Dislocation Density Evolution Research Articles

Orientation competition growth and mechanism of SrTiO3 film on CeO2 layer

A series of SrTiO3 films were deposited on CeO2 layer by pulsed laser deposition at substrate temperature in the range of 300 °C–700 °C. It was found that the (110)-oriented and (200)-oriented SrTiO3 grains coexisted on the CeO2 layer. Although the (110)-oriented grains dominated during the deposition, the dominance was weakened with increasing substrate temperature. The competition mechanism of SrTiO3 grains along different orientations was explained in view of the diffusion energy and the evolution of dislocation density. The dependence of the film stoichiometry on the substrate temperature and the effects of residual contaminants in the chamber were also studied by X-ray photoelectron spectroscopy.

Modeling discontinuous dynamic recrystallization containing second phase particles in magnesium alloys utilizing phase field method

Pre-existing second phase particles can induce particle stimulated nucleation (PSN) and pinning effect on grain boundaries during DRX process of magnesium alloys. The interaction among pinning effect, PSN mechanism and strain-induced grain boundary migration (SIBM) nucleation mechanism imposes challenge in quantitative study of microstructure evolution. A phase field model that describes discontinuous dynamic recrystallization process considering second phase particles (PF-DDRX-SP) which mainly distribute along grain boundaries is developed. The second phase order parameter with diffusion interface is introduced to the free energy function. With considering the pinning effect of second phase particles on grain boundaries, the grain boundary energy couples the interaction between second phase and grains. The effect of second phase on dislocation density evolution is considered in the model, and the PSN and SIBM mechanism are both executed by limiting the nucleation position to the grain boundary and the second phase interface. For the validation, the initial topology consistent with initial microstructure is applied to the simulation of DRX kinetics and flow behavior of AZ80 magnesium alloy, and great reliability and accuracy of developed model is indicated. Furthermore, through the model, the microstructure evolution with different particle size and with different volume fraction of round particle during DRX process were simulated. The results show that particles with higher dispersion reduce the number of DRX nuclei, which indicate that second phase particles suppress the nucleation at grain boundaries because of the pinning effect. More importantly, the proposed model could also quantitatively predict the relationships between the parameters of second phase particles and DRX behaviors, and enable to optimize the initial second phase structure in a uniform grain structure during thermomechanical process.

Dislocation Mechanics of Extremely High Rate Deformations in Iron and Tantalum

Abstract High strain rate simulations were performed using the multiscale dislocation dynamic plasticity (MDDP) method to calculate different rise times and load durations in mimicking high deformation rate shock or isentropic (ramp) testing of α-iron and tantalum crystals. The focus for both types of loading on both materials was on the inter-relationship between the (dislocation-velocity-related) strain rate sensitivity and the (time-dependent) evolution of dislocation density. The computations are compared with model thermal activation strain rate analysis (TASRA), phonon drag, and dislocation-generation predictions. The overall comparison of simulated tests and previous experimental measurements shows that the imposition of a rise time even as small as 0.2 ns preceding plastic relaxation via the MDDP method is indicative of relatively weak shock behavior.

Surface hardening analysis for shot peened GH4720Li superalloy using a DEM-FEM coupling RV simulation method

A systematic study was performed to analyze the surface hardening of shot-peened GH4720Li superalloy by combining experiments and numerical simulations. Firstly, it was proved that fine grain strengthening (FGS) and work hardening (WH) are two main strengthening mechanisms of the hardened layer for the plate specimen after shot peening (SP). Then, in order to improve the simulation efficiency, a coupled discrete element method-finite element method model (DEM-FEM) was integrated into the representative volume model to obtain strength distribution quantitatively. The simulation of grain refinement was realized through the dislocation density evolution equation and the degree of WH was characterized by the equivalent plastic strain. Motived by the Vickers hardness test principle, a novel expression between strength and hardness was finally deduced considering both WH and FGS mechanisms, based on which the hardness distribution was evaluated after SP treatment. The hardness by the numerical framework revealed a good agreement with the experimental observations.

