Dislocation Flow Research Articles

Hot deformation behavior of Hastelloy-X preforms built using directed energy deposition based laser additive manufacturing

Hastelloy-X (Hast-X) preforms built using Laser Directed Energy Deposition (LDED) are investigated for hot workability using hot deformation tests (temperature: 1223–1373 K, strain rate: 0.01–10 s−1). Strain hardening is observed at lower strain due to dislocation pileup and flow softening is observed at higher strain. Cyclic strain rate jump test and jump temperature tests are performed to calculate strain sensitivity factor and activation energy (Q), respectively. The derived constitutive equations are found to be in good agreement with experimental results with maximum deviation of 20%. Average Q value is found to be 280 kJ·mol−1, which is lower than that for similar alloys in wrought condition. The lower ‘Q’ value confirms the suitability of hot working of LDED built Hast-X as a potential method to build high strength engineering components.

On the importance of dislocation flow in continuum plasticity models for semiconductor materials

Abstract Crystalline defects, such as dislocations, may have a strong negative influence on the performance and quality of electronic devices. Modelling the defect evolution of such systems helps to understand where defects occur, how they evolve and interact, Modelling also might allow to avoid – or at least to reduce – the number of line defects in such materials. A widely used continuum model for predicting the evolution of dislocation density in semiconductors is the Alexander-Haasen (AH) model (Alexander and Haasen, Solid state physics,1969) which describes the evolution of dislocation density through a local dislocation multiplication law; the motion of dislocations, i.e. dislocation flow, is not considered. Within this work, the underlying assumptions for the validity of the AH model are studied and compared to a more complex continuum model of dislocation dynamics (CDD) which explicitly considers dislocation fluxes. We use a simplified 2D scenario of a 4H-SiC crystal at the end of the growth as a benchmark system. Our comparisons show that considering the motion of dislocations can have a significant influence on the evolution and final distribution of dislocation density, which may strongly limit the applicability of the AH model. Based on the CDD model, we then investigate the cooling process and study the effect of the cooling rate on the resulting dislocation microstructure.

In-situ TEM characterization of the tensile deformation of ion-irradiated HT-UPS steel at RT and 400 °C

High-temperature ultra-fine precipitate strengthened (HT-UPS) steel samples were irradiated with 1 MeV Kr ions, and in-situ tensile deformed at room temperature (RT) and 400 °C. The dislocation flow in irradiated samples was significantly restricted by the irradiation defects, and the deformation took place in localized deformation bands. While in unirradiated specimens, the deformation happened evenly across the grains. As a result of the localized deformation, intricate deformation band structures were observed in the irradiated specimens, which are composed of a central band and two defect reduced zones on the two sides. The irradiation defects were in-situ observed to interact with deformation induced dislocations, and were removed by the latter. Despite of the differences, the irradiated samples reserved similar work hardening behaviors as the unirradiated samples. The deformation inside the defect reduced bands in irradiated samples showed similar characteristics as in the unirradiated sample. The last stage deformation also showed similar deformation characteristics, regardless of the irradiation history.

Composition and Face Polarity Influences on Mechanical Properties of (111) Cd1−yZnyTe Determined by Indentation

(111)-oriented CdZnTe semiconductor material exhibits a crystal polarity and hence, a face terminated by Cd atoms, conventionally called (111) A face with an opposite face terminated by Te atoms, called (111) B face. These A and B faces have different properties. Their mechanical properties have been studied by mechanical indentation. Sample surfaces were carefully prepared and mechanically and chemically polished, while the crystalline orientation and material defectivity was monitored on both faces using x-ray rocking curve measurements around the (222) orientation in order to evaluate faces with similar quality. The elastic moduli and hardness values of the A and B faces of CdZnTe were similar. Hardness increased from 0.60 GPa to 0.90 GPa with Zn concentration on the B face as a result of solution strengthening. Crack formation and propagation was carefully studied. Both toughness value and crack resistance were affected by polarity. A model involving plastic dislocation flow is proposed to interpret the results.

