Dislocation Microstructure Evolution Research Articles

Mesoscale dislocation dynamics modeling of incipient plasticity under nanoindentation

A mesoscale dislocation dynamics model which couples three-dimensional dislocation dynamics (DD), and finite element method (FEM) was used to investigate the mechanical response of Aluminum (Al) single crystal under spherical nanoindentation. Together with an atomistically informed nucleation model, the dislocation dynamics model can capture both the dynamic evolution of dislocations under the complex stress state of indentation and the corresponding constitutive response of material. The resulting load-displacement curves and the evolution of dislocation microstructures were analyzed to provide insights into the underlying deformation mechanism for incipient plasticity under nanoindentation. Our model could show the transition of the governing mechanism for plasticity from nucleation-controlled plasticity to pre-existing source-driven plasticity with increasing indenter size, as shown in recent experiments. In addition, it could capture a clear picture on incipient plasticity including the formation of prismatic loops through successive cross-slips of nucleated dislocations, such as rhombus loop and prismatic helical structures, which agrees well with atomistic modeling results.

Statistical analysis of discrete dislocation dynamics simulations: initial structures, cross-slip and microstructure evolution

Over the past decades, discrete dislocation dynamics simulations have been shown to reliably predict the evolution of dislocation microstructures for micrometer-sized metallic samples. Such simulations provide insight into the governing deformation mechanisms and the interplay between different physical phenomena such as dislocation reactions or cross-slip. This work is focused on a detailed analysis of the influence of the cross-slip on the evolution of dislocation systems. A tailored data mining strategy using the ‘discrete-to-continuous (D2C) framework’ allows to quantify differences and to quantitatively compare dislocation structures. We analyze the quantitative effects of the cross-slip on the microstructure in the course of a tensile test and a subsequent relaxation to present the role of cross-slip in the microstructure evolution. The precision of the extracted quantitative information using D2C strongly depends on the resolution of the domain averaging. We also analyze how the resolution of the averaging influences the distribution of total dislocation density and curvature fields of the specimen. Our analyzes are important approaches for interpreting the resulting structures calculated by dislocation dynamics simulations.

Effect of residual stress in gradient-grained metals: Dislocation dynamics simulations

A three-dimensional discrete dislocation dynamics (DDD) method was used to investigate the effect of residual stress on the stress-strain response of gradient nano-grained (GNG) metals. The GNG polycrystalline model was constructed, and different residual stress distributions were introduced in the DDD framework. The simulation shows that the distribution of residual stress has a significant influence on the tensile stress-strain curve. For a GNG sample containing both compressive and tensile residual stresses, the flow stress is firstly lower but ultimately higher than that of the sample without residual stress, which is caused by the combined effects of residual stress and gradient-grained structure. The evolution of dislocation microstructures indicates that the initial tensile residual stress in the sub-surface of the sample can promote the dislocation activation and thus lead to the decrease of overall yield stress. Whereas the compressive residual stress in the topmost surface of the sample can suppress the dislocation activation and multiplication in other regions, resulting in finally higher flow stress in comparison to that of the sample without residual stress. In addition, it is demonstrated that the reduction in the elastic modulus for GNG samples with residual stress observed in some experiments is due to the earlier plastic deformation that occurred in the region with initial tensile residual stress. The present study provides insights into the individual and combined effects of residual stress and gradient-grained structure in GNG metals.

Load versus displacement-controlled nanocompression: Insights from atomistic simulations

The mechanics of nano-objects strongly depend on the experimental setup used. Indeed, experimental devices generate stress either by controlling the force exerted by the grips (or indenters) or by monitoring their displacements, while software-based feedback loops are also developed to control displacements using force actuators. Often, nanomechanical experiments are interpreted using intrinsically displacement-controlled molecular dynamics simulations, without questioning the influence of the control mode. In this study, we develop an original strategy to perform load-controlled molecular dynamics simulations applied here to nanoparticles under compression as a test-case. While displacement-controlled simulations show intermittent plasticity and load drops, load-controlled simulations are characterized by strain-bursts more in line with load-controlled experiments. Here, a special attention is paid to the dislocation microstructure evolution depending on the control mode. Finally, interpretations of recent experiments based on atomistic simulations are revised, including the envelope load model usually used to correlate displacement-controlled atomistic simulations and load-controlled experiments at small-scales.

