Dislocation-based Crystal Plasticity Research Articles

Simulation of Dynamic Recrystallization for Pure Ni Based on Multi-phase-field and Dislocation-based Crystal Plasticity Models Considering Change in Environmental Temperature

Simulation of Dynamic Recrystallization for Pure Ni Based on Multi-phase-field and Dislocation-based Crystal Plasticity Models Considering Change in Environmental Temperature

Investigation of grain boundary and orientation effects in polycrystalline metals by a dislocation-based crystal plasticity model

Polycrystalline metal with well-designed grain structure exhibits different strength and ductility compared with the conventional macro scale materials. In the present study, the mechanisms of strain hardening and inhomogeneous deformation in polycrystals are analyzed by considering the interaction between dislocations and grain boundaries. Firstly, a dislocation density based crystal plasticity model is developed and then used to quantitatively study the grain size and orientation effects in polycrystals. With the decrease of grain size, the accumulation and interaction of dislocations are promoted in the grain, resulting in back-stress hardening. Simultaneously, two opposite effects of the inhomogeneity in grain orientation are obtained by evaluating the local Schmidt factors in each grain and their standard deviation. The findings highlight the effect of grain boundary on the strength and provide quantitative insight into the effect of grain orientation on ductility.

Study of two hardening mechanism caused by geometrically necessary dislocations in thin films with passivation layer

At microscale, thin films with passivation layer exhibit strong size effect during loading and prominent Bauschinger effect during reverse loading. It is commonly recognized that the hardening, which is caused by geometrically necessary dislocations (GNDs) near the passivation layer, is responsible for these phenomena. However, GNDs may contribute to hardening either by slip resistance via a generalized Taylor equation or by back stress originating from elastic interaction between dislocations. Which one dominates the thin film plasticity has not been well understood yet. In this paper, a dislocation-based crystal plasticity model is proposed, which includes both slip resistance and back stress hardenings. The model is applied to simulate passivated thin films with different thickness and the results are compared with experimental data. In the case where slip resistance hardening is considered, the predicted size effect of flow stress is much smaller than that in experiments and there is no obvious Bauschinger effect. While in the case where back stress hardening is considered, the predicted size effect matches well with experiments and the Bauschinger effect is clearly revealed. Also, it is found that the reverse plastic flow during unloading comes from the heterogeneous distribution of stress caused by the pile up of dislocations near the passivation layer.

An analysis of the influence of grain size on the strength of FCC polycrystals by means of computational homogenization

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 simulation strategy and all the model parameters are obtained from dislocation dynamics simulations or experiments at lower length scales and the simulation results were in good agreement with experimental data in the literature. The model is applied to explore the influence of different microstructural factors (initial dislocation density, width of the grain size distribution, texture) on the grain size effect. It is found that the initial dislocation density, ρi, plays a dominant role in the magnitude of the grain size effect and that dependence of flow stress with an inverse power of grain size (σy−σ∞∝dg−x) breaks down for large initial dislocation densities (>1014 m−2) and grain sizes dg> 40 μm in FCC metals. However, it was found that the grain size contribution to the strength followed a power-law function of the dimensionless parameter dgρi for small values of the applied strain (< 2%), in agreement with previous theoretical considerations for size effects in plasticity.

Dislocation-based crystal plasticity FE analysis for kink band formation in Mg-based LPSO phase considering higher-order stress

An FE analysis has been performed for a single crystal of long-period stacking ordered phase on the basis of the dislocation-based crystal plasticity model considering higher-order stress. The mesh dependence on the kink band formation has been discussed from the viewpoint of the strain gradient and size effect. Then, it is shown that the mesh dependence of kink deformation in the FE analysis can be removed even when the scale ratio is relatively small. Moreover, it is indicated that the disclination quadrupole structure in the kink band can be expressed qualitatively by use of the incompatibility of crystal slip.

