Dislocation-based Model Research Articles

Dynamic deformation and fracture of brass: Experiments and dislocation-based model

In this work, we perform a comprehensive study of the dynamic deformation and fracture of brass, including Taylor tests with classical and profiled cylinders and ball throwing experiments reaching the strain rates of about (0.1−1)/μs, as well as atomistic and continuum-level numerical modeling. Molecular dynamics (MD) simulations are used to construct the equation of state (EOS) of brass and to study its fracture characteristics at shear deformation under negative pressure. An original model of fracture under combined tensile-shear loading is formulated, which takes into account both the accumulation of empty volume in the process of lattice loosening due to the lattice defect production in the course of plastic deformation and further mechanical growth of voids controlled by the dislocation plasticity. This atomic-scale model is transmitted to the macroscopic experiment-scale level and embedded into 3D dislocation plasticity model to describe the dynamic deformation and fracture of brass using the numerical scheme of smoothed particle hydrodynamics (SPH). A part of experimental data is used to find the optimal parameters of the dislocation plasticity model by means of the Bayesian global optimization method accelerated with the help of artificial-neural-network (ANN)-based emulator of the 3D model. Another part of experimental data is used to fit the fracture model parameter. The remaining experimental data, which are not used in the parameterization, are applied to verify the parameterized model. The developed physical-based model provides correct and meaningful description of the dynamic deformation and fracture of brass, while the developed formalized approach to its parameterization opens a way to wider use of this type of models in the engineering applications, including studies on dynamic performance and high-speed processing technologies.

Revealing the fatigue strengthening and damage mechanisms of surface-nanolaminated gradient structure

Extending the fatigue life of metals is a critical concern for maintaining material and component integrity in engineering systems. The integration of gradient structures within materials represents a highly promising approach to enhance the fatigue properties in metallic materials, while a detailed mechanistic understanding of the fatigue damage evolution of such structures is yet to be developed. Here, we report that the surface-nanolaminated gradient structure comprised of nanolaminates and hierarchical twins imparts remarkable resistance to both low-cycle and high-cycle fatigue. A dislocation-based strain gradient crystal plasticity model is developed to investigate the strengthening and damage mechanisms of our gradient structure. The size dependence of the initial dislocation density, its evolution and back stress hardening are taken into account and verified by the experimental data. The simulation results reveal that the strain delocalization and back stress hardening induced by the structure gradient significantly mitigate the fatigue damage accumulation. Additionally, in contrast to conventional gradient structures, the mechanical stability of the present structure enables these strengthening mechanisms to persist until crack initiation. These effects, combined with the sequential toughening mechanisms activated in the surface-nanolaminated gradient structure, ensure a marked life extension under low-cycle fatigue (by a factor of four), outperforming conventional gradient and other microstructural design strategies. Finally, a multiscale anti-fatigue design principal for damage homogenization is given based on the prior quantitative analysis.

Uncovering Nanoindention Behavior of Amorphous/Crystalline High-Entropy-Alloy Composites.

Amorphous/crystalline high-entropy-alloy (HEA) composites show great promise as structural materials due to their exceptional mechanical properties. However, there is still a lack of understanding of the dynamic nanoindentation response of HEA composites at the atomic scale. Here, the mechanical behavior of amorphous/crystalline HEA composites under nanoindentation is investigated through a large-scale molecular dynamics simulation and a dislocation-based strength model, in terms of the indentation force, microstructural evolution, stress distribution, shear strain distribution, and surface topography. The results show that the uneven distribution of elements within the crystal leads to a strong heterogeneity of the surface tension during elastic deformation. The severe mismatch of the amorphous/crystalline interface combined with the rapid accumulation of elastic deformation energy causes a significant number of dislocation-based plastic deformation behaviors. The presence of surrounding dislocations inhibits the free slip of dislocations below the indenter, while the amorphous layer prevents the movement or disappearance of dislocations towards the substrate. A thin amorphous layer leads to great indentation force, and causes inconsistent stacking and movement patterns of surface atoms, resulting in local bulges and depressions at the macroscopic level. The increasing thickness of the amorphous layer hinders the extension of shear bands towards the lower part of the substrate. These findings shed light on the mechanical properties of amorphous/crystalline HEA composites and offer insights for the design of high-performance materials.

