Dislocation-based Crystal Plasticity Model Research Articles

Effect of micron-scale nonmetallic inclusions on fatigue crack nucleation in a nickel-based superalloy

Micron-level nonmetallic inclusions are likely to be a limiting factor for further improvement in the fatigue resistance of nickel-based superalloys. To investigate the fatigue response of nickel-based superalloys containing micro-inclusions, a dislocation-based crystal plasticity model was employed for numerical simulations, and the local energy storage density criterion was used for damage evolution analysis. The results showed that, as a hard phase, micro-inclusions interfered with the plastic deformation of the matrix, as evidenced by the inhomogeneous slipping of the main slip systems and the activation of new slip systems. Additionally, micro-inclusions induced the accumulation of geometrically necessary dislocations (GNDs) around them. When micro-inclusions appeared on grain boundaries, the above factors changed the energy required for local deformation through potential hardening effects in the model and ultimately affected the evolution of the local energy storage density. When micro-inclusions appeared inside grains, the evolution of local energy storage was often dominated by plastic deformation only. The above mechanism is microstructure sensitive and spatially limited, which leads to the dispersion of lifetimes and negligible effect of micro-inclusions on distal grains.

Crystal plasticity analysis of the evolutions of temperature, stress and dislocation in additively manufactured tungsten

Additive manufacturing (AM) has brought new opportunities for the fabrication of refractory metal tungsten (W). However, the cracking issue in additive manufactured pure W has not been solved, restricting its application. The cracking behavior is associated with the high residual stress, which is caused by the high temperature gradient and cooling rate during AM, as well as the internal brittleness of W. In order to solve this problem, the evolution of the internal microstructure and the corresponding thermal and loading conditions during AM has to be systematically investigated, but the related work is very rare. In the current work, a thermal-mechanical coupled dislocation-based crystal plasticity model is developed, which considers the temperature dependent plasticity induced by the thermal-activated kink-pair mechanism of screw dislocation. This model is applied to investigate the evolution of temperature, stress, and dislocation behaviors in single crystal and polycrystalline W during AM. The influences of crystal orientation and adding alloying element Ta are also discussed from the microscopic and macroscopic perspectives.

Polyphase crystal plasticity for high strain rate: Application to twinning and retwinning in tantalum

Upon increasing strain rate a switch operates in tantalum response from a plasticity dominated regime to a twinning dominated regime. This transition is investigated by means of a polyphase crystal plasticity model which combines a Phase Field-Reaction Pathway formalism and a dislocation-based crystal plasticity model. The proposed formalism for twinning considers an unbounded number of variants which permits the observation of twinning, detwinning and retwinning phenomena. The crystal plasticity model takes into account slip systems interactions and includes two glide regimes to deal with high strain rates. A model for dislocation inheritance during twinning is proposed. Simulations highlight a dual role of plasticity: strain hardening inside the matrix may, under certain conditions, hinder the formation of twin variants whereas plasticity inside the variants further relaxes the residual stress due to twins interaction and contributes to shape the variant.

Dislocation Density Evolution in Low-Cycle Fatigue of Steels Using Dislocation-Based Crystal Plasticity

Dislocation accumulation caused by a crystallographic slip or plastic flow is one of the most critical factors for the growth of fatigue cracks. The dislocation density-based crystal plasticity method accounting for mobile and immobile dislocation densities has been widely used to evaluate crack behavior in polycrystals. However, the evolution of mobile and immobile dislocation densities in fatigue has not been carefully investigated, especially during the crack nucleation period. In the present study, a dislocation-based crystal plasticity model is employed and verified with experimental results. A representative domain with 39 grains is used to evaluate the dislocation density evolution in fatigue crack nucleation. The results indicate that mobile and immobile dislocation densities evolve at a decreasing rate in low plasticity and a constant rate in large plasticity for loading cases with constant strain amplitudes, whereas an increasing rate of dislocation density evolution is observed for loading cases with variable strain amplitudes. By analogy with cumulative plastic strain, a fatigue crack nucleation criterion is proposed, which is correlated well with the Coffin-Manson relationship. Based on a grain level analysis, a loading case with a low strain rate results in transgranular or mixed-mode (intergranular and transgranular) fatigue damage. In comparison, immobile dislocation density at a high strain rate mainly builds up at the grain boundary, indicating intergranular fatigue damage.

Phase-field and dislocation-based crystal plasticity analysis on lath martensitic structures formation in polycrystalline metastable austenitic steel

Although strength of TRIP steels can be compatible with ductility owing to deformation-induced martensitic transformation, there is currently no model describing simultaneously the deformation and microstructure formation processes of TRIP steel. In this report, we introduce the basis vectors of martensitic transformation derived in the previous report into the crystal plasticity model and develop a new material model based on a dislocation-based crystal plasticity model coupled with a multi-phase-field one. Also, we consider plastic deformation of austenite phase for more realistic analyze. After that, we use this model to reproduce the formation process of martensitic lath-block structure in a metastable austenitic polycrystal. As a result, it is shown that the microstructure of lath martensite is numerically formed in a polycrystalline micro-specimen using 6 variants in a CP group.

