Thermodynamic dislocation theory incorporating dislocation impediment by the grain boundaries is developed to analyze the shear test of polycrystals. With a small set of physics based material parameters, we are able to simulate the stress-strain curves for the load and its reversal, which are consistent with the experimental curves of Thuillier and Manach [2009]. Representative distributions of plastic slip under load and its reversal are presented, and their evolution explains the extended length of the transition stage during load reversal.
Continuum dislocation dynamics (CDD) represents the evolution of systems of curved and connected dislocation lines in terms of density-like field variables which include the volume density of loops (or 'curvature density') as an additional field. Since dislocation curvature represents a spatial derivative of the underlying discrete dislocation density tensor, the curvature field evolution equation of necessity contains numerically inconvenient higher-order derivatives of the density fields. We propose a simple approximation to express curvature in terms of density fields, and demonstrate its a…
Starting from the assumption that all possible orientations of grains are equally probable, we prove that the geometric factor of thermodynamic dislocation theory for polycrystals subjected to axially symmetric tension or compression must be equal to 2. We then use large-scale least-square analysis to identify the physics based parameters of this theory and show that the simulated stress-strain curves for OFHC copper, ARMCO iron and 4340 steel agree well with the experiments of Johnson and Cook.
In this paper we present a simple and effective numerical method which allows a fast Fourier transformation-based evaluation of stress generated by dislocations with arbitrary directions and Burgers vectors if the (site-dependent) dislocation density is known. Our method allows the evaluation of the dislocation stress using a rectangular grid with shape-anisotropic discretization cells without employing higher multipole moments of the dislocation interaction coefficients. Using the proposed method, we first simulate the stress created by relatively simple nonhomogeneous distributions of vertic…
A physically-informed continuum crystal plasticity model is presented to elucidate the deformation mechanisms and dislocation evolution in body-centered-cubic (bcc) tantalum widely used as a key structural material for mechanical and thermal extremes. We show our unified structural modeling framework informed by mesoscopic dislocation dynamics simulations is capable of capturing salient features of the large inelastic behavior of tantalum at quasi-static (10$^{-3}$ s$^{-1}$) to extreme strain rates (5000 s$^{-1}$) and at room temperature and higher (873K) at both single- and polycrystal levels…
A continuum theory based on thermodynamics has been developed for modeling diffusional creep of polycrystalline solids. It consists of a coupled problem of vacancy diffusion and mechanics where the vacancy generation/absorption at grain boundaries is driven by grain boundary dislocations climb. The model is stated in terms of general balance laws and completed by the choice of constitutive equations consistent with classical non-equilibrium thermodynamics. The kinetics of diffusional creep is derived from physically-based mechanisms of climb of dislocations at grain boundaries, thus introducin…
The effect of grain size on the flow strength of FCC polycrystals was analyzed by means of computational homogenization. The mechanical behavior of each grain was dictated by a dislocation-based crystal plasticity model in the context of finite strain plasticity and takes into the account the formation of pile-ups at grain boundaries. All the model parameters have a clear physical meaning and were identified for different FCC metals from dislocation dynamics simulations or experiments. It was found that the influence of the grain size on the flow strength of FCC polycrystals was mainly dictate…
The effect of grain size on the flow stress of FCC polycrystals is analyzed by means of a multiscale strategy based on computational homogenization of the polycrystal aggregate. The mechanical behavior of each crystal is given by a dislocation-based crystal plasticity model in which the critical resolved shear stress follows the Taylor model. The generation and annihilation of dislocations in each slip system during deformation is given by the Kocks-Mecking model, which was modified to account for the dislocation storage at the grain boundaries. Polycrystalline Cu is selected to validate the s…
