For the bicrystals and polycrystals, the grain boundaries exerted resistance to the crack propagation. To study the interactions between cracks and grain boundaries, four cases of grain boundary interfaces for copper and two cases of grain boundaries for nickel were simulated. In copper bicrystals, the crack path deviated and moved from one grain to another for high misorientations, while there were voids nucleating at grain boundaries in front of the crack tip that linked back with the main crack. Similar to macroscale fatigue, dislocation substructures were observed to develop in the atomic lattice during cyclic loading. In nickel bicrystals, for large misorientations, the cracks were stopped by grain boundaries. For small misorientations, the crack propagated through the grain boundary, but the growth rate was reduced due to the resistance of the grain boundary. Fatigue-crack growth rates for nanocracks were computed and compared with growth rates published in the literature for microstructurally small cracks (micron range) and long cracks (millimeter range). A nanostructurally small crack (NSC) was introduced in terms of the CTOD. The quantified NSC growth rates in copper single crystals were very similar with those experimentally measured for small cracks (micron range) and with those at stress-intensity-factor ranges lower than the threshold for long cracks (millimeter range). The atomistic simulations indicated that reversible plastic slip along the active crystallographic directions at the crack tip was responsible for advancing the crack during applied cycling. In the case of single or double plastic slip localization at the crack tip, a typical Mode I fatigue crack arose along a slip band and then grew into a mixed Mode I + II crack growth mechanism. For crystal orientations characterized by multiple slip systems concomitantly active at the crack tip, the crack advance mechanism was characterized by nanovoid nucleation in the high density nucleation region ahead of the crack tip and by linkage with the main crack leading to crack extension. To facilitate observations of fatigue-crack growth, the simulation of a copper polycrystal was performed at low temperature 20 K as well. The crack propagated along persistent slip bands within the grain. The crack propagated along grain boundaries when the angle between the direction of crack propagation and the grain boundary was small, while it was impeded by the grain boundary when the angle was large. The results obtained for the crack advance as a function of stress intensity amplitude are consistent with experimental studies and a Paris law exponent of approximately two.