Dislocation Density Evolution Research Articles

A new numerical framework for the full field modeling of dynamic recrystallization in a CPFEM context

This work describes the coupling of a level-set (LS) based numerical framework for microstructural evolutions modeling with a crystal plasticity finite element method (CPFEM), in order to propose a new full field approach dedicated to dynamic recrystallization (DRX) modeling. These developments are proposed for 3D polycrystalline metals subjected to large deformations at high temperatures.CPFEM is one of the best available alternatives to model the evolution of dislocation densities and misorientation during plastic deformation. The dislocation density and misorientation is then used as input data for the recrystallization model. Grain boundary migration (GBM) is modeled by using a kinetic law which links the velocity of the grain boundaries, described by LS functions, with the thermodynamic driving pressures. The nucleation of new grains is modeled by using phenomenological laws, which define the number of nucleation sites as a function of the dislocation density and the misorientation. The link between the CPFEM and the GBM model gives an accurate description of the DRX phenomenon, which is intended to model industrial processes.In this work the methods and the coupling algorithm are presented, along with an analysis of the different numerical parameters and strategies to define nucleation. The calibration and validation of the model against experimental data for 304L steel will be presented in a future work.

Effect of heat treatment on the tensile behavior of selective laser melted Ti-6Al-4V by in situ X-ray characterization

Selective Laser Melted Ti-6Al-4V (as-SLMed) exhibits decreased yield strength, increased work hardening, and increased ductility after heat treatment at 730 °C (HT-730) or 900 °C (HT-900) for 2 h. To understand the change of mechanical properties, in situ high energy X-ray diffraction (HEXRD) is used to examine the phase composition, load partitioning, slip system activity, and dislocation density evolution in all three specimens. The as-SLMed specimen is dominated by martensitic α΄. After heat treatment, α΄ partly or fully decomposes into α+β, reducing the yield strength. In HT-730, β precipitates with confined size show much higher lattice strain than the α΄/α matrix during deformation; in HT-900, the lattice strain difference is mostly eliminated. This is a key reason for the increased ductility in HT-900. From the anisotropic lattice strain development, basal slip is identified as the easiest slip system in α΄/α. Using an elasto-plastic self-consistent (EPSC) model, the critical resolved shear stress ratio between prismatic slip and basal slip (CRSSprism/CRSSbasal) is estimated to be 1.31 and 1.16 in the as-SLMed and the HT-900 specimens, respectively. The α phase in HT-900 is able to activate multiple slip systems and accumulate more dislocations during plastic deformation. This explains why HT-900 has better ductility and higher work hardening rate than the other two specimens.

A critical evaluation of microstructure-texture-mechanical behavior heterogeneity in high pressure torsion processed CoCuFeMnNi high entropy alloy

The present study aims to understand the evolution of textural and microstructural heterogeneity and its effect on evolution of mechanical properties of an equiatomic FCC CoCuFeMnNi high entropy alloy (HEA) disc subjected to high pressure torsion (HPT). HPT was performed on disc specimen with a hydrostatic pressure of 5 GPa for 0.1, 0.5, 1 and 5 turns at room temperature where the hardness saturated at 1941 MPa at the periphery of the sample after five turns. Synchrotron diffraction texture analysis of five-turn HPT sample reveals characteristic shear texture with the dominance of A {11⇀1⇀}<110> and A* {11⇀1⇀}<112> components near central region of the disc and it shifts to C {001}<110> component near the periphery of the disc. X-ray diffraction analysis shows decrease in crystalline size with simultaneous increase in dislocation density for five-turn HPT sample with increasing strain from centre to the periphery of the disc. Microstructural analysis using electron back scatter diffraction and transmission electron microscopy indicates extensive grain fragmentation (≈55 nm) at the periphery of five-turn sample. The evolution of hardness from centre to the periphery of the disc cannot be explained only on the basis of evolution of grain size and dislocation density. The increase in contribution from solid solution strengthening due to partial dissolution of copper rich nano-clusters is expected to be the underlying cause for increase in the hardness. Thus, evolution of gradient microstructure, texture, and chemistry opens up new vistas for designing functionally graded materials for engineering applications.

