Dislocation Density Model Research Articles

Microstructural Evolution of As-cast 42CrMo Ring during Hot Rolling

In order to avoid traditional ring parts hot rolling process problems of many times heating and so on, the as-cast 42CrMo alloy ring short process flow blank-casting and rolling compound forming process is taken as the research object, a series of experiments are performed on the Gleeble-1500D machine and metallographic microscope, the flow stress curves under temperatures of 850-1 150 ℃ and strain rates of 0.05-5 s-1 are obtained. The dislocation density variation and the grain growth kinetics of each dynamically recrystallizing grain are calculated by transforming the flow stress curves. In addition, the nucleation and the growth kinetics of dynamically recrystallized grains are evaluated. The grain topology deformation technology is studied, and the grain topology structures are optimized by use of the principal component analysis. The results show that the Kock-Mecking(KM) dislocation density equation can be employed to calculate the dislocation evolution during dynamic recrystallisation of 42CrMo alloy. The KM dislocation density model coupled with cellular automata method and optimized grain topology transformation technology can simulate dislocation density during dynamic recrystallization process accurately.

열간 유동응력 예측을 위한 물리식 기반 동적 재결정 모델

In the current study, a new dynamic recrystallization model for predicting high temperature flow stress is developed based on a physical model and the mean field theory. In the model, the grain aggregate is assumed as a representative volume element to describe dynamic recrystallization. The flow stress and microstructure during dynamic recrystallization were calculated using three sub-models for work hardening, for nucleation and for growth. In the case of work hardening, a single parameter dislocation density model was used to calculate change of dislocation density and stress in the grains. For modeling nucleation, the nucleation criterion developed was based on the grain boundary bulge mechanism and a constant nucleation rate was assumed. Conventional rate theory was used for describing growth. The flow stress behavior of pure copper was investigated using the model and compared with experimental findings. Simulated results by cellular automata were used for validating the model.

A multiscale coupled Monte Carlo model to characterize microstructure evolution during hot rolling of Mo-TRIP steel

A multiscale modelling framework has been proposed to characterize microstructure evolution during hot strip rolling of transformation-induced plasticity (TRIP) steel. The modelling methodology encompasses a continuum dislocation density evolution model coupled with a lumped parameter heat transfer model which has been seamlessly integrated with a mesoscale Monte Carlo (MC) simulation technique. The dislocation density model computes the evolution of dislocation density and subsequently constitutive flow stress behaviour has been predicted and successfully validated with the published data. A lumped-parameter transient heat transfer model has been developed to calculate the average strip temperature in the time domain. The heat transfer model incorporates the effect of plastic work for different strain rates in the energy conservation formulation. A coupled initial value problem solver has been developed to integrate the system of stiff ordinary differential equations in the time domain to predict dislocation density and temperature profiles simultaneously. The temporal evolution of microstructure during hot rolling of TRIP steel is simulated by the MC method incorporating thermal and dislocation density data from the continuum models. Simulated microstructural maps, kinetics of recrystallization and grain size evolution have been generated in a 200×200 lattice system at different strain rates and temperatures. The simulation code has been implemented in a high-performance grid computing network. The predicted temporal evolution of grain size, recrystallized fractions and flow stress have been validated with the published literature and found to be in good agreement, confirming the predictive capability of the integrated model.

Hybrid dislocation dynamics based strain hardening constitutive model

In this article, a Hybrid strain-hardening Model for slip driven plasticity is introduced. The model distinguishes between the contributions of glissile and stored dislocations, and polar and non-polar dislocations. The core idea relies on a two step-approach in which all glissile non-polar dislocations on given slip systems are represented by a virtual dislocation loop which evolution is modeled by a dislocation dynamics approach, while transformations of dislocations from glissile to stored, resulting from short-range dislocation–dislocation interactions, are based on phenomenological relations informed by dislocation dynamics simulations on dislocation pair interactions. The constitutive model developed should then allow for a reduction in fitting parameters and should be suitable to predict complex loading. Besides, the Hybrid Model is able to predict dislocation densities for all kinds of populations, including junctions. As a first application, the resulting Hybrid continuum/discrete dislocation density Model is utilized for predicting the stress–strain response of single crystal aluminum as a function of its orientation, slip activity, and junction formation.

