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Register a new userDiffuse-interface polycrystal plasticity: Expressing grain boundaries as geometrically necessary dislocations
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Added by
Nikhil Chandra Admal
Publication date
2017
fields
Physics
and research's language is
English
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The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradient into lattice and plastic parts, i.e. F(X,t) = F^L(X,t) F^P(X,t), an initial stress-free polycrystal is constructed by imposing F^L to be a piecewise constant rotation field R^0(X), and F^P = R^0(X)^T, thereby having F(X,0) = I, and zero elastic strain. This model serves as a precursor to higher order crystal plasticity models with grain boundary energy and evolution.
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Plastic deformation in polycrystals is governed by the interplay between intra-granular slip and grain boundary-mediated plasticity. However, while the role played by bulk dislocations is relatively well-understood, the contribution of grain boundaries (GBs) has only recently begun to be studied. GB plasticity is known to play a key role along with bulk plasticity under a wide range of conditions, such as dynamic recovery, superplasticity, severe plastic deformation , etc., and developing models capable of simultaneously capturing GB and bulk plasticity has become a topic of high relevance. In this paper we develop a thermodynamically-consistent polycrystal plasticity model capable of simulating a variety of grain boundary-mediated plastic processes in conjunction with bulk dislocation slip. The model starts from the description of a single crystal and creates lattice strain-free polycrystalline configurations by using a specially-designed multiplicative decomposition developed by the authors. This leads to the introduction of a particular class of geometrically necessary dislocations (GND) that define fundamental GB features such as misorientation and inclination. The evolution of the system is based on an energy functional that uses a non-standard function of the GND tensor to account for the grain boundary energy, as well as for the standard elastic energy. Our implementation builds on smooth descriptions of GBs inspired on diffuse-interface models of grain evolution for numerical convenience. We demonstrate the generality and potential of the methodology by simulating a wide variety of phenomena such as shear-induced GB sliding, coupled GB motion, curvature-induced grain rotation and shrinkage, and polygonization via dislocation sub-grain formation.
We reveal that phononic thermal transport in graphene is not immune to grain boundaries (GBs) aligned along the direction of the temperature gradient. Non-equilibrium molecular dynamics simulations uncover a large reduction in the phononic thermal conductivity ($kappa_p$) along linear ultra-narrow GBs comprising periodically-repeating pentagon-heptagon dislocations. Greens function calculations and spectral energy density analysis indicate that $kappa_p$ is the complex manifestation of the periodic strain field, which behaves as a reflective diffraction grating with both diffuse and specular phonon reflections, and represents a source of anharmonic phonon-phonon scattering. Our findings provide new insights into the integrity of the phononic thermal transport in GB graphene.
With numerical simulations of the mW model of water, we investigate the energetic stability of crystalline clusters for both Ice I (cubic and hexagonal ice) and for the metastable Ice 0 phase as a function of the cluster size. Under a large variety of forming conditions, we find that the most stable cluster changes as a function of size: at small sizes the Ice 0 phase produces the most stable clusters, while at large sizes there is a crossover to Ice I clusters. We further investigate the growth of crystalline clusters with the seeding technique and study the growth patterns of different crystalline clusters. While energetically stable at small sizes, the growth of metastable phases (cubic and Ice 0) is hindered by the formation of coherent grain boundaries. A five-fold symmetric twin boundary for cubic ice, and a newly discovered coherent grain boundary in Ice 0, that promotes cross nucleation of cubic ice. Our work reveals that different local structures can compete with the stable phase in mW water, and that the low energy cost of particular grain boundaries might play an important role in polymorph selection.
We present a thermodynamic description of crystal plasticity. Our formulation is based on the Langer-Bouchbinder-Lookman thermodynamic dislocation theory (TDT), which asserts the fundamental importance of an effective temperature that describes the state of configurational disorder and therefore the dislocation density of the crystalline material. We extend the TDT description from isotropic plasticity to crystal plasticity with many slip systems. Finite-element simulations show favourable comparison with experiments on polycrystal fcc copper under uniaxial compression, tension, and simple shear. The thermodynamic theory of crystal plasticity thus provides a thermodynamically consistent and physically rigorous description of dislocation motion in crystals. We also discuss new insights about the interaction of dislocations belonging to different slip systems.
Predicting the dramatic changes in material properties caused by irradiation damage is key for the design of future nuclear fission and fusion reactors. Self-ion implantation is an attractive tool for mimicking the effects of neutron irradiation. However, the damaged layer of implanted samples is only few microns thick, making it difficult to estimate macroscopic properties. Here we address this challenge using a combination of experimental and modelling techniques. We concentrate on self-ion-implanted tungsten, the front-runner for fusion armour components and a prototypical bcc material. To capture dose-dependent evolution of properties, we experimentally characterise samples with damage levels from 0.01 to 1 dpa. Spherical nano-indentation of <001> grains shows hardness increasing up to a dose of 0.032 dpa, beyond which it saturates. AFM measurements show pile-up increasing up to the same dose, beyond which large pile-up and slip-steps are seen. Based on the observations we develop a crystal plasticity (CPFE) model for the irradiated material. It captures irradiation-induced hardening followed by strain-softening through interaction of irradiation-defects and gliding dislocations. Shear resistance of irradiation-defects is derived from TEM observations of similarly irradiated samples. Nano-indentation of pristine and implanted tungsten of doses 0.01, 0.1, 0.32 and 1 dpa is simulated. Two model parameters are fitted to the experimental results of the 0.01 dpa sample and are kept unchanged for all other doses. Peak load, indent surface profiles and damage saturation predicted by the CPFE model closely match experimental observations. Predicted lattice distortions and dislocation distributions around indents agree with corresponding measurements from HR-EBSD. Finally, the CPFE model is used to predict the macroscopic stress-strain response of similarly irradiated bulk tungsten material.
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