A dislocation-based crystal plasticity model for single-crystal micropillars based on strain burst with stochastic characteristics

A dislocation-based crystal plasticity model for single-crystal micropillars based on strain burst with stochastic characteristics

Effect of loading modes on uniaxial creep-fatigue deformation: A dislocation based viscoplastic constitutive model

A comprehensive investigation was conducted on the stress-strain responses and microstructural evolutions of 9Cr3Co3WCu martensitic steel at 650 ℃ subjected to low cycle fatigue tests, strain-controlled creep-fatigue tests (SNCFTs), and hybrid stress-strain-controlled creep-fatigue tests (HSSCFTs). The creep strain accumulation per cycle in HSSCFTs exhibited three stages: an initial decrease in the early cycles, followed by a prolonged period of steady increase, culminating in a rapid increase prior to fracture. In contrast, the creep strain accumulation in SNCFTs showed a consistent decreasing trend throughout the test. Through the employment of advanced characterization techniques, the evolution of dislocation density exhibited a decreasing rate in all cases, and a fracture morphology characterized by a large size of creep voids was observed in HSSCFTs. Consequently, a dislocation-based viscoplastic constitutive model was developed, incorporating a relaxation parameter, a slip deformation resistance model and a dislocation density evolution model interacting with the grain boundary. The proposed model demonstrated excellent congruences under fatigue, creep, creep-fatigue, and multi-step creep- fatigue tests between experimental and simulated results, thereby confirming its capability to comprehensively capture cyclic deformation under various loading modes.

Plastic deformation and fracture of AlMg6/CNT composite: A damage evolution model coupled with a dislocation-based deformation model

Understanding the plastic deformation and fracture behavior of Carbon nanotube (CNT)-reinforced aluminum composites is crucial for determining the factors controlling their strength and ductility. This article presents a novel approach by proposing a coupled micromechanical dislocation-based constitutive model combined with the Gurson-Tvergaard-Needleman (GTN) damage evolution model. The objective of this research is to accurately predict the load-displacement behavior of an AlMg6/CNT composite, which is manufactured through accumulative roll bonding (ARB), from yield to fracture. The study investigates the correlations between the number of ARB passes, which affects the dislocation density of the matrix, and the distribution of CNTs in the composite, with the GTN parameters. The analysis reveals that the volume fraction of void nucleating particles (fN) is a critical parameter influencing the ductility of the composite ductility. Initially, due to CNT agglomeration, they act as nucleation sites for damage, resulting in an increase in fN and a decrease in ductility. However, as the number of ARB passes increases, leading to a homogeneous CNT distribution, fN decreases, and CNTs contribute to improved strength and ductility of the composite. The proposed model accurately predicts the load-displacement curve of the composite during uniaxial tensile testing, taking into account the effect of ARB passes. The research findings provide insights for future extensions of the GTN model, aimed at enhancing its theoretical framework and applicability in the field.

Effect of an edge dislocation on hydride growth in zirconium: elastic complex potential study

The formation of hydrides can significantly decrease the mechanical reliability of Zr servicing in the nuclear reactor. This study investigates the effect of the local stress field resulting from the hydride eigenstrain and dislocations on hydrogen transport and explores the hydride growth regulation. The stress functions, which can be extended and further applied to the realistic crystal structure and servicing status, are derived using the dislocation-based strain nucleus model and elastic complex potential method. The nonhomogeneous equation of hydrogen transport governed by diffusion and hydrostatic stress gradient is analytically solved. The results show that: (1) In the absence of dislocations, the hydride grows toward 112¯0 direction under the hydrostatic stress gradient resulting from the hydride eigenstrain. (2) The lower the temperature is, the higher the hydrogen concentration gradient in the adjacent area of the hydride is. The higher hydrogen fraction can also accelerate the growth rate. (3) Dislocation defects are capable of inducing triangle-shaped and asymmetric growth tendencies and providing new nucleation loci for hydrides. Based on the significant hydrostatic stress gradient led by dislocation singularity, this study analytically explains the autocatalysis and new-nucleation-locus effects raised by the in-situ observations.