Effects of crystallography on hot-spot formation in porous RDX single crystals

The thermomechanical behavior of porous RDX single crystals is studied under dynamic loading using an anisotropic dislocation-based crystal plasticity model that accounts for deformation-induced heating. A micromechanics-based framework is proposed to account for micro-inertially confined dynamic collapse of pores. A suite of finite element calculations are carried out to systematically elucidate the role of crystallographic orientation on hot-spot formation. Under particular loading orientations, the porous RDX crystals are found to be quite sensitive to deviatoric and volumetric strain localizations, even for loading situations that do not particularly promote strain localization in isotropic materials. Due to the anisotropy-induced strain localizations, fairly severe hot-spots are predicted even under moderate applied strains. The susceptibility of porous RDX to strain localize and form severe hot-spots under particular loading orientations has important implications for accidental detonation of these energetic materials.

Modelling and simulation of dynamic recrystallisation based on multi-phase-field and dislocation-based crystal plasticity models

ABSTRACT The mechanical properties of metals used as structural materials are significantly affected by hot (or warm) plastic working. Therefore, it is industrially important to predict the microscopic behaviour of materials in the deformation process during heat treatment. In this process, a number of nuclei are generated in the vicinity of grain boundaries owing to thermal fluctuation or the coalescence of subgrains, and dynamic recrystallisation (DRX) occurs along with the deformation. In this paper, we develop a DRX model by coupling a dislocation-based crystal plasticity model and a multi-phase-field (MPF) model through the dislocation density. Then, the temperature dependence of the hardening tendency in the recrystallisation process is introduced into the DRX model. A multiphysics simulation for pure Ni is conducted, and then the validity of the DRX model is investigated by comparing the numerical results of microstructure formation and the nominal stress–strain curve during DRX with experimental results. The obtained results indicate that in the process of DRX, nucleation and grain growth occur mainly around grain boundaries with high dislocation density. As deformation progresses, new dislocations pile up and subsequent nucleation occurs in the recrystallised grains. The influence of such microstructural evolution appears as oscillation in the stress–strain curve. From the stress–strain curves, the temperature dependence in DRX is observed mainly in terms of the yield stress, the hardening ratio, and the change in the hardening tendency after nucleation occurs.

Unravelling Anisotropy Evolution during Spiral Pipe Forming: a Multiscale Approach

Spiral forming of bainitic steel coils into large diameter pipes involves a complex deformation history with several strain path changes. These lead to mechanical properties on pipe which are macroscopically different compared to coil. A detailed understanding of the property evolution during spiral pipe forming is crucial to tailor the coil material and to ensure safe pipe operation. However, it has proven difficult to correctly reproduce the anisotropic strength evolution during pipe forming with available phenomenological hardening models. Unravelling the factors contributing to macroscopic anisotropy is inherently a multi-scale problem due to the complex microstructures exhibited by modern bainitic linepipe steels. They promote a large Bauschinger effect, aside from cross loading-effects and more or less pronounced Lüders banding. Here, we present selected experimental and numerical results related to our efforts to predict the mechanical properties of bainitic steel pipes manufactured from hot rolled coils. Across the scales, we consider sources for anisotropy, such as residual stresses, crystallographic texture and grain substructure. A dislocation-based crystal plasticity model incorporated into a computationally efficient hierarchical multi-scale forming simulation is employed to predict texture and strength changes.

Effect of slip transmission at grain boundaries in Al bicrystals

The effect of slip transfer on the deformation mechanisms of Al bicrystals was explored using a rate-dependent dislocation-based crystal plasticity model. Three different types of grain boundaries (GBs) were included in the model by modifying the rate of dislocation accumulation near the GB in the Kocks-Mecking law, leading to fully-opaque (dislocation blocking), fully-transparent and partially-transparent GBs. In the latter, slip transmission is only allowed in pairs of slip systems (SS) in neighbour grains that are suitably oriented for slip transfer according to the Luster-Morris parameter. Modifications of the GB character led to important changes in the deformation mechanisms at the GB. In general, bicrystals with fully-opaque (dislocation blocking) boundaries showed an increase in the dislocation density near the GB, which was associated with an increase in the Von Mises stress. In contrast, the dislocation pile-ups and the stress concentration were less pronounced in the case of partially-transparent boundaries as the slip in one grain can progress into the next grain with some degree of continuity. No stress concentrations were found at these boundaries for fully-transparent boundaries, and there was continuity of strain across the boundary, which is not typical of most experimentally observed GBs (Hémery et al., 2018; Bieler et al., 2019). Simulations of ideal bicrystals oriented for favorable slip transfer on the most highly favored slip system in grains with high Schmid factors for slip transfer depends on the number of active SS in operation in the neighborhood indicating that most boundaries will lead to nearly opaque conditions while some boundaries will be transparent. Finally, the model was applied to a particular experimentally observed GB in which slip transfer was clearly operating indicating that the model predicted a nearly transparent GB.

Grain boundary strengthening of FCC polycrystals

Abstract

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.

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.

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.

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.

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.