Effects of non-isothermal annealing on microstructure and mechanical properties of severely deformed aluminum samples: Modeling and experiment

Abstract In order to investigate the evolution of microstructure and flow stress during non-isothermal annealing, aluminum samples were subjected to strain magnitudes of 1, 2 and 3 by performing 2, 4 and 6 passes of multi-directional forging. Then, the samples were non-isothermally annealed up to 150, 200, 250, 300 and 350 °C. The evolution of dislocation density and flow stress was studied via modeling of deformation and annealing stages. It was found that 2, 4 and 6 passes multi-directionally forged samples show thermal stability up to temperatures of 250, 250 and 300 °C, respectively. Modeling results and experimental data were compared and a reasonable agreement was observed. It was noticed that 2 and 4 passes multi-directionally forged samples annealed non-isothermally up to 350 °C have a lower experimental flow stress in comparison with the flow stress achieved from the model. The underlying reason is that the proposed non-isothermal annealing model is based only on the intragranular dislocation density evolution, which only takes into account recovery and recrystallization phenomena. However, at 350 °C grain growth takes place in addition to recovery and recrystallization, which is the source of discrepancy between the modeling and experimental flow stress.

Deformation behaviour of TiN and Ti–Al–N coatings at 295 to 573 K

Temperature-dependent nanoindentation testing was employed to investigate the deformation behaviour of magnetron sputtered (100) TiN and Ti1-xAlxN (x = 0.34, 0.52, 0.62) coatings in the temperature range from 295 to 573 K. The maximum temperature is sufficiently below the deposition temperature of 773 K to guarantee for stable microstructure and stress state during testing. The TiN coating displayed the same hardness as bulk single crystal (SC) TiNbulk. The addition of aluminium to TiN (to form single-phase face centred cubic structured Ti1-xAlxN coatings) increased the room temperature hardness due to increased bond strength, lattice strain and higher activation energy for the dislocation slip. For coatings with a low aluminium content, Ti0.66Al0.34N, the decrease in hardness with temperature was similar to the TiN coating and SC-TiNbulk. In contrast, the hardness of coatings with moderate, Ti0.48Al0.52N, and high, Ti0.38Al0.62N, aluminium contents varied little up to 573 K. Thus, the Ti1-xAlxN matrix is mechanically more stable at elevated temperatures than its TiN relative, by providing a lower decrease in lattice resistance to the dislocation flow with increasing temperature. The findings suggest that the addition of Al to TiN (to form Ti1-xAlxN solid solutions) not only improves the hardness but also leads to stable hardness with temperature, and emphasizes the importance of bonding states and chemical fluctuations, next to structure and morphology of the coatings that develop with changing the chemistry.

New insight for mechanical properties of metals processed by severe plastic deformation

The steady state is expected when applying severe plastic deformation (SPD) techniques to process metals. In this study, we propose a method to study the steady state regarding the microstructural features and the mechanical properties, which are verified by the experimental results. More importantly, the initial state of as-prepared metal depending mainly on the processing conditions is critical for the subsequent constitutive relations. Within the framework of dislocation-based crystal plasticity, it is revealed that the dislocation density and flow stress will not change during further deformation when the initial dislocation density is equal to the steady-state value under the loading conditions. In addition, if the initial dislocation density is larger or smaller than the steady-state value, then the dislocation density and flow stress will decrease or increase with increasing strain, and tend to approach the steady-state value. These mechanisms provide not only a physical interpretation for various experimental observations such as near-perfect elastoplasticity, strain hardening and strain softening, but also insightful guidance for investigating the strengthening mechanisms in gradient nano-grained metal produced by SPD.