Effects of surface curvature and dislocation dynamics: Dynamical deformation mechanisms for uniaxial compression tests at the nanoscale

The understanding of size effects in micro-crystal plasticity has been in-part based on controlled uniaxial mechanical testing of crystalline micropillars that may be monitored in-situ, using modern microscopy approaches. Nevertheless, it has always been clear that mechanics and materials science are not ideally decoupled in uniaxial micropillar compression, thus agreement between experiments and theory remains challenging. We present a theoretical analysis of the uniaxial compression of micropillars with curved top free surfaces, in consistency with modern experimental thresholds. By using coupled Finite Element and Discrete Dislocation Dynamics simulations we investigate the effect of the small curvature to dislocation microstructure evolution at constant displacement rate. The uniaxial compression of flat micropillars is shown to be consistent with existing literature, with homogeneous stress build up and random activation of sources inside the volume. However, in the presence of a small top-surface micropillar curvature, there are significant dynamical effects on dislocation mechanisms and an overestimate of strain at yielding that leads to large errors on capturing elastic compression moduli and avalanche noise characteristics. Characteristically, for 10 nm-high isotropic curvature, large (>100MPa) stress drops emerge in the average stress, that become larger as the initial dislocation density increases, in direct contrast to expectations and findings for ideally flat micropillars.

The Response Mechanism of Crystal Orientation to Grain Boundary Dislocation under Uniaxial Strain: A Phase-Field-Crystal Study

An exploration of dislocation microstructure evolution with different misorientation angles was performed using phase field crystal method (PFC). The microcosmic evolution process of grain boundaries under external stress, as well as the corresponding energy curve and stress–strain curve, are analyzed. The relationship between the misorientation angle and the dislocations emission frequency is discussed. Three forms of dislocations reaction on the evolution process of 6° and 10° are analyzed in detail, which are respectively type I semi-annihilation, type II semi-annihilationand full-annihilation. Among them, the nature of type I semi-annihilation is a combination of dislocation and a single edge dislocation reaction with a single edge dislocation left. The essence of type II semi-annihilation is a pair of dislocation and the other pair of dislocation reaction leaving two edge dislocations. The essence of full-annihilation is that two pairs of dislocations or single edge dislocations with opposite Burger vectors react with each other and the distortion area disappears. When the misorientation angle is 10°, the dislocation reaction and the dislocation motion ability of the system are stronger than 6°. The peak of the energy curve is related to the number of dislocation proliferations in the evolution process. An emission frequency and average density of dislocations of 10° is greater than 6°. The causes of plastic deformation are revealed to a certain extent by stress–strain curves.

Thermodynamic considerations on a class of dislocation-based constitutive models

Dislocations are the main carriers of plastic deformation in crystalline materials. Physically based constitutive equations of crystal plasticity typically incorporate dislocation mechanisms, using a dislocation density based description of dislocation microstructure evolution and plastic flow. Typically, such constitutive models are not formulated in a thermodynamic framework. Nevertheless, fundamental considerations of thermodynamic consistency impose constraints on the admissible range of model parameters and/or on the range of application of such models. In particular, it is mandatory to ensure that the internal energy increase associated with dislocation accumulation is properly accounted for in the local energy balance. We demonstrate on some examples taken from the literature how failure to do so can lead to constitutive equations that violate the first and second laws of thermodynamics either generally or in some particular limit cases, and we discuss how to formulate constraints that recover thermodynamic consistency.

Effect of size and orientation on stability of dislocation networks upon torsion loading and unloading in FCC metallic micropillars

At the continuum length scale, mechanical properties of metals show relatively weak orientation dependence; however, they exhibit strong anisotropic behaviors as the size of sample decreases to micron and nanometer length scales. In this study, three-dimensional dislocation dynamics (DD) simulations are performed to investigate the orientation-dependent plasticity in submicron face-centered cubic (FCC) micropillars subjected to torsion. Accommodating results from atomistic modeling, updated surface nucleation schemes in DD models have been developed for three orientations ([001], [101], and [111]), allowing investigation of the dislocation microstructure evolution and the corresponding anisotropic mechanical response upon torsional loading and unloading. The DD simulation results show that the coaxial and hexagonal networks formed in [101] and [111] oriented nanopillars, respectively, exhibited excellent plastic recovery, while the rectangular network formed in the [001] crystal orientation was more stable and did not experience as much plastic recovery.

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.

Evolution of dislocation microstructure in irradiated Zr alloys determined by X-ray peak profile analysis.