Insights for the strength and ductility of precipitation hardening Al–Li–Sc alloys

Al–Li alloys with high elastic modulus, low density and high specific strength have been widely used in aerospace industry. However, although Al3Li precipitates enhance the strength significantly, the appearance of shearable Al3Li precipitates usually decreases the ductility, leading to the strength-ductility trade-off. In this study, the strategy of microalloying is applied to fabricate an Al–2.46 Li–0.2 Sc (wt.%) alloy with tunable precipitate sizes by heat treatment. This alloy exhibits a good combination of strength and ductility when the precipitate radius is smaller than 6.7 nm or larger than 16.4 nm. The strengthening mechanisms in Al–Li–Sc alloy with different precipitate sizes are quantitatively discussed. With the increase of precipitate size, the dominant precipitation strengthening mechanism changes. The influence of precipitate on ductility is mainly achieved by influencing the dynamic recovery rate of dislocation which can be illustrated by a dislocation-based model. When the precipitate size is relatively small or large, the Al–Li–Sc alloy exhibits a higher ductility owing to a lower dynamic recovery rate. This study provides insight for understanding the strength and ductility in Al–Li–Sc alloy as well as potential theoretical guideline for designing novel high-performance Al–Li based alloys.

Dislocation-Based Finite Element Modeling of an Off-Axis Twist Extrusion with Variable Helix Angles

Dislocation-Based Finite Element Modeling of an Off-Axis Twist Extrusion with Variable Helix Angles

Understanding the strain localization in additively manufactured materials: Micro-scale tensile tests and crystal plasticity modeling

Metallic parts fabricated by additive manufacturing (AM) usually exhibit unique microstructures and non-negligible residual stresses compared with the counterparts produced by conventional manufacturing. These inherent microstructural factors strongly affect the mechanical response of the as-built AM parts. In this study, we focus on the strain localization behavior of 316L stainless steel produced by laser powder-bed-fusion. In-situ tensile tests under a scanning electron microscope are performed, and the digital image correlation method is used to measure the strain distribution combined with electron backscatter diffraction. Meanwhile, a dislocation-based crystal plasticity finite element model incorporating residual stresses is developed to study the origins of the strain localization in the AM material. The results indicate that strain localization in AM materials is closely associated with microstructural features, encompassing behaviors related to slip activities, interactions with neighboring grains and dislocation evolutions. Additionally, the columnar grain features also render the strain distribution sensitive to the loading direction. The strain localization is serious in some small grains with high residual stresses, while in large grains the effect is less significant. These factors collectively contribute to the increasing likelihood of strain localization occurring in the AM microstructures with heterogeneous grain size and texture distribution. This work provides detailed insights into the strain localization in AM materials and would facilitate the manufacturing parameter optimization of AM materials by tuning the microstructure to reduce deformation inhomogeneity.

A dislocation-based damage-coupled constitutive model for single crystal superalloy: Unveiling the effect of secondary orientation on creep life of circular hole

Circular holes in single crystal (SX) turbine blades are susceptible to creep failure at high temperatures, due to the stress concentrations near the holes. In this study, a dislocation-based damage-coupled constitutive model for SX superalloys is developed, validated, and applied to unveil the effect of secondary orientation on the creep life of circular holes. The structure-induced geometrically necessary dislocations (GND) density resulting from the macroscopic strain gradient is incorporated. The dissipated energy is employed as the indicator to predict crack nucleation. Initially, the specimens without a hole are employed to calibrate the parameters and validate the model in the absence of structure-induced GND. Creep experiments incorporating the digital image correlation technique are conducted on the specimens with a hole under different secondary orientations, which aims to validate the simulated strain distribution, crack nucleation location, and creep life under the influence of structure-induced GND. The results indicate that the incorporation of structure-induced GND contributes to mitigating the conservatism in the creep life prediction of circular holes. Because, the GND can enhance dislocation hardening near the hole, extending the predicted life and improving the accuracy of life prediction. Meanwhile, both experiments and simulations indicate that the secondary orientation influences the crack nucleation locations at the hole edge. The variation in the creep life at different secondary orientations is attributed to the changes in both the maximum value and uniformity of resolved shear stresses distributed across slip systems. Finally, the model is applied to simulate the creep behavior of a circular hole under various secondary orientations, stresses, and temperatures. An empirical model is developed to rapidly evaluate the creep life of a circular hole in the SX superalloy, which facilitates the engineering application of the proposed model.