Flow Stress Evolution in Further Straining of Severely Deformed Al

To investigate the flow stress evolution in further straining of severely deformed Al sheets, a comprehensive model which considers both mechanical and metallurgical alterations is needed. In this study, constrained groove pressing (CGP) as a severe plastic deformation method, and a flat rolling process for further straining are utilized. Using basic mechanical models, strain and strain rate were calculated for this process. Dislocation density and flow stress evolutions were predicted by utilizing initial mechanical data, considering the ETMB (Y. Estrin, L. S. Toth, A. Molinari, and Y. Brechet) dislocation density model. Based on these model predictions, the combination of the CGP process with a further rolling process results in higher flow stresses than repeating the specific process discretely. This phenomenon can be attributed to the ability of the rolling process to produce a greater strain rate, which, in turn, leads to the higher flow stresses. Thorough data from the mechanical tests as well as X-ray diffraction profiles strongly support the validity of the model in the prediction of flow stress and dislocation density, respectively.

Interaction Length for Dislocations in Compositionally-Graded Heterostructures

Several simple models have been developed for the threading dislocation behavior in heteroepitaxial semiconductor materials. Tachikawa and Yamaguchi [Appl. Phys. Lett., 56, 484 (1990)] and Romanov et al. [Appl. Phys. Lett., 69, 3342 (1996)] described models for the annihilation and coalescence of threading dislocations in uniform-composition layers, and Kujofsa et al. [J. Electron. Mater., 41, 2993 (2013)] extended the annihilation and coalescence model to compositionally-graded and multilayered structures by including the misfit dislocation-threading dislocation interactions. However, an important limitation of these previous models is that they involve empirical parameters. The goal of this work is to develop a predictive model for annihilation and coalescence of threading dislocations which is based on the dislocation interaction length Lint. In the first case if only in-plane glide is considered the interaction length is equal to the length of misfit dislocation segments while in the second case glide and climb are considered and the interaction length is a function of the distance from the interface, the length of misfit dislocations, and the density of the misfit dislocations. In either case the interaction length may be calculated using a model for dislocation flow. Knowledge of the dislocation interaction length allows predictive calculations of the threading dislocation densities in metamorphic device structures and is of great practical importance. Here we demonstrate the latter model based on glide and climb. Future work should compare the two models to determine which is more relevant to typical device heterostructures.

Density-based constitutive modelling of P/M FGH96 for powder forging

A set of viscoplastic constitutive equations is presented in this study to predict hot compressive deformation behaviour and densification levels of powder metallurgy (P/M) FGH96 nickel-base superalloy during direct powder forging (DPF) process. The constitutive equations make use of the elliptic equivalent stress proposed in porous material models, and unify the evolution of relative density, normalised dislocation density, isotropic hardening and flow softening of the powder compact. A gradient-based optimisation technique is adopted to determine the material constants using the experimental data obtained from Gleeble isothermal uniaxial compression tests of HIPed FGH96 at different temperatures and strain rates. The developed constitutive equations are incorporated into finite element code DEFORM via user-defined subroutine for coupled thermo-mechanical DPF process modelling. The constitutive equations benefiting from the viscoplastic densification model of the calibrated Abouaf, among the six studied porous material models, compare favourably with the experimental data, while the equations integrating the porous material model of Shima and Oyane provide excellent agreement with experiments in the low density outer region of the powder compact.

Changes in the diffusion properties of nonequilibrium grain boundaries upon recrystallization and superplastic deformation of submicrocrystalline metals and alloys

The effect of an increase in the coefficient of the grain-boundary diffusion upon recrystallization and superplastic deformation of submicrocrystalline (SMC) materials prepared by severe plastic deformation has been studied. It is shown that the coefficient of the grain-boundary diffusion of the SMC materials is dependent on the intensity of the lattice dislocation flow whose value is proportional to the rate of the grain boundary migration upon annealing of SMC metals or the rate of the intragrain deformation under conditions of superplastic deformation of SMC alloys. It is found that, at a high rate of grain boundary migrations and high rates of superplastic deformation, the intensity of the lattice dislocation flow bombarding grain boundaries of SMC materials is higher than the intensity of their diffusion accommodation, which leads to an increase in the coefficient of the grain-boundary diffusion and a decrease in the activation energy. The results of the numerical calculations agree well with the experimental data.