Unraveling the discontinuous plastic flow of a Co-Cr-Fe-Ni-Mo multiprincipal-element alloy at deep cryogenic temperatures

We report an analysis of the discontinuous plastic flow of a multiprincipal-element alloy, ${\mathrm{Co}}_{17.5}{\mathrm{Cr}}_{12.5}{\mathrm{Fe}}_{55}{\mathrm{Ni}}_{10}{\mathrm{Mo}}_{5}$ (atomic percent, at. %), in the temperature range of 0.5--4.2 K showing serrated deformation curves. Using the analytical techniques, we studied the statistics of the stress drops associated with the unstable plastic flow. The analysis showed that the complexity and heterogeneity of a discontinuous plastic flow were reduced when the temperature was lowered. This behavior was associated with the effects of dynamic recovery and adiabatic heating on the dislocation-density evolution.

Shape controlling and property optimization of TA32 titanium alloy thin-walled part prepared by hot forming

The hot flow behaviors, microstructure evolution and fractographs were studied to optimize the hot forming process of the TA32 titanium alloy thin-walled part. A set of microstructure-based constitutive equations were developed based on the experimental data, which described the relationships among the hot flow stresses and the evolution of phase volume fraction, dislocation density, grain size and damage. The constitutive model was imported into ABAQUS 6.14 to simulate the hot forming process for a typical thin-walled part. The effective strain, dislocation density and damage distribution as well as forming defects of formed parts under different process parameters were predicted. A qualified part without wrinkling and fracture defects was produced at a loading speed of 5 mm/s at 800 °C by the modified blank shape, where the maximum damage value was only 18.3%. The accuracy of constitutive model and finite element (FE) simulation was verified by the microhardness tests, which indicates that the FE model based on physical internal-state variables can well optimize the hot forming process of TA32 titanium alloy complex parts.

Dislocation drag and its influence on elastic precursor decay

Plastic deformation is mediated by the creation and movement of dislocations, and at high stress the latter is dominated by dislocation drag from phonon wind. By simulating a 1-D shock impact problem we analyze the importance of accurately modeling dislocation drag and dislocation density evolution in the high stress regime. Dislocation drag is modeled according to a first-principles derivation as a function of stress and dislocation character, and its temperature and density dependence are approximated to the extent currently known. Much less is known about dislocation density evolution, leading to far greater uncertainty in these model parameters. In studying anisotropic fcc metals with character dependent dislocations, the present work generalizes similar earlier studies by other authors.

Numerical study on laser shock peening of TC4 titanium alloy based on the plate and blade model

The compressive residual stresses and grain refinement induced by laser shock peening (LSP) are two very important surface strengthening mechanisms that are responsible for the significant improvements of the mechanical property and fatigue performance of metallic materials. A computation framework linking the dislocation-mechanism-based constitutive model with the dislocation density evolution model was developed and implemented into ABAQUS/Explicit code for numerical simulations of the residual stresses and grain refinement induced by LSP of TC4 titanium alloy. Two kinds of three-dimensional finite element models involving the plate model and TC4 blade model were respectively created to simulate the multi-LSP processes, and the effect of laser spot overlap ratio was accordingly investigated in detail. The obtained results show that with the increase of laser spot overlap ratio, the depths of both the compressive residual stresses and grain refinement increase, and with respect to the same depth, the compressive residual stresses increase and the refined cell size decreases. An attempt was made to employ the artificial neural networks (ANNs) to estimate the residual stresses and grain refinement induced by LSP of the whole TC4 blade model, and the ANNs-estimation approach presents the excellent efficiency in predicting the multi-LSPed results with inexpensive cost of numerical computation.