Insights into flow stress and work hardening behaviors of a precipitation hardening AlMgScZr alloy: Experiments and modeling

Flow stress and work hardening behaviors, as two important aspects of mechanical behaviors, have been studied extensively and their interpretation for the case of pure metals via dislocation theory is well established. The introduction of precipitates inevitably affects the flow stress and work hardening rate, since the precipitates can evidently change the dislocation behaviors, both their gliding facilities and their storage mechanisms. Thus, different precipitate-dislocation interaction modes (i.e. shearing and bypassing mechanisms) would lead to different dislocation behaviors and resultant different flow stress and work hardening behaviors. In this study, we investigate the influence of shearable, non-shearable and mixed shearable/non-shearable precipitates on flow stress and work hardening behaviors in the case of AlMgScZr alloys, where precipitates and solid solution can be decoupled, based on experiments and a modified dislocation-based model. We show that, the introduction of shearable precipitates and shearable/non-shearable transition have important effects on flow stress and work hardening behaviors. By quantitatively characterizing different precipitate-dislocation interactions and the evolution of dislocation density during the deformation, the intrinsic influencing mechanisms of precipitates on flow stress and work hardening behaviors are demonstrated.

Prediction of grain size and dislocation density in the cold spraying process using a dislocation-based model

The cold spray particle deposition process was simulated by modeling the high-velocity impacts of spherical particles onto a flat substrate at different velocities. In addition to simulating the single particle, this study also employed a unique simulation technique to predict the evolution of the material's microstructure under real process conditions. A dislocation-based model was implemented as a VUMAT subroutine to model the microstructure. Additionally, Python scripting was also utilized in the multi-particle impact simulation to create particles and assign velocity and interaction randomly. The relationships between stress-strain values and material microstructure are linked together. By using this model, calculations were done for the equivalent plastic strain, dislocation density, and grain size in the particle, substrate, and interface. At the interface, there were high levels of plastic strain and strain rates reaching up to, which formed a bond between the particles and the substrate. It was found that a minimum plastic strain of approximately 1 is needed to create this bond. At velocities exceeding a critical velocity, a jet was produced. The particle grain size in regions distant from the interface measured between 200 and 500 nm, which is in good agreement with the experimental results. The smallest grain size was observed at the interface, measuring 140 nm. The validation outcomes demonstrated that the suggested model effectively replicates the cold spraying process. As a result, the suggested model has the capability to predict and evaluate the changes in the material's microstructure during the cold spraying process using various factors.

Theoretical model of the temperature-dependent ultimate tensile strength from the viewpoint of dislocation kinetics approach for FCC metals

In this work, based on the force-heat equivalence energy density principle and the theory of dislocation kinetics, a dislocation-based theoretical model of temperature-dependent ultimate tensile strength without fitting parameters is developed. The novelty of this model is that the theoretical characterization of the temperature-dependent dislocation annihilation energy barrier is implemented, and the new temperature-dependent expressions of the dislocation annihilation term and the dislocation storage term in the dislocation kinetics approach are derived. The model is well validated by comparing against available experimental results of pure face-centered cubic metals in a wide temperature range with the lowest temperature close to absolute temperature 0 K and the highest temperature close to melting point. Furthermore, the analysis results of the model show that increasing the dislocation storage coefficient and reducing the dislocation annihilation coefficient are effective measures to improve the ultimate tensile strength of metal materials, particularly at lower temperatures. The theoretical model provides a clear and profound physical basis for understanding the evolution of ultimate tensile strength at different temperatures.