Multiple slip dislocation patterning in a dislocation-based crystal plasticity finite element method

Dislocation structures forming during cyclic loading of fcc metals are fatigue damage precursors. Their specific structures are caused by the motion and interactions of dislocations. Depending on the load conditions, the grain orientation, the stacking fault energy, a variety of different dislocation structures appear in the material such as labyrinths, cells, veins and persistent slip bands. We present a continuum dislocation-based model for cyclic fatigue and incorporate it into a crystal plasticity finite element solver. A method for the simulation of dislocation junction formation is introduced, which reproduces the behaviour of discrete objects, such as dislocations, in a continuum framework. The formation of dislocation walls after 50 and 100 deformation cycles at 0.95% and 0.65% strain amplitude starting from an initial random dislocation distribution is predicted for 〈001〉 and 〈11¯0〉 oriented crystals. Simulations and cyclic tension-compression experiments of polycrystalline 316L stainless steel are performed to compare our model with another model based on edge and screw dislocation densities. The simulated dislocation structures and experimental results, obtained with the electron channeling contrast imaging technique, are compared using a 2D orientation distribution function of the dislocation structures. The dominant orientation of dislocation walls is predicted by the new model; it turns out to be perpendicular to the intersection line between the two slip planes involved in their formation and at an angle of around 45o from the loading axis. This agrees well with the experimental observations and represents a step forward for understanding the formation mechanism of these dislocation structures.

A dislocation-based crystal plasticity framework for dynamic ductile failure of single crystals

A framework for dislocation-based viscoplasticity and dynamic ductile failure has been developed to model high strain rate deformation and damage in single crystals. The rate-dependence of the crystal plasticity formulation is based on the physics of relativistic dislocation kinetics suited for extremely high strain rates. The damage evolution is based on the dynamics of void growth, which are governed by both micro-inertia as well as dislocation kinetics and dislocation substructure evolution. An averaging scheme is proposed in order to approximate the evolution of the dislocation substructure in both the macroscale as well as its spatial distribution at the microscale. Additionally, a concept of a single equivalent dislocation density that effectively captures the collective influence of dislocation density on all active slip systems is proposed here. Together, these concepts and approximations enable the use of semi-analytic solutions for void growth dynamics developed in (Wilkerson and Ramesh, 2014), which greatly reduce the computational overhead that would otherwise be required. The resulting homogenized framework has been implemented into a commercially available finite element package, and a validation study against a suite of direct numerical simulations was carried out.

Multiscale Simulation of Dynamic Recrystallization for α-Mg Phase in Mg/LPSO Alloys Based on Multi-Phase-Field and Dislocation-Based Crystal Plasticity Model

Magnesium alloy with Long-Period Stacking Ordered Structure (LPSO) and α-Mg (ordinary HCP structure) phase is expected for a new structural material due to its excellent mechanical properties. Its materials strengthening arises from the kink band formation in LPSO phase and the grain refinement of α-Mg phase in the vicinity of LPSO phase because of recrystallization. In the present study, a multiscale and multiphysics computation for the dynamic recrystallization in α-Mg phase is carried out by coupling the dislocation-based crystal plasticity model for HCP crystals proposed previously by the authors with the multi-phase field model through dislocation density. In the present model, not only the environmental temperature-dependences of nucleation and nucleus growth but also a pinning effect of boundary migration of recrystallized grain boundary owing to existence and influence of additive elements are newly taken into account. Furthermore, grain size behaviors of recrystallized nuclei are investigated for various volume fractions of additive element and ratios of grain boundary segregation.

Numerical study of the size-dependent deformation morphology in micropillar compressions by a dislocation-based crystal plasticity model

In recent years, size-dependent deformation morphology has been observed in uniaxial micropillar compression experiments. After deformation, large pillar shows a barrel shape while small pillar shows a clear shear band. Meanwhile, one or more slip systems are activated at different sizes. In order to reveal the underlying mechanism of this size-dependent phenomenon, a dislocation-based crystal plasticity model is developed in this paper to simulate the uniaxial compression tests for different sizes of pillars with material imperfection. The simulation results show that: (1) The transition from barrel shape to severe shear with decreasing pillar size is well captured by the newly developed model. Two slip systems operate equally in large pillar and only one slip system is activated in small pillar. (2) The back stress induced by dislocation mutual interactions plays an important role in size-dependent deformation morphology. High back stress in small pillar impedes the second slip system to operate. (3) The critical size of transition from double slip (or multiple slip) to single slip is obtained and it is quantitatively comparable with experiments in a specific case. (4) Material softening is necessary to trigger slip band. It can be concluded that the competition between the short range back stress and the external resolved shear stress results in the transition from barrel shape to shear band during the micropillar compression tests.