Critical Layer Thickness: Theory and Experiment in the ZnSe/GaAs (001) Material System

The critical layer thickness (CLT) determines the criteria for dislocation formation and the onset of lattice relaxation. Although several theoretical models have been developed for the critical layer thickness, experimentally-measured CLTs in ZnSe/GaAs (001) heterostructures are often at variance with one another as well as with established theories. In a previous work [T. Kujofsa et al., J. Vac. Sci. Technol. B, 34, 051201 (2016)], we showed that the experimentally measured CLT may be much larger than the equilibrium value when using finite experimental resolution. In this work, we apply a general dislocation flow model to determine the apparent critical layer thickness as a function of the experimental resolution for ZnSe/GaAs (001) heterostructures. More importantly, we compare the results utilizing different equilibrium theories and therefore varying driving forces for the lattice relaxation in order to determine which established models are consistent with several measured values of CLT for ZnSe/GaAs (001) once kinetically-limited relaxation and finite experimental strain resolution are taken into account.

A continuum approach to combined γ/γ′ evolution and dislocation plasticity in Nickel-based superalloys

In single crystal Nickel-based superalloys subject to creep loading, the γ/γ′ phase microstructure co-evolves with the system of dislocations under load. Computational modeling thus requires multiphysics approaches capable of describing and simulating both phase and defect microstructures within a common conceptual framework. To do so, we formulate a coupled continuum model of the evolution of phase and dislocation microstructures. The simulated γ/γ′ phase microstructure accounts for concentration as well as crystallographic order parameters. Dislocation microstructure evolution is described in terms of dislocation densities and associated stress-driven dislocation fluxes. The creep strain curve is obtained as a natural by-product of the microstructure evolution equations. We perform simulations of γ/γ′ evolution for different dislocation densities and establish the driving forces for microstructure evolution by analyzing in detail the changes in different contributions to the elastic energy and chemical free energy density, as well as the evolution of stress concentrations that may trigger the transition from dislocation flow in the γ channels towards shearing of the γ′ precipitates. Our investigation reveals the mechanisms controlling the process of directional coarsening (rafting) and demonstrates that the kinetics of rafting significantly depends on characteristics of the dislocation microstructure. In addition to rafting under constant load, we investigate the effect of changes in loading conditions and explore the possibility of improving creep properties by pre-rafting along a different loading path.

Yielding transitions and grain-size effects in dislocation theory

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, Andrade, and Chokshi [Metall. Mater. Trans. A 26, 2881 (1995)MMTAEB1073-562310.1007/BF02669646] 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 and plastic deformation at yield points; thus it can be used to predict grain-size dependence of both yield stresses and flow stresses.

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.

Modelling the temperature rise effect through high-pressure torsion

An approach composed of the thermodynamics-based dislocation model and the Taylor theory is used to investigate the evolution of microstructure and flow stress during high-pressure torsion (HPT). The incremental temperature rise is considered through the modelling of HPT. The temperature can affect the annihilation of dislocations and thus the dislocation density. The model predicts the dislocation density, sub-grain size and flow stress during HPT. The modelling results are compared with the experimental data and the modelling results without considering the incremental temperature rise. A remarkable agreement is observed between the modelling results with considering the temperature rise effect and the experimental data.

Strain gradient plasticity-based modeling of hydrogen environment assisted cracking

Finite element analysis of stress about a blunt crack tip, emphasizing finite strain and phenomenological and mechanism-based strain gradient plasticity (SGP) formulations, is integrated with electrochemical assessment of occluded-crack tip hydrogen (H) solubility and two H-decohesion models to predict hydrogen environment assisted crack growth properties. SGP elevates crack tip geometrically necessary dislocation density and flow stress, with enhancement declining with increasing alloy strength. Elevated hydrostatic stress promotes high-trapped H concentration for crack tip damage; it is imperative to account for SGP in H cracking models. Predictions of the threshold stress intensity factor and H-diffusion limited Stage II crack growth rate agree with experimental data for a high strength austenitic Ni-Cu superalloy (Monel®K-500) and two modern ultra-high strength martensitic steels (AerMet™100 and Ferrium™M54) stressed in 0.6 M NaCl solution over a range of applied potential. For Monel®K-500, KTH is accurately predicted versus cathodic potential using either classical or gradient-modified formulations; however, Stage II growth rate is best predicted by a SGP description of crack tip stress that justifies a critical distance of 1 μm. For steel, threshold and growth rate are best predicted using high-hydrostatic stress that exceeds 6 to 8 times alloy yield strength and extends 1 μm ahead of the crack tip. This stress is nearly achieved with a three-length phenomenological SGP formulation, but additional stress enhancement is needed, perhaps due to tip geometry or slip-microstructure.