Mechanics and Energetics of Kink Deformation Studied by Nonlinear Continuum Mechanics Based on Differential Geometry

This study conducts dislocation-based modeling and numerical analysis for kink deformation using the theory of nonlinear continuum mechanics based on differential geometry. The kinematics of the continuum is represented by the reference, intermediate, and current states, which are related to the multiplicative decomposition of the deformation gradient into plasticity and elasticity. The intermediate state is determined by the Cartan first structure equation, whereas the current state is obtained from the stress equilibrium equation. Kink deformation is modeled by a planar array of edge dislocations, and the governing equations are solved numerically using the finite element method. Quantitative verification of the model is conducted by comparing the bending angle at a kink interface and the theoretical prediction given for the tilt grain boundary. We construct two types of ortho-type kink models for several interface lengths to understand the energetics and mechanics of the kink growth process. The present numerical analysis demonstrates the significant stress concentration at the growth front due to the formation of wedge disclination. We also discuss the material strengthening mechanism from elastic strain energy, nonsingular stress fields, and nonlinear elastic interaction between the disclinations.

Effects of fluid flow in triple porosity medium on fracture width and its propagation during lost circulation control

During oil and gas well construction, lost circulation is one of the major challenges, and to migrate the problem, lost circulation materials (LCMs) should be used to resist fracture reopening with the hypothesis of fracture tip isolation. A triple porosity medium Darcy flowing model was developed to capture pressure distribution along the fracture surface, coupled with a dislocation-based fracture mechanics model to calculate fracture width and assess its propagation. In the model, mud cake on wellbore and fracture surface was considered as the third type of pore medium. The rest dual pore medium models incorporate the fluid flow through LCMs within fracture and the fluid leakoff from fracture into matrix. Sensitivity analyses of the key parameters, such as triple pore medium permeability, viscosity, wellbore pressure, plugging location are implemented, and the results emphasize that fracturing resistance effect of LCMs was controlled not only by the fluid flow within fractures, but also by the flow through mud cake on wellbore into matrix. To inhibit fracture reopening, in high permeability formations, both reduction of mud cake permeability and LCMs permeability were required while in lower permeability formations, fluid flow within fractures dominates and should be minimized. Besides, tip isolation can be achieved by extending sealing fracture length. However, high wellbore pressure or long operation time will result in elevated distances and unallowable fluid loss. Then, wellbore pressure must be reduced to cure the lost circulation. More viscosity of the fluid and total integrity plugging of LCMs are another major factor extending the time for pressure transfer to fracture tip, resisting unexpected fracture propagation. The method proposed in this study clarifies that tip isolation can be realized by fracture plugging and reduction of fluid filtration from the wellbore to matrix. Moreover, operational insights on LCMs design can also be derived.

Thermo-kinetic characteristics on stabilizing hetero-phase interface of metal matrix composites by crystal plasticity finite element method

Using dislocation-based constitutive modeling in three-dimension crystal plasticity finite element (3D CPFE) simulations, co-deformation and instability of hetero-phase interface in different material systems were herein studied for polycrystalline metal matrix composites (MMCs). Local stress and strain fields in two types of 3layer MMCs such as fcc/fcc Cu–Ag and fcc/bcc Cu–Nb have been predicted under simple compressive deformations. Accordingly, more severe strain-induced interface instability can be observed in the fcc/bcc systems than in the fcc/fcc systems upon refining to metallic nanolayered composites (MNCs). By detailed analysis of stress and strain localization, it has been demonstrated that the interface instability is always accompanied by high-stress concentration, i.e., thermodynamic characteristics, or high strain prevention i.e., kinetic characteristics, at the hetero-phase interface. It then follows that the thermodynamic driving force ΔG and the kinetic energy barrier Q during dislocation and shear banding can be adopted to classify the deformation modes, following the so-called thermo-kinetic correlation. Then by inserting a high density of high-energy interfaces into the Cu-Nb composites, such thermo-kinetic integration at the hetero-phase interface allows a successful establishment of MMCs with the high ΔG-high Q deformation mode, which ensures high hardening and uniform strain distribution, thus efficiently suppressing the shear band, stabilizing the hetero-phase interface, and obtaining an exceptional combination in strength and ductility. Such hetero-phase interface chosen by a couple of thermodynamics and kinetics can be defined as breaking the thermo-kinetic correlation and has been proposed for artificially designing MNCs.