Dislocation density and grain size evolution in hard machining of H13 steel: numerical and experimental investigation

In this research, the microstructure evolution in the machined subsurface is numerically simulated through a developed multi-physics model applied to H13 hot work die steel. The multi-physics model based on dislocation density evolution is utilized to predict the change of grain size through finite element analysis by varying cutting parameters. In spite of the cutting conditions, the simulated grain size on the top-most machined surface is around 330nm, and the machining-affected depth with refined grain varies in the range of 25–45μm. In addition, the appeared periodical fluctuation of dislocation density and grain size in a wavy configuration induced by the generated serrated chip segments is revealed. The efficacy of the proposed finite element model is verified and the probable mechanism of grain refinement is demonstrated with the assistance of TEM observation, which in turn promotes the in-depth understanding of microstructure evolution during metal cutting.

Micromechanical modeling of work hardening for coupling microstructure evolution, dynamic recovery and recrystallization: Application to high entropy alloys

A dislocation density-based multiscale constitutive model is developed to describe the hot deformation of high entropy alloys. The work hardening process of high entropy alloy is divided into several stages according to the change of hardening rate. As crystalline material, high entropy alloys are regarded as two-phase materials. In the current study, a physical-based constitutive model with three key microstructural state variables, cell mobile dislocation density, cell immobile dislocation density and wall immobile dislocation density, is proposed to simulate the phases deformations. The physical mechanisms including strain hardening, dynamic recovery, and recrystallization are considered in describing the evolution of dislocation densities. It is noted that the competition and interaction among the three mechanisms result in a typical hardening behavior of high entropy alloys. The dislocation density-based constitutive model is embedded in the modified Mori-Tanaka scheme to describe the hardening behaviors of two-phase materials with an elastic phase cell wall and an elastic-inelastic phase cell interior. The model is applied for simulating the hardening curves of CoCrFeMnNiC0.5 high entropy alloy at different temperatures and strain rates. Compared with experimental data, it shows that the developed model can describe hot deformation of high entropy alloys with reasonable accuracy. The macroscopic inelastic strain in the Mori-Tanaka scheme is calculated by a classical plasticity method. The simulation results show that the modified method can give a more accurate prediction compared to the average inelastic strain of all phases.

Abnormal TRIP effect on the work hardening behavior of a quenching and partitioning steel at high strain rate

Quenching and partitioning (Q&P) steels possess high strength and good ductility because of the transformation of metastable austenite to martensite, which is referred to transformation-induced plasticity (TRIP) effect. In literature, TRIP effect generally results in an enhancement of work hardening rate during tensile test. Nevertheless, the present work observes an abnormal TRIP effect in a 1500 MPa Q&P steel. Although a considerable amount of retained austenite transformed to martensite during the tensile test at a strain rate of 1000 s − 1, no obvious enhancement of work hardening rate was observed. To explore the underlying mechanisms for such an abnormal TRIP effect, the evolution of dislocation density and martensitic transformation were characterized by synchrotron X-ray diffraction and electron microscopy. Comparing the quasi-static and high-strain-rate results, it is found that the dislocation density in the martensite matrix is suppressed at 1000 s − 1, resulting in a lower work hardening. Furthermore, the transformed martensite deforms plastically at 1000 s − 1. Without the composite-like deformation behavior (elastically in hard transformed martensite and plastically in soft martensite matrix), the corresponding work hardening is reduced.