Dynamics of Kinetically Limited Strain and Threading Dislocations in Temperature- and Compositionally Graded ZnSSe/GaAs (001) Metamorphic Heterostructures

We have investigated the evolution of the strain and threading dislocation density in metamorphic compositionally and temperature-graded ZnSySe1−y buffer layers. Linear variation in composition in conjunction with temperature grading may allow control over the relaxation process. Previously, we reported the development of a general kinetic model based on dislocation flow, which accounted for the time evolution of the strain relaxation in semiconductor structures under kinetically limited conditions, including interactions of threading and misfit defects. In this work, we studied ZnSySe1−y/GaAs (001) heterostructures with linear compositional grading and a convex-upward (type A), linear (type B) or convex-downward (type C) temperature grading profile. The thermal budget available for relaxation in these types of structures is controlled by the temperature grading profile, made up of combinations of linear ramps and constant-temperature sections. In all cases, the temperature was varied from T0 (400°C to 600°C) at the substrate interface to TF = 300°C at the surface. We also investigated the effect of varying the compositional gradient in the range from 0.18%/μm to 1.6%/μm. Structures with higher average temperature (greater thermal budget) and/or higher grading coefficient exhibited greater extent of relaxation and therefore reduced residual strain. Furthermore, controlling the extent of strain relaxation enabled optimization of the dislocation densities in these heterostructures.

Modeling and application of constitutive model considering the compensation of strain during hot deformation

Hot compression tests were conducted on homogenized 5052 aluminum and AZ31 magnesium alloys to establish a strain compensated Arrhenius constitutive model in the temperature range of 573–723 K and 523–673 K with strain rates of 0.001, 0.01, 0.1 and 1 s−1 by using a Gleeble-1500D thermo-simulator. The presented constitutive model, as well as the dynamic recrystallization (DRX) kinetics of both studied alloys, was incorporated into ABAQUS User Subroutine UHARD to provide an effective means to study hot deformation. The simulated results were subsequently referred to the cellular automaton (CA) method to simulate the microstructural evolution of the 5052 and AZ31 alloys. Results show that the constitutive model considering strain compensation offers a high accuracy. In terms of force and volume fraction of DRX, the results of the Finite Element Method (FEM) are in good agreement with the experimental results. The microstructural evolution of both homogenized 5052 and AZ31 alloys during hot compression was simulated using CA coupled the FEM results. Owing to the close connection between dislocation density and flow stress, the alloys present similar characteristics with prolonged simulation time. The mean grain sizes of both studied alloys decrease with increasing strain, revealing that a large deformation degree leads to refined grains. The mean re-grain size initially peaks and then decreases smoothly with increasing strain because of the coupled effect the nucleation and growth of re-grains.

Hydrogen-induced softening in nanocrystalline Ni investigated by nanoindentation

The influence of hydrogen on the plastic deformation of nanocrystalline nickel was analysed by recourse to nanoindentation on the uncharged and hydrogen-charged samples. It was revealed that, in nanocrystalline Ni, hydrogen significantly decreases hardness but does not alter the strain rate sensitivity. Through thermal desorption spectroscopy measurement, charged hydrogen was expected to reside in face-centred cubic lattice, grain boundaries (GBs) and vacancies rather than dislocations. The hydrogen-induced softening behaviour is discussed in terms of the possible roles of hydrogen in GB-assisted dislocation flow mechanism.