Microstructural effects and mechanical response of microalloyed ferrite and austenite subjected to metal forming at extremely different rates of deformation

The mechanical behaviors and microstructures of severely deformed microalloyed austenitic M_A and ferritic M_F steels were analyzed in wires drawn from wire rods (6.5 mm in diameter) down to the final diameter of 0.75 mm. The deformation induced microstructures in the cold drawn wires under “static” (low speed wire drawing) and “dynamic” (high speed wire drawing) conditions were compared and analyzed. The analysis has been focused on a detailed characterization of the effects of microalloying on the dislocation substructure development and the in-situ recrystallization. The correlations between mechanical behavior and dislocation substructure development with increasing deformation reveals that precipitation strengthening and microstructure refinement are the dominating mechanisms that control the mechanical behaviors of wires, especially in those subjected to deformation under dynamic loading conditions. An approach has been presented to model the evolution of work hardening process during complex deformation. Additional advantage of the presented approach is its capability of tracking evolution of dislocation density during the deformation process. The changes of dislocation density calculated for both materials show similar behaviour, but higher values of the dislocation densities were observed in the specimens of M_F than in the case of M_A.

Cell structure formation in a two-dimensional density-based dislocation dynamics model

Cellular patterns formed by self-organization of dislocations are a most conspicuous feature of dislocation microstructure evolution during plastic deformation. To elucidate the physical mechanisms underlying dislocation cell structure formation, we use a minimal model for the evolution of dislocation densities under load. By considering only two slip systems in a plane strain setting, we arrive at a model which is amenable to analytical stability analysis and numerical simulation. We use this model to establish analytical stability criteria for cell structures to emerge, to investigate the dynamics of the patterning process and establish the mechanism of pattern wavelength selection. This analysis demonstrates an intimate relationship between hardening and cell structure formation, which appears as an almost inevitable corollary to dislocation dominated strain hardening. Specific mechanisms such as cross slip, by contrast, turn out to be incidental to the formation of cellular patterns.

Effect of crystallographic orientation on mechanical properties of single-crystal CoCrFeMnNi high-entropy alloy

Using molecular dynamics (MD) simulation, the influence of crystallographic orientation on the mechanical properties and microstructure evolution of the single-crystal CoCrFeMnNi high-entropy alloy as a face-centered cubic (FCC) metal is explored and quantified by nanoindentation. At the elastic stage of P-h curve, the results of MD-simulation are almost consistent with that of Hertz contact theory fitting, which ensures the accuracy of our results. The plastic deformation is studied by correlating the P-h curve with the instantaneous defect structure, and dominated by nucleation of Shockley partial dislocations or the movements of stacking faults. Furthermore, we discuss the effects of crystallographic orientations [ 001 ] , [ 110 ] , and [ 111 ] on the mechanical response of materials and the microstructure evolution. The slip mode and the stress-concentrated region are controlled by the crystallographic orientations, and an obvious pop-in behaviors are viewed in [ 111 ] -oriented sample, without appearing in other samples. The microstructure evolution exhibits distinct anisotropy causing the discrepancy of dislocation density and hardness. By analyzing the evolution of dislocation density and hardness, the linear relationship between the square root of dislocations density and hardness is revealed, and in good agreement with the classic Taylor hardening expression where the pre-factor is strongly dependent on the crystallographic orientation. In the study, the atomistic results are consistent with those predicted by the classic continuum mechanical theory, which contributes to the application of classic mechanical theory in molecular dynamics simulation.

Viscoplastic constitutive modeling of boron steel under large strain conditions and its application in hot semi-cutting