Viscoplastic flow of polycrystalline metallic materials is the result of motion and interaction of dislocations, line defects of the crystalline structure. In the microstructural (physics-based) constitutive model presented in this paper, the main underlying microstructural processes influencing viscoplastic deformation and mechanical properties of metals in cold and warm regimes are statistically described by the introduced sets of postulates/axioms for continuum dislocation dynamics (CDD). Three microstructural (internal) state variables (MSVs) are used for statistical quantifications of dif…
The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of yielding transitions and grain-size effects in polycrystalline solids. Calculations are based on the 1995 experimental results of Meyers et al. for polycrystalline copper under strain-hardening conditions. The main assertion is that the well known Hall-Petch effects are caused by enhanced strengths of dislocation sources at the edges of grains instead of the commonly assumed resistance to dislocation flow across grain boundaries. The theory describes rapid transitions between elastic an…
Grain structure plays a key role in the mechanical properties of alloy materials. Engineering the grain structure requires a comprehensive understanding of the evolution of grain boundaries (GBs) when a material is subjected to various manufacturing processes. To this end, we present a computationally efficient framework to describe the co-evolution of bulk plasticity and GBs. We represent GBs as diffused geometrically necessary dislocations, whose evolution describes GB plasticity. Under this representation, the evolution of GBs and bulk plasticity is described in unison using the evolution e…
The effect of slip transfer on the flow strength of various FCC polycrystals was analyzed by means of computational homogenization of a representative volume element of the microstructure. The crystal behavior was governed by a physically-based crystal plasticity model in the framework of finite strains where slip transfer at grain boundaries was allowed between slip systems suitably oriented according to geometrical criteria. Conversely, slip transfer was blocked if the conditions for slip transfer were not fulfilled, leading to the formation of dislocation pile-ups. All the model parameters …
It is well known that grain boundaries (GBs) have a strong influence on mechanical properties of polycrystalline materials. Not as well-known is how different GBs interact with dislocations to influence dislocation movement. This work presents a molecular dynamics study of 33 different FCC Ni bicrystals, each subjected to four different strain states to induce incident dislocation-GB interactions for 132 unique configurations. The resulting simulations are analyzed to determine properties of the interaction that affect the likelihood of transmission of the dislocation through the GB in an effo…
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…
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 gradien…
The thermodynamic theory of dislocation/grain boundary interaction, including dislocation pile-up against, absorption by, and transfer through the grain boundary, is developed for nonuniform plastic deformations in polycrystals. The case study is carried out on the boundary conditions affecting work hardening of a bicrystal subjected to plane constrained shear for three types of grain boundaries: (i) impermeable hard grain boundary, (ii) grain boundary that allows dislocation transfer without absorption, (iii) grain boundary that absorbs dislocations and allows them to pass later.
Hydrogen atoms absorbed by metals in the hydrogen-containing environments can lead to the premature fracture of the metal components used in load-bearing conditions. Since metals used in practice are mostly polycrystalline, grain boundaries (GBs) can play an important role in hydrogen embrittlement of metals. Here we show that the reaction of GB with lattice dislocations is a key component in hydrogen embrittlement mechanism for polycrystalline metals. We use atomistic modeling methods to investigate the mechanical response of GBs in alpha-iron with various hydrogen concentrations. Analysis in…
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 she…
The thermodynamic dislocation theory presented in preceding papers is used here to describe shear-banding instabilities. Central ingredients of the theory are a thermodynamically defined effective configurational temperature, and a formula for the plastic deformation rate determined by thermally activated depinning of entangled dislocations. An important feature of this paper is an interpretation of yielding transitions in polycrystalline solids.