Evolution of microstructures, dislocation density and arrangement during deformation of low carbon lath martensitic steels

In this paper, the role of solute carbon on the strengthening and work hardening behavior of lath martensite was studied by analyzing the microstructures and dislocation density in the undeformed and deformed conditions. An increase in carbon content from 0.18% to 0.30% decreases the martensite start (Ms) temperature, leading to refinement of both the block and lath widths. Although reduction of the “effective grain size” is observed via Electron Backscatter Diffraction (EBSD) and Electron Channeling Contrast Imaging (ECCI) techniques, this effect is considered secondary in increasing the strength of lath martensite with increased carbon content. The higher strength is attributed mainly to the phase transformation-induced dislocation density in the high-carbon martensite. Comparing this total dislocation density calculated using a Convolutional Multiple Whole Profile (CMWP) fitting procedure with the estimated geometrically necessary dislocations (GND) from the misorientation distribution of EBSD analysis, it appears that a high fraction of the dislocations in lath martensitic steel is GND. Furthermore, the analysis of the samples strained to a different level suggests that the dislocation density shows minimal change during deformation, whereas the dislocation arrangement rapidly decreases at the beginning of the plastic deformation. Finally, the strain hardening behavior of the lath martensitic steel is quantitatively described by considering lath width, dislocation density, and dislocation arrangement parameters through the α coefficient in Taylor's equation.

Stress response and microstructural evolution of nickel-based superalloys during low cycle fatigue: Physics-based modelling of cyclic hardening and softening

Low cycle fatigue is one of the main life limiting factors in gas turbine discs. The plastic deformation behaviour that leads to crack initiation is not fully understood, and phenomenological descriptions fail to explain the stress response typical of nickel-based superalloys, which consists of cyclic hardening followed by cyclic softening. In this study, samples of nickel-based superalloy 718Plus with different ageing heat treatments are fatigued for 500 cycles at room temperature, their microstructures characterised and their slip localisation behaviour quantified via electron channelling contrast imaging (ECCI). A physics-based mesoscopic model is developed to investigate the effects of ageing and loading conditions on cyclic deformation behaviour. The formation of slip bands and evolution of the local dislocation density are used to describe cyclic hardening, while continued precipitate shearing from the accumulation of slip irreversibilities is modelled as the source of cyclic softening. Both mechanisms are then coupled via a parameter for the volume fraction of slip bands. The model successfully reproduces the trends observed for the different conditions, with overaged samples eventually surpassing the cyclic stress of the peak-aged specimens due to a slower softening rate. Curves from the literature for superalloy Nimonic PE16 are also reproduced for different ageing conditions and strain amplitudes. Further electron microscopy near surface cracks reveals the presence of precipitate-free deformation bands only in the underaged condition, which is explained in terms of a saturation point for the shearing process.

Shock wave compression behavior and dislocation density evolution in Al microstructures at the atomic scales and the mesoscales

Molecular dynamics simulations are carried out to investigate the deformation response during shock compression of nanocrystalline Al microstructures at the atomic scales. The shock response is investigated for various grain sizes (18 nm–100 nm) and impact velocities (700 m/s to 1500 m/s). The simulations suggest an increase in shock front width and a decay in the velocity and the amplitude of the elastic precursor wave (Hugoniot elastic limit) as the wave travels through the microstructure. For a limited sample depth of 500 nm of polycrystalline Al, the Hugoniot elastic limit (HEL) values are higher for larger grain sizes due to a lower density of grain boundaries and higher for higher piston velocities/shock pressures. Quasi-coarse-grained dynamics (QCGD) simulations are carried out to extend this investigation of the shock response of polycrystalline microstructures to the mesoscales. The capability of QCGD simulations to reproduce the atomic scale evolution of dislocation density fractions and shock wave structures is first demonstrated for a 100 nm grain-sized Al system. The evolution of shock front width, HEL, and dislocation densities are investigated for microstructures with grain sizes ranging from 100 nm to 800 nm and system lengths ranging from 600 nm to 9.6 μm. The MD and QCGD simulations indicate that the decay behavior is attributed to the capability of the shock wave to generate Shockley partial dislocations in the compressed microstructure. The simulations indicate that grain size and impact velocities affect the rates of generation of Shockley partials and hence affect the decay of the HEL. The MD and QCGD predicted values for HEL reported here show excellent agreement with the experimentally observed sample thickness dependence for Al. An empirical model is developed to predict the HEL of Al microstructures with grain size, shock pressure and sample depth as variables.