Validation of a Model of Plastic Deformation of Niobium Microalloyed Steels in the Two‐Phase Temperature Region

AbstractThis article describes a thermo‐mechanical‐microstructural model for deformation of niobium microalloyed steel in the two‐phase range of temperatures. Results of physical and numerical modeling are presented. The physical simulation experiments include plastometric and dilatometric tests, as well as industrial rolling trial. Plastometric tests were performed to describe the flow stress for the wide range of temperatures, including ferritic, two‐phase, and austenitic states. Two‐stage deformation tests were performed to identify the microstructure evolution model. Dilatometric tests were used to identify the model of phase transformation. A model of the kinetics of the precipitation was adapted from the literature. The coefficients in all the models were identified using inverse analysis. Developed models were implemented in the finite element code. In order to improve the accuracy of the flow stress predictions in the two‐phase phase temperature range, internal variable dislocation density model was included, as well. The proposed combination of models correctly predicted microstructure changes and mechanical properties in the two‐phase range, during the transformations of the thermo‐mechanical treatment. Industrial trials were performed for the final validation of the models.

Modeling the Flow Curve of Hot Deformed Austenite

A 0.02%C plain carbon and a 0.22%C TRIP steel were tested in compression in the temperature range 900°C to 1150°C and strain rate range 0.05s-1 to 1s-1. Thirty-two experimental flow curves were obtained in this way. The critical conditions for the initiation of dynamic recrystallization were determined by the double differentiation method. Using a dislocation density model to describe the austenite flow stress, the work hardening parameters r and h were derived and are used to model the flow curve in the absence of dynamic recrystallization. The latter was employed to calculate the fractional softening attributable to dynamic recrystallization. The kinetics of dynamic recrystallization are then described using Avrami kinetics. Finally, the dependences of the Avrami and work hardening parameters on Z, the Zener-Hollomon parameter, are used to model compression flow curves at strain rates an order of magnitude greater than the ones employed in the tests.

Deformation Behavior of 6061 Aluminum Alloy Through Tube Channel Pressing: Severe Plastic Deformation

The deformation behavior of solid solution-treated AA6061 tubes in a novel severe plastic deformation process named Tube Channel Pressing has been assessed. In order to do so, an analysis based on the finite element method and dislocation density model is utilized, and microhardness measurement is carried out to verify the trends of analysis results. By comparing FEM results with experimental data, the optimized geometrical parameters controlling the deformation behavior of the tube in tube channel pressing are determined to obtain the best strain homogeneity and minimum dimensional changes in tube.

Crystal plasticity approach for predicting the Bauschinger effect in dual-phase steels

Abstract A multi-scale micro-mechanical model was proposed to predict the cyclic behavior of dual-phase steels. The approach proposed in this study incorporates a simplified dislocation density model into the crystal plasticity finite element method (CP-FEM). The back stress resulting from dislocation pileups was used to reproduce the transient hardening behavior during load reversal. The simulations conducted using representative volume elements for the dual-phase steels lead to the following conclusions: (1) the large Bauschinger effect (BE) and permanent softening in dual-phase steels originate primarily from the inhomogeneity due to the soft and hard phases; (2) the elastic incompatibility due to the grain orientation distribution generates some BE, but is not sufficient to explain the measured stress–strain curve; and (3) the inclusion of the back stress produced by the dislocation pileup can explain the strain hardening stagnation during reverse loading.

Simulation of Recrystallization Behavior and Austenite Grain Size Evolution during Hot Deformation of Low Carbon Steel Using the Flow Stress

Microstructure evolution can cause changes in dislocation density during hot plastic formation of metals and greatly influence the shape of flow curves. Recrystallization kinetics and average grain size were simulated by the coupled flow stress model describing dislocation development and microstructure evolution. The model for microstructure evolution considered different kinds of recrystallization in the same process rooted from nucleation and grain growth. Flow stress was calculated from the average dislocation density determined by the dislocation density model, which took into account hardening and recovery during the hot deformation process. Model parameters were defined by inverse analysis of flow curves obtained from hot compression tests and were completed through solving a nonlinear least-squares problem with constraints using optimization methods. Finally, the results obtained by the proposed model were compared with experimental results.

Deformation behaviour of a ferritic hot-work tool steel with respect to the microstructure

A ferritic hot-work tool steel was investigated, which is in use as die for extrusion processes and exposed to cyclic load spectra with overlapping of both, thermal and mechanical loads. The occurring stresses and temperatures in the tool material were used to simulate the material behaviour of the tool steel in service by means of Abaqus StandardTM v.6.8–3 software in conjunction with Z-Mat package. A sensitivity analysis of the used elastic–viscoplastic Chaboche model was performed to characterize the most influencing parameters. To describe the microstructure evolution during thermo-mechanical loads via a physical based approach and to compare it with the phenomenological predictions, precipitation kinetics simulations as well as a dislocation density model for thermal creep using the rate theory, were applied to characterize the hardening and softening behaviour.