Effect of micron-scale nonmetallic inclusions on fatigue crack nucleation in a nickel-based superalloy

Micron-level nonmetallic inclusions are likely to be a limiting factor for further improvement in the fatigue resistance of nickel-based superalloys. To investigate the fatigue response of nickel-based superalloys containing micro-inclusions, a dislocation-based crystal plasticity model was employed for numerical simulations, and the local energy storage density criterion was used for damage evolution analysis. The results showed that, as a hard phase, micro-inclusions interfered with the plastic deformation of the matrix, as evidenced by the inhomogeneous slipping of the main slip systems and the activation of new slip systems. Additionally, micro-inclusions induced the accumulation of geometrically necessary dislocations (GNDs) around them. When micro-inclusions appeared on grain boundaries, the above factors changed the energy required for local deformation through potential hardening effects in the model and ultimately affected the evolution of the local energy storage density. When micro-inclusions appeared inside grains, the evolution of local energy storage was often dominated by plastic deformation only. The above mechanism is microstructure sensitive and spatially limited, which leads to the dispersion of lifetimes and negligible effect of micro-inclusions on distal grains.

A dislocation-based model for shear cracks in arbitrary orientations under contact loading

Mechanical transmission components are generally under the risk of contact fatigue, resulting in cracks initiated from the subsurface. When subject to compressive stress, these cracks might be forced to be closed, thus their faces are in partial slip contact. Under such conditions, the interactions of stick and slip zones cannot be directly determined, which is one of the greatest challenges of contact fatigue problems. In this study, the distributed dislocation technique is adopted to investigate the stick–slip friction along the alignment of shear cracks in arbitrary orientations in a half-plane under contact loading. The unknown dislocation density describing the crack face displacement is iteratively calculated based on the stress conditions and then introduced to update the surface gap between contacting bodies. The complex expressions of the influence coefficients used to determine the stress and displacement induced by the dislocations are derived and the FORTRAN codes are provided in the Supplementary Materials. A step-by-step loading method is proposed to progressively capture the slip history of crack faces. The model is also capable of simulating rolling contact problems. The results are comparable to those predicted using the finite element method with more robust convergence properties. The effects of friction coefficient, crack alignment, and locations of crack faces are discussed in detail. The model paves the foundation for further studies on competing mechanisms of crack propagation and crack face wear, and provides insights into the frictional fracture of materials under contact loading.

Simulation of Work Hardening in Machining Inconel 718 with Multiscale Grain Size.

Machining nickel-based alloys always exhibits significant work-hardening behavior, which may help to improve the part quality by building a hardened layer on the surface, while also causing severe tool wear during machining. Hence, modeling the work-hardening phenomenon plays a critical role in the evaluation of tool wear and part quality. This paper aims to propose a numerical model to estimate the work-hardening layer for a deeper understanding of this behavior, employing both recrystallization-based and dislocation-based models to cover workpieces with multiscale grain sizes. Different user routines are implemented in the finite element method to simulate the increase in hardness in the deformed area due to recrystallization or changes in the dislocation density. The validation of the proposed model is performed with both literature and experimental data for Inconel 718 with small or large grain sizes. It is found that the recrystallization-based model is more suitable for predicting the work-hardening behavior of small-grain-size Inconel 718 and the dislocation-based model is better for that of large-grain-size Inconel 718. Further, as an important type of cutting tool in machining Inconel 718, the chamfered tools with different edge geometries are employed in the simulations of machining-induced work hardening. The results illustrate that the uncut chip thickness and chamfer angle have a significant influence on the work-hardening behavior.