Dislocation-based Plasticity Research Articles

Improved elongation in high-strength low-alloy steel by non-monotonic tensile loading and dislocation-based phenomenological plasticity modeling

In this study, three types of tensile testing of high-strength low-alloy steel were conducted as (a) Let the cross-head monotonically move upward. (b) At every 1 mm of elongation after the initial 2-mm elongation, unload and hold the stress at 0 for 1, 5, or 10 s and then reload. (c) At every 1 mm of elongation after the initial 2-mm elongation, hold cross-head displacement for 1, 5, or 10 s and then reload. Obtained stress–strain curves revealed that the uniform and total elongations were greater when the time between the unloading/holding and reloading was longer. An electron back-scattering diffraction measurement clarified that, in contrast to monotonic tensile testing, 〈111〉 (slip direction) was not aligned in the tensile direction and as-rolled alignment of 〈110〉 remained unchanged even after the elongation reached the uniform elongation in non-monotonically loaded specimens. This texture difference is a possible reason for improved elongations. A dislocation-based phenomenological plasticity model was also established to explain the improved uniform elongation. A low-temperature creep model was adopted to describe the change after unloading/holding. The model successfully reproduced the stress–strain relationship in non-monotonic loading and the improved uniform elongation.

Atomistic study of crack-tip plasticity in precipitation hardened monocrystalline aluminum

Understanding the atomistic mechanisms of dislocation-based plasticity ahead of a crack-tip in precipitation hardened alloys is a challenging problem due to the complexity of the interactions between the precipitates in the microstructure and the variety of defects nucleated at the crack-tip, such as dislocations, stacking faults and micro-twins. In this paper, we use classical molecular dynamics simulations to perform a comprehensive atomistic analysis of the factors that influence the motion of dislocations ahead of a crack-tip in precipitation hardened aluminum. Specifically, the effects of planar copper GPII zones on the motion of dislocations emitted at the crack-tip of an aluminum crystal in four different crystal orientations under constant strain-rate loading were investigated. By placing the precipitates close to the crack-tip, it was found that they did not affect the nucleation of the first dislocation significantly unless they were located immediately ahead. Moreover, in some crystal orientations, subsequent nucleations were appreciably delayed due to the shielding effect of the first dislocation interacting with the precipitate. Following emission, the interaction between the emitted dislocations and the precipitates consisted of different mechanisms, including shear cutting, Orowan looping, and cross-slip, depending on the crystal orientation. The resistance to dislocation motion caused by the precipitates was quantified by determining the interaction time between each dislocation and the precipitates. It was found that although the applied load in each unit cell was high, the dislocations could be significantly slowed down in some of the crystals. This resulted in less dislocation activity ahead of the crack-tip, especially in the crystals for which micro-twinning was the dominant driver of plasticity. The results of this work pave the way for the development of accurate models to predict the evolution of plasticity in metallic materials by providing a quantified assessment of dislocation motion in complex alloy microstructures.

Non-Schmid effect of pressure on plastic deformation in molecular crystal HMX

The energetic molecular crystal cyclotrimethylene trinitramine (HMX) is a key constituent in common plastic bonded explosives. Its plastic deformation under shock conditions is important in reaction initiation and detonation. Here, we study the effect of high pressure on dislocation slip using isothermal-isobaric atomistic simulations. We consider two slip planes, (011) and (101), that are reported to be most active under ambient conditions. For all slip systems considered, the effect of pressure is to increase the critical resolved shear stress for dislocation slip. Pressure may fully inhibit dislocation-based plasticity if the resolved shear stress is not increased in proportion. On the other hand, at sufficiently high shear stresses, the crystal loses shear stability. Therefore, in a broad range of shock conditions, plastic deformation takes place by a combination of dislocation glide in some slip systems and localization in some other systems, with dislocation activity being gradually inhibited as the shock pressure increases. This provides new data on the physical basis of plastic deformation in HMX, indicating that mesoscale representations of plasticity must include shear localization, which is more important under these conditions than dislocation plasticity.