STOCHASTIC PROCESSES OF {1012} DEFORMATION TWINNING IN HEXAGONAL CLOSE-PACKED POLYCRYSTALLINE ZIRCONIUM AND MAGNESIUM

Deformation twinning is an important mechanism for metals with hexagonal close-packed (hcp) crystal structures such as titanium, magnesium, beryllium, and zirconium, as well as metals with other low-symmetry crystal structures. This article presents a multiscale constitutive model for the plastic deformation of hcp polycrystalline metals that is built upon the viscoplastic self-consistent (VPSC) polycrystal scheme. This framework includes a novel probabilistic model for predicting when, where, and which variants nucleate, a dislocation density model for crystallographic slip, and a micromechanical model for twin lamella thickening and twin reorientation. Length scales of an individual slip or twinning system and the polycrystalline aggregate are interactively connected. Here, this constitutive model is applied to high-purity magnesium (Mg) and zirconium (Zr) deformed under loading conditions where twinning is intense. Correlations are made between the formation of deformation twins, bulk stress-strain behavior and texture development, and individual grain properties such as size and crystallographic orientation.

Microstructure Simulation of Aluminium Alloy Wheel Die Forging Using Cellular Automaton

The prediction of dynamic recrystallization (DRX) plays an important role in design of hot forging process. In this work, a simulation model coupled cellular automaton (CA) with FEM was proposed to quantitatively simulate the microstructure evolution and flow stress during 7050 aluminium alloy wheel die forging. The model of dislocation density was established by isothermal compression test on Gleeble-1500. The physical fields, such as temperature, strain rate and strain, were obtained by DEFORM-3D for microstructure simulation. To refine grain size and improve uniformity, the isothermal forging parameters for 7050 aluminium alloy wheel were optimized by CA simulation. The simulation results showed that DRX percentage increased from 9.9% to 50% by using isothermal forging instead of hot die forging, while the flow stress decreased from 84MPa to 40MPa. Uniform density and small grain related with high mechanical properties were achieved via isothermal die forging process. The experiments of scaled wheel die forging were carried out on a hydraulic press with nominal working pressure 3150KN to verify simulation results. The good agreement between the simulation results and the experimental results indicate that the simulation model presented in this work can be used to predict the microstructure evolution of forging and optimization of forging process.

Mechanical Property Mapping of Cold Sprayed Ti Splats and Coatings

Profile nanoindentation and nanoindentation mapping were used to investigate the mechanical properties of commercially pure cold spray Ti splats and coatings deposited at increasing deposition velocities. Three regions in the cold spray Ti splats have been indentified: the impact region, the jetting region, and the upper splat region. The mechanical properties measured in these regions were tied to the cold spray deposition process with help of optical and scanning electron microscopes. The jetting region was observed to contribute to a metallurgical bonding of cold spray splats to cold spray splats and was measured to have low hardness in comparison to the splat impact site and similar to the hardness in the upper splat region. No increase in the profile coatings hardness with increase in the particle in-flight velocity and coating thickness was found. A correlation between the mechanical properties and the presently known deposition temperature, stress and dislocation density models was made.

Inverse Regression Analysis Method to Determine Mathematical Model of Dislocation Density Using Flow Stress Curves

The flow stress curves of Q345B microalloyed steel during hot compression deformation were obtained at 900-1100°C and strain rates of 0.01-10s-1 on Gleeble-3500 thermo-mechanical simulator. Based on the experimental results, a inverse regression analysis method was proposed to determine the mathematical model of dislocation density and its correlation coefficients using the flow stress curves, so as to laid the foundations for calculating carbonitrides precipitates, deformation resistance and the end-rolled strength of microalloyed steels during hot rolling precisely. The effects of the deformation parameters (strain rate and deformation temperature) and microstructural evolution (work-hardening, dynamic recovery and dynamic recrystallization) on dislocation density were taken into account. Finally, the validity of the proposed model is discussed considering the plausibility of the parameters assessed for evaluating the dislocation density. It was proved that the model was reasonable and it could provide a guide to production.