High-Temperature Deformation Behavior of 718Plus: Consideration of γ′ Effects

The hot deformation behavior of 718Plus is modeled through a physically based hybrid dislocation density model, which includes the effects of precipitating particles. It is well known that the service performance and hot flow characteristics of this alloy are strongly dependent on the microstructure, particularly the grain size and second-phase particles. Thus, comprehension and modeling of the hot flow behavior is an important task. In precipitation hardening alloys (superalloys, microalloyed steels, etc.), it is particularly challenging to model the microstructural evolution in the processing windows, where material softening and precipitation processes take place concurrently. In this work, the initial stages of the deformation are studied. A model based on dislocation density evolution is presented. As in conventional approaches, the dislocation density is considered as a competition between dislocation generation and dynamic recovery at the early stages of deformation. Recovery is assumed to be driven by glide and climb of dislocations, which are considered to be proportional to the strain rate and damped by the existence of second-phase particles. It is known that under high-temperature deformation conditions, 718Plus may undergo dynamic precipitation. Second-phase particles in the material may impede the grain boundary motion and contribute to an increase in flow stress. To account for the dynamic precipitation, the present model combines experimental results and precipitation models to predict volume fraction and particle size. The effect of aging is studied through transmission electron microscopy (TEM) characterization of the specimens from interrupted tests at the onset of dynamic recrystallization. Stress contribution due to different modes of dislocation precipitation interaction are modeled and integrated to the phenomenological dislocation density–based hardening models.

Effects of electron beam manufacturing induced defects on fracture in Inconel 718

The effects of electron beam manufactured (EBM) process-induced defects on local microstructural failure initiation and propagation in IN 718 have been investigated. Predictions for transgranular fracture, based on local cleavage plane stresses, and for intergranular fracture, based on dislocation-grain boundary (GB) interactions and evolving dislocation pileups, were combined with a crystalline dislocation-density plasticity approach to understand the influence of AM process-induced defects, such as porosity, NbC precipitates, and regions of dry powder. High local stresses along the peripheries of pores caused crack nucleation, and mismatches in deformation behavior between NbC precipitates and the surrounding matrix led to local stress gradients that induced crack nucleation and decohesion at precipitate/matrix interfaces. Regions of unmelted powder had significant stress accumulations that initiated failure at low nominal strains. Failure due to high localized stresses near regions of unmelted powder was dominant over precipitate/matrix decohesion and crack nucleation near pore peripheries. Based on the predictions, the mechanical behavior of AM alloys is governed by local dislocation-density evolution near process-induced defects, which preferentially nucleate material failure. Furthermore, interactions between these different defect types can significantly accelerate failure initiation and propagation.

Prediction of Microstructure Evolution for Additive Manufacturing of Ti-6Al-4V

A key challenge for successful exploitation of additive manufacturing (AM) across a broad range of industries is the development of fundamental understanding of the relationships between process control and mechanical performance of manufactured components. The present work is focused on the development of predictive methods for process-structure-property control of AM. In particular, laser beam powder bed fusion (PBF-LB) is identified as a key process for manufacture of metallic AM components. Ti-6Al-4V alloy is an important metal alloy for numerous high-performance applications, including the biomedical and aerospace industries. This paper presents initial developments on a model for microstructure prediction in PBF-LB manufacturing of Ti-6Al-4V, primarily focused on solid-state phase transformation and dislocation density evolution. The motivation is to quantify microstructure variables which control mechanical behavior, including tensile strength and ductility. A finite element (FE) based model of the process is adopted for thermal history prediction. Phase transformation kinetics for transient non-isothermal conditions are adopted and implemented within a stand-alone code, based on the FE-predicted thermal histories of sample material points. The evolution and spatial variations of phase fractions, α lath width and dislocation density are presented, to provide an assessment of the resulting microstructure-sensitivity of mechanical properties.

Verification of Dislocation Density and Dynamic Recrystallization in Deformed Pure Copper

The mechanisms of dynamic recovery and dynamic recrystallization significantly affect the mechanical behavior and microstructure of the materials deformed at high temperatures. The modified Kocks and Mecking (K–M) model was used to assess the evolution of dislocation density of pure copper under high-temperature compression. The relationship between the deformation conditions and model parameters was derived and verified. The model offers quantitative prediction of flow stress curves, a recrystallized fraction, and recrystallized grain size under different conditions. The model can well integrate the recrystallization mechanism during deformation. The dislocation density and dynamic recrystallization evolution of pure copper provide a basis for optimizing thermomechanical processing in different fields of industry.