During neutron irradiation of metals, owing to the enhanced number of vacancies and interstitial atoms, the climb motion of dislocations becomes significant at room temperature, leading to a recrystallization of the material. Moreover, the vacancies and interstitial atoms tend to form prismatic dislocation loops that play a crucial role in the plastic properties of the materials. X-ray peak profile analysis is an efficient nondestructive method to determine the properties of dislocation microstructure. In the first half of this article, the foundation of the asymptotic peak broadening theory and the related restricted-moments peak-evaluation method is summarized. After this, the microstructural parameters obtained by X-ray peak profile analysis are reported for irradiated E110 and E110G Zr alloys used as cladding material in the nuclear industry.

Spectral discrete dislocation dynamics with anisotropic short range interactions

Discrete dislocation dynamics models dislocation-mediated plastic deformation and microstructural evolution in solids whilst discretely representing and tracking all line defects present in the medium. Hybrid methodologies for evaluating mechanical fields using continuum approaches while retaining the discrete formalism for evaluating dislocation kinematics and interactions have greatly improved the numerical efficiency of the method. In the present work, we propose a spectrally-based continuum solution of the mechanical fields based on the field dislocation mechanics framework which produces highly accurate elastic fields near dislocation cores in both isotropic and anisotropic media. Application of the model to a few elementary cases (i.e. dislocation junction formation, dislocation migration) show that the model proposed predicts accurate elastic fields both on the short and long range.

Dislocation motion and microstructure evolution deformed during creep at room temperature in Ti-6Al-4V alloy

Dislocation motion and microstructure evolution deformed during creep at room temperature in Ti-6Al-4V alloy

Atomic simulation of crystal orientation effect on coating surface generation mechanisms in cold spray

Cold spray (CS) as a new surface modification method is widely applied in improving surface quality. The effect of crystal orientation of powder particles on coating surface generation mechanisms in cold spray is systematically investigated by molecular dynamics (MD) simulations in this work. The amorphization tendency and temperature distribution in the jetting region in our simulation are consistent with previous experimental results. In particular, our results show that crystal orientation affects the interactions between the powder particles and the surface of the substrate dramatically, leading to different atomic stress distribution, dislocation density evolution and microstructure evolution processes in the particle/substrate interface region for powder particles with different crystal orientations. The coating surface generation mechanism related to the slip plane system will be discussed.

Dislocation Dynamics Simulations of Dislocation-Particle Bypass Mechanisms

Effect of precipitation strengthening on metal is generally attributed to the dislocation interaction with the precipitate which acts as the barrier to the dislocation motion on the slip plane. In order to achieve better understanding of critical events of dislocation motion and evolution of dislocation microstructure, we have developed numerical simulation method of dislocation-dislocation and dislocation-particle interactions by means of discrete dislocation dynamics at mesoscopic scale. In this work, Green’s function method is utilized for the computation of the stress fields of dislocation and misfitting particle, and the interaction forces acting on the dislocation. We also proposed the efficient algorithm of the connectivity vector for the dislocation line elements, linked-list data structure, to deal with the flexible interaction of dislocation line elements. The geometrical effect of dislocation slip planes on the dislocation bypassing behaviors is tested by changing the relative height of dislocation slip plane against the center plane of spherical particle, where cross slip event is also taken into account for the dislocation motion. Simulation results show a wide variety of topological changes of dislocation during motion on the slip planes around the particle, which results from the stress field of the particle varied with the relative height between the dislocation slip plane and center plane of particle. The full analysis of the mechanisms of dislocation line bypassing misfitting particle has been explained in this study.

Effects of laser shock processing and shot peening on 253 MA austenitic stainless steel and their consequences on fatigue properties

A comparative study of the influence of laser shock peening without coating (LSPwC) and shot peening (SP) treatments on the low cycle fatigue life of 253 MA austenitic stainless steel was investigated. LSPwC treatments were performed with 2500 pulse/cm2 and 5000 pulse/cm2. To evaluate the effects of each treatment, residual stress, roughness, hardness, and microstructure were analyzed. It is of particular interest the correlation of the fatigue performance with the dislocation microstructure evolution. The results reveal that all the surface treatments increase the surface hardness, induce compressive residual stresses (CRS) and a high density of mechanical twins and dislocations. The stability of the workhardened near surface microstructure results in the improvement of the fatigue life of peened 253 MA. Moreover, the best improvement of fatigue life reached for SP is mainly due to the highest number of twins and the more superficial CRS.

Televacuna: ¿a qué estás esperando?

Discrete dislocation dynamics models dislocation-mediated plastic deformation and microstructural evolution in solids whilst discretely representing and tracking all line defects present in the medium. Hybrid methodologies for evaluating mechanical fields using continuum approaches while retaining the discrete formalism for evaluating dislocation kinematics and interactions have greatly improved the numerical efficiency of the method. In the present work, we propose a spectrally-based continuum solution of the mechanical fields based on the field dislocation mechanics framework which produces highly accurate elastic fields near dislocation cores in both isotropic and anisotropic media. Application of the model to a few elementary cases (i.e. dislocation junction formation, dislocation migration) show that the model proposed predicts accurate elastic fields both on the short and long range.