A STUDY OF DYNAMIC RECRYSTALLIZATION IN TA15 TITANIUM ALLOY DURING HOT DEFORMATION BY CELLULAR AUTOMATA MODEL

The dynamic recrystallization (DRX) of TA 15 ( Ti -6 Al -2 Zr -1 Mo -1 V ) titanium alloy during the hot deformation process was studied by the Cellular Automata (CA) model which is base on the dislocation density theory. To build the CA model, the dislocation density model, dynamic recovery model, nucleation model and grain growth model were introduced and developed. The influences of strain rate on the microstructure evolution and flow stress character were investigated which shows that high strain rate leads to later DRX appearance, high flow stress peak value, small mean size of recrystallizing grains( R -grains) and low DRX percentage, but they have the similar Avrami curve. The characteristic of DRX process in a modeling non-uniform temperature filed (NTF) has been studied. All the simulation results show good agreement with the pioneer's work and experimental results.

Simulation of dynamic recrystallization for aluminium alloy 7050 using cellular automaton

The prediction of microstructure evolution plays an important role in the design of forging process. In the present work, the cellular automaton (CA) program was developed to simulate the process of dynamic recrystallization (DRX) for aluminium alloy 7050. The material constants in CA models, including dislocation density, nucleation rate and grain growth, were determined by the isothermal compress tests on Gleeble 1500 machine. The model of dislocation density was obtained by linear regression method based on the experimental results. The influences of the deformation parameters on the percentage of DRX and the mean grain size for aluminium alloy 7050 were investigated in details by means of CA simulation. The simulation results show that, as temperature increases from 350 to 450 °C at a strain rate of 0.01 s−1, the percentage of DRX also increases greatly and the mean grain size decreases from 50 to 39.3 μm. The mean size of the recrystallied grains (R-grains) mainly depends on the Zener-Hollomon parameter. To obtain fine grain, the desired deformation temperature is determined from 400 to 450 °C.

Dislocation density model for the effect of grain size on the flow stress of a Ti–15.2 at.% Mo β-alloy at 4.2–650 K

Hall–Petch (H–P) plots of the effect of grain size d = 4.6–22 μm on the flow stress σ at 4.2–650 K of a β-Ti–15.2 at.% Mo alloy gave that the parameter σ i increased with strain ɛ and with decrease in temperature T. In contrast, the parameter K H–P was relatively independent of ɛ and T. The corresponding dislocation density ρ increased with ɛ and with decrease in d, giving the well-known relation σ/ M ≈0.5 μbρ 1/2, where M is the Taylor factor. The magnitudes of σ i and K H–P calculated from ρ were in reasonable agreement with those obtained from the H–P plots. The grain size dependence of σ was in accord with Li's grain boundary ledge mechanism.

Effect of grain size from mm to nm on the flow stress and plastic deformation kinetics of Au at low homologous temperatures

Three grain size regimes were identified: Regime I ( d > ∼0.5 μm), Regime II ( d ≈ 10–500 nm) and Regime III ( d < ∼10 nm). Grain size hardening in accord with the Hall–Petch (H–P) equation occurred in Regimes I and II, grain size softening with the flow stress proportional to d −1 occurred in III. The rate-controlling mechanism in Regime I was concluded to be the intersection of dislocations, that in II grain boundary shear promoted by the pile-up of dislocations and that in III grain boundary shear without pile-ups. The transition from I to II occurred when the dislocation cell size became larger than the grain size, that from II to III when the dislocation elastic interaction spacing became larger than the grain size. The H–P behavior in Regime I is in accord with the dislocation density model, that in II with the dislocation pile-up model. The general behavior of Au is similar to that reported previously for Cu and Ag.

Effect of grain size from millimeters to nanometers on the flow stress and deformation kinetics of Ag

Abstract Data on the effects of grain size, d = 9 nm to 0.26 mm on the flow stress and plastic deformation kinetics of Ag at low homologous temperatures were evaluated. Two regimes were identified for this grain-size range: Regime I ( d > 500 nm) and Regime II ( d ≈ 10–500 nm). The effect of grain size on the flow stress in both regimes could be described by a Hall–Petch equation. K H–P was however significantly smaller and σ i larger for Regime II compared to I. Dislocation activity occurred in both regimes; dislocation cells were observed in Regime I, but not reported for II. The available data suggest that the dislocation density model governs the grain-size dependence of the flow stress in Regime I and that dislocation pile-up applies in Regime II. The rate-controlling mechanism(s) in each of the two regimes are discussed.

Finite Element Simulation of an Industrial hot Rolling Schedule of Aluminium using Integrated Microstructure Models

The final properties of aluminum products largely depend on their temperature and forming history. To predict them, it is advantageous to combine process models and microstructural models. Here, the integration of a physically based dislocation density model with a full-constraints Taylor model into the FEM code Larstran/Shape is shown. Finally, the application of this modeling scheme to an industrial hot rolling schedule is demonstrated.