Enhanced Precipitation and Recrystallization in a Mg-Zn Alloy During Low-Temperature Extrusion

Lightweight magnesium (Mg) alloys have great potential to be used in a variety of structural applications. However, Mg’s hexagonal crystal lattice and the limited number of deformation slip systems create fundamental challenges during forming. Furthermore, the selection and amounts of alloying additions can lead to complex phases and transformations or location-sensitive precipitate reactions (i.e., in grain or grain boundary regions). Mg-Zn alloys are promising candidates for applications requiring high strength due to their high hardening response. In this study, we processed solution treated Mg-3Zn (wt.%) using equal channel angular extrusion (ECAE) along the Bc route at 150 oC. The microstructure of the extruded material showed two distinct regions. The grain interior showed a dense distribution of nano precipitates. The grain boundary region contains recrystallized ultrafine grains with some reprecipitation occurring inside them. We employed the Lukác-Balík strain hardening model to estimate the dislocation density evolution during the processing, and we linked these dislocations to the high density of precipitates seen in the grain interiors.

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.

On the assessment of creep damage evolution in nickel-based superalloys through correlative HR-EBSD and cECCI studies

The evolution of dislocation density with creep strain in single-crystal superalloys is studied quantitatively using high-resolution electron backscatter diffraction (HR-EBSD) and electron channelling contrast imaging under controlled diffraction conditions (cECCI). Data regarding dislocation density/structure is measured for deformation at 900 °C and 450 MPa up to ≈ 1% plastic strain. Effects of chemical composition are elucidated via three purpose-designed superalloys of differing rhenium and ruthenium contents. The evidence indicates that dislocation avalanching is already prevalent at plastic strains of ≈ 0.1%; thereafter, an exponential decay in the dislocation multiplication rate is indicative of self-hardening due to dislocation constriction within the matrix channels, as confirmed by the imaging. The results are rationalised using discrete dislocation dynamics modelling: a universal dislocation evolution law emerges, which will be useful for alloy design efforts.

Mechanical Behavior and Deformation Kinetics of Aluminum Alloys Processed through Cryorolling and Subsequent Annealing

The influence of cryorolling (CYR) on the microstructure, mechanical properties, and formability of heat-treatable (AA 6061) and non heat-treatable (AA 5083) aluminum alloys was investigated. Solutionized (SL) AA 5083 and AA 6061 alloy plates are cryorolled to reduce the thickness from 6.5 to 1 mm (the total true strain of 1.87). Short annealing treatment is performed on cryorolled samples at different temperatures with a fixed annealing time to improve ductility. The effect of annealing temperature on microstructure, mechanical properties, and formability was systemically studied. The results showed grain refinement after CYR with higher dislocation density when compared to the SL condition, and their effect is reflected in the mechanical properties. The limiting dome height test is used in the present work to compare the formability of cryorolled and annealed samples. The formability characteristics correlated well with the strain hardening behavior, which is modeled using the Kocks–Mecking–Estrin (KME) dislocation density model. The dislocation density evolution in the original KME model was modified to consider the contributions of grain size, solutes, and precipitates. The tensile curves predicted from the KME model correlated well with the experimental curves in all the conditions investigated. In addition to that, the predicted dislocation density using the modified KME model agreed well with the dislocation density determined experimentally.