Dislocation and back stress dominated viscoplasticity in freestanding sub-micron Pd films

A dislocation-based crystal plasticity model is developed in order to study the mechanical and creep/relaxation behaviour of polycrystalline metallic thin films. The model accounts for the confinement of plasticity due to grain boundaries and for the anisotropy of individual grains, as well as for the significant viscoplastic effects associated to dislocation dominated thermally activated mechanisms. Numerical predictions are assessed based on experimental tensile test followed by relaxation on freestanding Pd films, based on an on-chip test technique. The dislocation-based mechanism assumption captures all the experimental trends, including the stress–strain response, the relaxation behaviour and the dislocation density evolution, confirming the dominance of a dislocation driven deformation mechanism for the present Pd films with high defects density. The model has also been used to address some original experimental evidences involving back stresses, Bauschinger effect, backward creep and strain recovery.

環境温度変化を考慮した転位-結晶塑性モデルおよびMulti-phase-fieldモデルに基づくLPSO型Mg二相合金の強化機構に対する検討

環境温度変化を考慮した転位-結晶塑性モデルおよびMulti-phase-fieldモデルに基づくLPSO型Mg二相合金の強化機構に対する検討

転位-結晶塑性シミュレーションによるMg基LPSO相単結晶におけるキンク帯形成位置の検討

転位-結晶塑性シミュレーションによるMg基LPSO相単結晶におけるキンク帯形成位置の検討

Multi-phase-field理論および転位-結晶塑性論に基づくLPSO型Mg二相合金に対する動的再結晶シミュレーション

Multi-phase-field理論および転位-結晶塑性論に基づくLPSO型Mg二相合金に対する動的再結晶シミュレーション

On the formation of adiabatic shear bands in textured HCP polycrystals

Adiabatic shear band (ASB) formation in textured HCP polycrystals has been investigated under regimes of high rate compression and shear loading using dynamic thermo-mechanically coupled, dislocation-based crystal plasticity modelling. The balance between rate of plastic dissipation leading to internal heat generation versus rate of thermal diffusion at a crystallographic length scale has been shown to be pivotal for the formation or otherwise of ASBs. Micro-texture has been found to have a key role in both advancing and inhibiting shear band growth, and its control offers the possibility of new alloys with higher impact strength over strain rate range1 × 10−2 to 1 × 105 s−1. Texture has been found to lead to wide variations in applied macroscopic strain at which ASB formation occurs, such that strain level in isolation is inappropriate as a universal indicator of ASB onset.High-rate shear loading is found to lead to lower onset strains for ASBs compared to high rate compression, but the dependence of both on texture leads to considerable variation in strain level for ASB formation. A preliminary map demarcating ASB onset has been established over regimes of applied strain and texture for dynamic shear and compression.

026 Multi-phase-fieldモデルおよび転位-結晶塑性モデルに基づくLPSO型Mg二相合金のα-Mg相に対する動的再結晶シミュレーション

026 Multi-phase-fieldモデルおよび転位-結晶塑性モデルに基づくLPSO型Mg二相合金のα-Mg相に対する動的再結晶シミュレーション

Mg基LPSO相単結晶におけるキンク帯形成の転位-結晶塑性シミュレーション

In this study, two-dimensional FE simulations for a single crystal of a Mg-based LPSO phase are performed to computationally reproduce a deformation kink in the LPSO phase using a dislocation-based crystal plasticity model for HCP crystals developed in our previous work. We take account of activities of only basal slip systems of which CRSSes are set to be consistent with the experimental results on the LPSO phase. In addition, the characteristic shape of the LPSO crystal caused by preferential growth along the a-axis is introduced into the specimen. Since we need to consider some initial imperfection to numerically express a buckling phenomenon such as the deformation kink, we assume a small inclination of the basal plane for the loading direction as the initial crystal orientation. Moreover, we apply rmin method for the slip increment to the analysis for stability of calculation. As a result of this simulation, we predict the kink band formation computationally through the accumulation of GN dislocation, disclination and the crystal lattice rotation. The validity of the present model is discussed by comparing obtained results with a well-known explanation for kink formation based on dislocation behaviors qualitatively. Then we conclude that the kink band is rapidly formed by localized basal slips.