Abstract To overcome the long process time of laser cutting and the high costs for repairing cold blanking tools of ultra-high strength hot stamping components, the hot semi-cutting process was proposed. The reliable testing and parameter identification method of the constitutive behavior under large strain conditions are essential for an accurate simulation of hot stamping and hot semi-cutting process. In the present work, a new testing and parameter identification method for the viscoplastic constitutive behavior of boron steel is proposed based on the Gleeble system, which includes a new grip design, shear specimen selection, and its relevant high-temperature and high-speed digital image correlation (DIC) technology. To obtain the stress-strain curves under large deformation, the FEM-based optimization method is also proposed to identify the hardening parameters. To cover a greater strain range, a new viscoplastic hardening model is proposed based on the dislocation density evolution under elevated temperature deformation conditions. The reliability of the proposed testing method and hardening model is verified by the analysis of uniformity of temperature and strain rate, and the comparison of predicted stress-strain curves with parameters identified from shear and tensile testing. The thermomechanical tension of the center-hole and notched specimen, and the hot semi-cutting process are carried out to verify the proposed testing method and hardening model. The results show that the shear specimen has a more uniform temperature and strain rate distribution in the deformation zone than the tensile specimen. Shear specimens can be used to test the hardening behavior under various process conditions until failure at the large strain. The insensitivity to phase transformations of shear testing is another advantage for identifying the constitutive behavior of the product phase formed during continuous cooling. The constitutive behavior of the boron steel under a large strain range can be accurately identified by using the FEM-based optimization method proposed in this paper. Besides, the mechanical response of the center-hole specimen, notched specimen, and the hot semi-cutting deformation predicted by the proposed hardening model shows accurate results.

A physically-based structure-property model for additively manufactured Ti-6Al-4V

A physically-based, mixed-phase structure-property model is presented for microstructure-sensitivity of tensile stress-strain response, including yield stress, ultimate tensile strength, uniform elongation and flow stress (strain hardening), for additively manufactured Ti-6Al-4V. The interdependent effects of solutes, grain size, phase volume fraction and dislocation density are explicitly included. Solid-state phase transformation and dislocation density evolution are incorporated to simulate the effects of martensite dissolution and α-β transformation at high temperature. Predictions are validated by comparison with measured tensile test data for (i) effects of additive manufacturing process conditions (such as build orientation and sample size) on tensile properties, based on the microstructure attributes inherited from the process, and (ii) the effect of temperature on tensile stress-strain response across a broad range of temperatures. The model is thus applicable for rapid process-structure-property prediction, in conjunction with AM process modelling, to capture the effects of key manufacturing variables and for process optimization.

An extended linear method to evaluate the viscoplastic behavior of boron steel at large strain with full-field measurements

The reliable parameter identification method of the constitutive behavior under large strain conditions is essential for accurate simulation in the hot stamping and warm-cutting process. In this paper, the linear stress-strain curve identification (LSSCI) method is extended to identify the viscoplastic behavior of boron steel at large strain based on the full-field measurements in the Gleeble system. An inverse LSSCI method to evaluate the strain rate sensitivity under different temperatures based on full-field measurements is presented. To overcome the fluctuation of the identified stress-strain curve at large strain, a constrained optimization method is proposed to solve the linear system. The numerical and experimental cases are performed to verify the accuracy and reliability of the proposed LSSCI method. The verification result shows that the identification error of the extended LSSCI method is generally less than 1%, and the maximum error is not more than 4%. The influence of strain rate, specimen shape, constitutive model, noise and discretization on the identification curves have been studied, the results show that the extended LSSCI method is robust when applied to viscoplastic material identification. To accurately describe the viscoplastic behavior of Boron steel at large strain, a unified viscoplastic (UVP) model is proposed based on the dislocation density evolution under elevated temperature. Finally, the tensile testing of shear and notched specimen are carried out to verify the accuracy and reliability of the proposed UVP model, the comparison of load-stroke curve shows that the large deformation behavior of the boron steel under various conditions can be accurately predicted by the UVP model with the parameters from the proposed LSSCI method.

Quantifying geometrically necessary dislocation density during hot deformation in AA6082 Al alloy