Dislocation density based modeling of three-stage work hardening behaviour of type 316LN SS with varying nitrogen content and its finite element implementation for different notch radii

Dislocation density based modified Kocks-Mecking approach has been employed to understand the influence of nitrogen on kinetics of dislocation storage and annihilation processes during tensile deformation of type 316LN stainless steel at 300 K. As compared to original Kocks-Mecking approach, the modified version based on the evolution of forest dislocation density and mean free path of dislocations provides better description of three-stage hardening behaviour of the steel at all the nitrogen content. The effect of increase in nitrogen on work hardening behaviour is clearly reflected in systematic increase in flow stress, mobile and forest dislocation densities and decrease in mean free path at a given plastic strain. The predicted decrease in mean free path with increasing nitrogen has not only influenced the enhancement of dislocation-dislocation interactions leading to higher storage of dislocation but also provides a large driving force for higher dynamic recovery in the steel. The material model is implemented into finite element code via user-defined material subroutine using implicit algorithm to study the influence of notch radius on tensile properties of type 316LN stainless steel for different nitrogen content. Detailed analysis showed that notch-strengthening effect increases with increase in nitrogen and decrease in notch radius in the steel.

On the evolution of mechanical properties and microstructure of ferritic-bainitic (FB) 2.25Cr-1Mo (Grade 22) steel during high-temperature creep

The development of creep damage in ferritic-bainitic 2.25Cr-1Mo (Grade 22) steel was studied by following the evolution of mechanical properties and microstructure by characterisation of a series of interrupted creep specimens (605 °C/80 MPa). The change in mechanical properties of the partially crept specimens was evaluated via hardness measurements, while the microstructural changes were characterized by a range of microscopy techniques. The nano-hardness measurements combined with a statistical analysis allowed for analysis of the strength of the present constitutive phases as a function of creep time (tc), and imparted creep strain (ɛc). In addition, a machine learning methodology was used to identify ferrite and bainite regions in Electron Back-Scatter Diffraction (EBSD) orientation maps, which then allowed for a study of the evolution of dislocation densities (Geometrically-Necessary Dislocations, GNDs) in each phase separately. It is shown that the amount of GNDs in the bainite is reduced significantly during the high-temperature creep, while there is a moderate increase in the amount of GNDs in ferrite grains. These trends are consistent with the observed changes in the strength (hardness) of each phase – bainite is significantly softening, while ferrite slightly hardening. The reduction of the amount of dislocations in the bainite and its consequent softening is caused by the progressive decomposition of the needle-like bainite present in the initial microstructure into polygonal fine-grained ferrite-like bainite. Transmission electron microscopy (TEM) confirmed the changes in dislocation density observations and was also used to identify changes in carbides during the high-temperature creep.

High-performance full-field crystal plasticity with dislocation-based hardening and slip system back-stress laws: Application to modeling deformation of dual-phase steels

This paper presents a microstructural cell-level crystal plasticity model aimed at predicting elasto-plastic, anisotropic, rate- and temperature-sensitive deformation of polycrystalline aggregates subjected to large plastic strains. The crystallography-based model embeds strain-path aware dislocation-based hardening and slip-system-level kinematic back-stress laws. The crystal-level response is linked to the microstructural cell-level response using an elasto-viscoplastic fast Fourier transform-based (EVPFFT) micromechanical homogenization. The overall model is ported on a high-performance computational platform integrating a graphics processing unit (GPU) to facilitate computationally efficient modeling of high-resolution microstructures. The high-performance multi-level EVPFFT is applied to modeling monotonic and cyclic deformation of dual-phase (DP) steel sheets. To this end, the effective elastic and flow stress behavior under monotonic and cyclic deformation is calculated for several steels: three DP, DP 590, DP 980, and DP 1180, and one martensitic (MS), MS 1700. Crystallographic textures and phase fractions of these steels are characterized using electron microscopy along with electron-backscattered diffraction to initialize the models. A comprehensive set of Young's modulus, Poisson's ratio, and flow stress data is used to calibrate and validate the model. The model parameters for ferrite and martensite are identified using data for two steels and used to predict the behavior of the other two streels. The model captures elasto-plastic monotonic behavior as well as the particularities pertaining to large strain cyclic deformation characteristics such as non-linear unloading upon the load reversal, the Bauschinger effect, and changes in hardening rate during strain reversals based on evolving microstructure including the evolution of dislocation density and crystallographic grain reorientation. In addition, it offers insights into the role of back-stress and dislocation annihilation on the cyclic deformation of DP steels.