OS0121-236 CRSSの寸法依存性を考慮したMg基LPSO相単結晶のマイクロピラーに対する転位-結晶塑性FEM解析

In this study, a finite element analysis based on a dislocation-based crystal plasticity model considering a size dependence of a critical resolved shear stress (CRSS) is performed to reproduce a size dependence of yield stress in a micropillar composed of single crystal of Mg-based LPSO phase. The CRSS model in which a size-dependent term is proportional to the inverse of a pillar diameter is applied and a numerical parameter is identified from experimental results. We consider four initial crystal orientations where a basal slip, prismatic slip, pyramidal slip and kink deformation are likely to occur. The results show that the applied model reproduces the size dependence of the yield stress. In addition, in the initial orientation where a kink deformation is tend to occur, the deformation mode changes according to the specimen size.

A phase-field model of twinning and detwinning coupled with dislocation-based crystal plasticity for HCP metals

In this study, a phase-field model describing both twinning and detwinning that is coupled with a dislocation-based crystal plasticity model is constructed for HCP metals, particularly for magnesium. The driving force of twinning is assumed to be resolved shear stress acting on the twin system. The plastic anisotropy of dislocation mobility in an HCP crystal is described via the dislocation mean free path model, which is incorporated into the hardening law. These models are coupled through an order parameter and stress. Using the present model, several FE analyses on single-crystal magnesium are carried out. The obtained results show that the nominal stress–strain response, twinning and detwinning behavior and the consistent value of twin shear around twins are reproduced by this model. In addition, from the results of tensile simulation of a specimen including a number of twin nuclei, twin nucleation is suggested to occur so as not to increase the mechanical energy by the accumulation of elastic strain and dislocation.

Investigation on Intragranular Stress of Mg Including Several Twin-Bands Using Dislocation-Based Crystal Plasticity and Phase-Field Models

A coupled model based on crystal plasticity and phase field theories that express both plastic anisotropy of HCP metals and expansion/shrinkage of twin-bands is proposed in the present study. In this model, the difference of the hardening rate in each slip system is expressed by changing their dislocation mobility as a numerical parameter defined in the crystal plasticity framework. The stress calculated via crystal plasticity analysis becomes to the driving force of multi-phase filed equations that express the evolution of twin bands of several variants, which include both the growth and shrinkage. Solving this equation set, the rate of twinning/detwinning and the mirror-transformed crystal basis in the twinned/detwinned phase are obtained and then, crystal plasticity analysis is carried out again. Using the present model, a uniaxial cyclic loading simulation along [0001] direction on the specimen including two variants of twin-bands is carried out by means of finite element method (FEM). The results show that the detwinning stress decreases with increase of the pre-tensioned strain. This is caused by a residual compression stress resulting from the twin shearing that occurs in the vicinity of two twin boundaries approaching each other.

A Dislocation-Based Crystal Plasticity Simulation on Kink Band Formation and Evolution in Polycrystalline Mg Alloy with LPSO Phase

A three-dimensional compression analysis is performed by finite element method using a dislocation-based crystal plasticity model to clarify the formation mechanism of kink band in a polycrystalline Mg alloy with a long-period stacking ordered structure (LPSO) phase. The crystalline structure of LPSO phase is regarded as a HCP for simplicity, however, any deformation twinning is not taken into account. In addition, the activities of non-basal systems are considerably limited in the LPSO phase setting the values of their critical resolved shear stresses to large ones. We analyze a simple polycrystalline specimen composed of two α-Mg matrix phases and a LPSO phase both having a rectangular shape and twist grain boundaries are introduced into the interface. The obtained result shows that the kink band formation in the alloy is accomplished by the basal slips with different variants and the non-basal slips are activated on the grain boundary to maintain the continuity of deformation.