Physically based constitutive equations incorporating the key microstructural mechanisms e.g. dislocations, grain size, etc, have been used widely to predict the stress-strain behaviour of alloys at plastic and viscoplastic conditions. This enables an accurate prediction of the formed geometry as well as the final underlying microstructures. However, these physically based constitutive equations have not been practically validated due to the lack of systematic experimental data at microscopic scale. This leads to a large number of unknown constants required to be determined through various optimization algorithms. The aim of this paper is to provide direct and systematic experimental data by revealing the dislocation (geometrically necessary one) density and grain size evolution of AA6082, which is a widely used high-strength aluminium alloy for automobile structural panels, as functions of strain, strain rate and temperature, and is the first-time using Electron Back Scattering Diffraction (EBSD) technique to visualize the microstructures during the hot deformation. The evolution of the dislocation accumulation during the hot tensile deformation at 300, 450, 530 °C using various strain rates (i.e. 1/s, 0.1/s, 0.01/s) was achieved. EBSD maps were analysed on samples submitted to a true strain level of ~0.1 and ~0.3 under each condition. These maps cover >3000 grains and enable to capture the statistical nature of the geometrically necessary dislocation densities during hot deformation. Despite the rapidly plateaued flow stress curves at high temperatures, a continuously increased average GND density was observed in AA6082 with the imposed true strain levels under all conditions. Dislocation channel structures were observed in the hot deformed samples. Dynamic recrystallization was also observed, which coupled with the GNDs and affected the hardening behaviour of the flow stress-strain curves. This work is the first study, using EBSD, to visualize the high temperature and high strain rate induced dislocation distributions over a relatively large area, providing valuable data that may be used for subsequently improving and calibrating the physically based material models.

Slip-free multiplication and complexity of dislocation networks in FCC metals

During plastic deformation of crystalline solids, intricate networks of dislocation lines form and evolve. To capture dislocation density evolution, prominent theories of crystal plasticity assume that 1) multiplication is driven by slip in active slip systems and 2) pair-wise slip system interactions dominate network evolution. In this work, we analyze a massive database of over 100 discrete dislocation dynamics simulations (with cross-slip suppressed), and our findings bring both of these assumptions into question. We demonstrate that dislocation multiplication is commonly observed on slip systems with no applied stress and no plastic strain rate, a phenomenon we refer to as slip-free multiplication. We show that while the formation of glissile junctions provides one mechanism for slip-free multiplication, additional mechanisms which account for the influence of coplanar interactions are needed to fully explain the observations. Unlike glissile junction formation which results from a binary reaction between a pair of slip systems, these new multiplication mechanisms require higher order reactions that lead to complex network configurations. While these complex configurations have not been given much attention previously, they account for about 50% of the line intersections in our database.

Evolution of dislocation and stacking-fault densities for a Cu-0.7Cr-0.07Zr alloy during cryogenic tensile test: An in-situ synchrotron X-ray diffraction analysis

Processing at cryogenic temperatures is one of the ways of improving mechanical properties of copper alloys. However, such processing routes may result in unstable microstructures, which make it difficult to understand the deformation mechanisms controlling microstructure evolution during cryogenic deformation. In this study, the microstructure evolution of a Cu-0.7Cr-0.07Zr alloy was analyzed as a function of the flow behavior during tensile tests performed at 123 K and 298 K, through in-situ X-ray diffraction (XRD) experiments in a synchrotron source. The tensile behavior was analyzed in terms of the dynamic recovery rate using the Kocks-Mecking model, while the evolution of stacking-fault density, dislocation density and crystallite size during the tests was estimated by the modified Williamson-Hall method. Solution-treated and peak-aged conditions were tested to assess the influence of particles distribution. At 298 K, the strain-hardening rate was controlled by dislocation glide and the flow stress was affected mainly by particle strengthening. At 123 K, a simultaneous increase in strength and ductility was attributed to the twinning induced plasticity (TWIP) effect, promoted by precipitate interfaces acting as nuclei for stacking-faults, thus delaying necking and increasing the plasticity. Based on the evolution of dislocation and stacking-fault densities with increasing plastic strain, it was concluded that, at 123 K, mechanical twinning predominated at strain levels below 0.15, mainly for aged conditions, while dislocation glide between twin boundaries, and its accumulation, started after TWIP mechanism reached its saturation. • In-situ synchrotron X-ray diffraction of Cu-0.7–0.07Zr has been performed. • Solutionized and peak-aged conditions were evaluated at 298 K and 123 K. • Both temperature and precipitates affected the plastic strain regime. • At 123 K, mechanical twinning predominated at strains below 0.15. • Twinning induced plasticity (TWIP) effect occurred during plastic flow at 123 K.