We study the mechanisms of slip transfer at a grain boundary, in titanium, using Differential Aperture X-ray Laue Micro-diffraction (DAXM). This 3D characterization tool enables measurement of the full (9-component) Nye lattice curvature tensor and calculation of the density of geometrically necessary dislocations (GNDs). We observe dislocation pile-ups at a grain boundary, as the neighbor grain prohibits easy passage for dislocation transmission. This incompatibility results in local micro-plasticity within the slipping grain, near to where the slip planes intersect the grain boundary, and we…
The influence of grain size on the flow stress of various FCC polycrystals (Cu, Al, Ag and Ni) has been analyzed by means of computational homogenization of a representative volume element of the microstructure using a FFT approach in combination with a strain gradient crystal plasticity model. The density of geometrically necessary dislocations resulting from the incompatibility of plastic deformation among different crystals was obtained from the Nye tensor, which was efficiently obtained from the curl operation in the Fourier space. The simulation results were in good agreement with the exp…
Ionic conductivity blocking at grain boundaries in polycrystalline electrolytes is one of the main obstacles that need to be overcome in order to improve the performance of solid state fuel cells and batteries. To this aim, harnessing the physical properties of grain boundaries in ionic conducting materials such as yttria stabilized zirconia (YSZ) down to the atomic scale arises as a greatly important task. Here we present a structural and compositional analysis of a single grain boundary in a 9 mol% yttria content YSZ bicrystal by means of aberration corrected scanning transmission electron m…
Misfit-dislocation hierarchy governs sliding of asymmetric non-CSL grain boundaries
Woodruff School of Mechanical Engineering, Georgia Institute of Technology（佐治亚理工学院机械工程学院）；School of Mechanics and Engineering Science, Peking University（北京大学力学与工程科学学院）；Institute of Microstructure and Property of Advanced Materials, Beijing Key Lab of Microstructure and Property of Advanced Materials, Beijing University of Technology（北京工业大学先进材料微结构及性能研究所）
A theory of flow stress, including the yield strength is proposed for the class of PC materials with equilibrium defect structure (EDS), which is established in the PC material after series of $N_0$ similar treatments of severe plastic deformation at fixed temperature T and characterized by stabilized scalar dislocation density (SDD) and average grain size d. We calculate both the stationary SDD $ρ(b,d,T)$ and suggest a way to calculate $\varepsilon$-evolution of an equilibrium SDD $ρ_{\varepsilon}$ in PC sample under quasy-static loading depending on the average size $d$ of a grain in the ran…
Segregated impurities at grain boundaries can dramatically change the mechanical behavior of metals, while the mechanism is still obscure in some cases. Here, we suggest an unified approach to investigate segregation and its effects on the mechanical properties of polycrystalline alloys using the example of 3$sp$ impurities (Mg, Al, Si, P, or S) at a special type $Σ5(310)[001]$ tilt grain boundary in Cu. We show that for these impurities segregating to the grain boundary the strain contribution to the work of grain boundary decohesion is small and that the chemical contribution correlates with…
Averaging in thermodynamic dislocation theory: general macroscopically uniform stress and strain states
Institute for Advanced Study in Technology, Ton Duc Thang University（Ton Duc Thang大学先进技术研究院）；Faculty of Civil Engineering, Ton Duc Thang University（Ton Duc Thang大学土木工程学院）
Slip transfer at grain boundaries and annealing twin boundaries was studied in polycrystalline Ni by means of slip trace analysis. Slip transfer or blocking was assessed in $>$ 200 boundaries and was related with geometrical criteria that establish the alignment between the active slip systems across the boundaries. It was found that slip transfer mainly occurs at low-angle regular grain boundaries and that a Luster-Morris parameter $>$ 0.8 stands for the best criterion to assess slip transfer. In the case of coherent or incoherent twin boundaries, slip transfer occurs when the residual Burger…
Molybdenum disulfide (MoS2) is a particularly interesting member of the family of two-dimensional (2D) materials due to its semiconducting and tunable electronic properties. Currently, the most reliable method for obtaining high-quality industrial scale amounts of 2D materials is chemical vapor deposition (CVD), which results in polycrystalline samples. As grain boundaries (GBs) are intrinsic defect lines within CVD-grown 2D materials, their atomic structure is of paramount importance. Here, through atomic-scale analysis of micrometer-long GBs, we show that covalently bound boundaries in 2D Mo…
One of the most important aims of grain boundary modeling is to predict the evolution of a large collection of grains in phenomena such as abnormal grain growth, coupled grain boundary motion, and recrystallization that occur under extreme thermomechanical loads. A unified framework to study the coevolution of grain boundaries with bulk plasticity has recently been developed by Admal et al. (2018), which is based on modeling grain boundaries as continuum dislocations governed by an energy based on the Kobayashi--Warren--Carter (KWC) model (Kobayashi et al., 1998, 2000). While the resulting uni…