Deformation mechanisms based constitutive modelling and strength-ductility mapping of gradient nano-grained materials

Gradient nano-grained (GNG) materials have shown synergetic high strength and ductility due to their unique gradient microstructure, where the grain size changes from tens of nanometers in the surface region to tens of micrometers in the core. This work develops a deformation mechanisms based constitutive model to describe the deformation behavior of GNG materials and to offer a guidance for the design of their microstructures. The established constructive model employs a modified Hall-Petch relation to describe the initial yielding. The different strain hardening behaviors of nano-grained and ultra-fine grained/coarse-grained regions in GNG materials are correlated with the different mechanisms of dislocation microstructure evolution. In addition, the mechanically driven grain growth observed in experiment is also taken into account to capture the effect of grain size evolution on strength and ductility. It is found that grain growth helps to reduce the heterogeneity of the internal stress and plastic strain fields, and thus delays failure of GNG materials. The model successfully predicts the tensile response of a GNG copper bar and captures the distinctive, inverse linear relation between strength and ductility typical of GNG materials. The model can serve as a potential tool for microstructure design of GNG materials by manipulation and optimization of the grain microstructure.

Research on Formation Conditions of the Ultrafine-Grained Structure of the Cylindrical Parts Manufactured by Power Spinning Based on Small Strains

Two different methods, power spinning and annealing (PSA), quenching and power spinning followed by annealing (QPSA), for manufacturing the cylindrical parts with ultrafine-grained (UFG) structure were reviewed, the dislocation density and microstructural evolution during the two different processes of PSA and QPSA were further studied. The results show that the required strains for obtaining the UFG structure by power spinning is only 0.92 when the initial microstructure of the material is in the phase of lath martensite. The dislocation density and storage energy are increased to 10 times that of the blank after quenching and power spinning and decreased to the level of the blank after recrystallization annealing. Microstructures with fine grain size after quenching, storage energy of 1.8 × 105 kJ/m3 obtained after power spinning and second phase particle with nano-scale precipitated during annealing are the necessary formation conditions for manufacturing the cylindrical parts with UFG structure based on small strains. Compared with the original tubular blank, the mechanical properties of the spun parts with UFG structure improves significantly. The tensile strength and hardness of the spun parts manufactured by QPSA method is 815 MPa and 305 HV, respectively, and the elongation is 17.5%.

Modeling the temperature and high strain rate sensitivity in BCC iron: Atomistically informed multiscale dislocation dynamics simulations

Multiscale discrete dislocation plasticity (MDDP) simulations are carried out to investigate the mechanical response and microstructure evolution of single crystal BCC iron subjected to high strain rate compression over a wide range of temperature. The simulations are conducted at temperatures ranging between 300 K and 900 K and strain rate ranging between 102 to107 s−1. Atomistically informed generalized mobility law was incorporated in MDDP to account for the effects of temperature and strain rate on dislocation mobility, lattice friction and elastic constants.MDDP based constitutive equations interrelating temperature and strain rate with the flow stress at high strain rate shock-less and shock conditions are proposed. The simulation results of the temperature and strain rate dependent yield strength and Hugoniot elastic limit are in good agreement with reported experimental results. Detailed investigations of the dislocation microstructure evolution show the formation of extended screw dislocation lines at temperatures below 340 K due to the large value of the lattice friction of the pure screw segments. Moreover, small sessile loops of radius in the order of few nanometers are formed. The formation of these sessile loops is facilitated by the easiness of multiple cross slip on available slip planes.

Dislocation Networks and the Microstructural Origin of Strain Hardening

When metals plastically deform, the density of line defects called dislocations increases and the microstructure is continuously refined, leading to the strain hardening behavior. Using discrete dislocation dynamics simulations, we demonstrate the fundamental role of junction formation in connecting dislocation microstructure evolution and strain hardening in face-centered cubic (fcc) Cu. The dislocation network formed consists of line segments whose lengths closely follow an exponential distribution. This exponential distribution is a consequence of junction formation, which can be modeled as a one-dimensional Poisson process. According to the exponential distribution, two non-dimensional parameters control microstructure evolution, with the hardening rate dictated by the rate of stable junction formation. Among the types of junctions in fcc crystals, we find that glissile junctions make the dominant contribution to strain hardening.