A concurrent atomistic-crystal plasticity multiscale model for crack propagation in crystalline metallic materials

This paper develops a coupled concurrent atomistic–continuum multiscale model for analyzing crack propagation and associated mechanisms in crystalline metallic materials. This modeling framework can be used to develop effective continuum-scale constitutive models for crack evolution in deforming domains characterized by crystal plasticity. The atomistic region is modeled by the molecular dynamics (MD) code LAMMPS, while the continuum region is modeled by a dislocation density crystal plasticity FE model. A novel method is developed to transfer discrete dislocations in the atomistic domains to dislocation densities in the continuum domain. Propagation of dislocation densities in the continuum domain is modeled by the advection equation of a conserved quantity using the reproducing kernel particle method (RKPM) in conjunction with the collocation method. Validation studies are conducted by comparing results of the concurrent model with those by MD for nickel single crystal specimen with an embedded crack. An analytical model of the crack tip nucleated dislocation density evolution is developed for inclusion in crystal plasticity models. The effect of applied strain-rate and temperature on the parameters of this model are studied.

Thermodynamic Modelling and Microstructural Study of Z-Phase Formation in a Ta-Alloyed Martensitic Steel.

A thermokinetic computational framework for precipitate transformation simulations in Ta-containing martensitic Z-steels was developed, including Calphad thermodynamics, diffusion mobility data from the literature, and a kinetic parameter setup that considered precipitation sites, interfacial energies and dislocation density evolution. The thermodynamics of Ta-containing subsystems were assessed by atomic solubility data and enthalpies from the literature as well as from the experimental dissolution temperature of Ta-based Z-phase CrTaN obtained from differential scanning calorimetry. Accompanied by a comprehensive transmission electron microscopy analysis of the microstructure, thermokinetic precipitation simulations with a wide-ranging and well-documented set of input parameters were carried out in MatCalc for one sample alloy. A special focus was placed on modelling the transformation of MX into the Z-phase, which was driven by Cr diffusion. The simulation results showed excellent agreement with experimental data in regard to size, number density and chemical composition of the precipitates, showing the usability of the developed thermokinetic simulation framework.

Multiscale constitutive modeling of additively manufactured Al–Si–Mg alloys based on measured phase stresses and dislocation density

To better understand and predict the mechanical properties of additive manufacturing (AM) Al–Si–Mg alloys, developing a physically-based constitutive model is crucial. Among different models, the dislocation-density-based Kocks-Mecking (K-M) constitutive model has been widely used. Unfortunately, two challenges arise when the K-M model is used for the multiphase Al alloys. Firstly, an accurate K-M model demands the separation of phase stresses. Secondly, a thorough analysis of the K-M model involves the measurement of dislocation density during deformation. In-situ neutron diffraction, a powerful method to measure the phase stress and dislocation density in bulk polycrystalline materials under loading, is employed to investigate the AM AlSi3.5Mg1.5 and AlSi3.5Mg2.5 (wt.%) alloys. Based on the present results and reported data of AlSi10Mg, a multiscale constitutive model is developed for different AM Al–Si–Mg alloys. At the microscale, the evolution of dislocation density in the Al matrix with plastic strain can be well predicted by the K-M model. Meanwhile, the developments of the average stresses in different phases with plastic strain can be well captured by the Voce model. The measured microscopic k2/nc values agree with the theoretical value two of the K-M model quite well. Here, nc is the characteristic factor of the microscale Voce model, while k2 is the coefficient associated with the dynamic recovery process in the microscale K-M model. At the macroscale, the mechanical behavior can also be well reproduced by the K-M model and the Voce model. However, the macroscopic K2/Nc ratio is far away from two, where Nc and K2 are the characteristic factor and coefficient of the macroscale Voce model and K-M model, respectively.