Elastic-plastic deformation of molybdenum single crystals shocked to 12.5 GPa: Crystal anisotropy effects

To understand crystal anisotropy effects on shock-induced elastic-plastic deformation of molybdenum (Mo), results from high-purity single crystals shocked along [110] and [111] orientations to an elastic impact stress of 12.5 GPa were obtained and compared with the [100] results previously reported [A. Mandal and Y. M Gupta, J. Appl. Phys. 121, 045903 (2017)]. Measured wave profiles showed a time-dependent response, and strong anisotropy was observed in the elastic wave attenuation with the propagation distance, elastic limits, shock speeds, and overall structure of the wave profiles. Resolved shear stresses on {110}〈111〉 and {112}〈111〉 slip systems provided insight into the observed anisotropy in elastic wave attenuation and elastic limits and showed that shear stresses, and not longitudinal stresses, are a better measure of strength in shocked single crystals. Under shock compression, resolved shear stresses at elastic limits were comparable to the Peierls stress of screw dislocations in Mo. Elastic wave attenuation was rapid when shear stresses were larger than the Peierls stress. Large differences in the elastic limits under shock and quasi-static loading are likely a consequence of the large Peierls stress value for Mo. Numerically simulated wave profiles, obtained using the dislocation-based plasticity model described in the [100] work, showed good agreement with all measured wave profiles but could not differentiate between the {110}〈111〉 and {112}〈111〉 slip systems. Overall, experimental results and corresponding numerical simulations for the three crystal orientations have provided a comprehensive insight into shock-induced elastic-plastic deformation of Mo single crystals, including the development of a continuum material model.

A dislocation-based stress-strain gradient plasticity model for strength and ductility in materials with gradient microstructures

ABSTRACTAlthough metallic materials with gradient microstructure exhibit notable performance in harsh environmental conditions, they can also exhibit unusual mechanical behaviour. This is attributed to both grain size and the gradient of grain size distribution in the structure. Metallic materials with a homogenous distribution of grain size follow the traditional Hall-Petch relationship, in which strength increases with decreasing grain size at the expense of ductility. However, studies show that materials with a gradient of grain size microstructure do not follow the Hall-Petch relationship, and thus have improved strength and ductility. This suggests that with creative design and engineering of microstructure, the strength-ductility trade-off can be reduced or prevented.In this study, we developed and implemented a dislocation density based model to investigate the mechanical behaviour of nano-microstructure. We designed a multi-scale modelling framework, coupling VPSC (Viscoplastic Self Consistent model) with CDD (Continuum Dislocation Dynamics), applying crystal plasticity equations to simulate dislocation interaction in polycrystalline metallic materials. We also developed design parameters and a model to predict the strength and ductility of materials with gradient microstructure.

Irradiation defect dispersions and effective dislocation mobility in strained ferritic grains: A statistical analysis based on 3D dislocation dynamics simulations

The influence of irradiation defect dispersions on plastic strain spreading is investigated by means of three-dimensional dislocation dynamics (DD) simulations, accounting for thermally activated slip and cross-slip mechanisms in Fe-2.5%Cr grains. The defect-induced evolutions of the effective screw dislocation mobility are evaluated by means of statistical comparisons, for various defect number density and defect size cases. Each comparison is systematically associated with a quantitative Defect-Induced Apparent Straining Temperature shift (or «ΔDIAT»), calculated without any adjustable parameters. In the investigated cases, the ΔDIAT level associated with a given defect dispersion closely replicates the measured ductile to brittle transition temperature shift (ΔDBTT) due to the same, actual defect dispersion. The results are further analyzed in terms of dislocation-based plasticity mechanisms and their possible relations with the dose-dependent changes of the ductile to brittle transition temperature.

Numerical simulation analyses of β ↔ δ phase transition for a finite-sized HMX single crystal subjected to thermal loading.

Phase transition of HMX single crystals is the very first process prior to chemical reaction and ignition of polymer-bonded explosives (PBX). A mesoscale β ↔ δ phase transition model is developed to investigate the role of solid phase transformation on the thermo-mechanical behavior of HMX single crystals. The model captures nonlinear elasticity, dislocation-based crystalline plasticity and temperature-dependent phase transition. Phase transition evolutions of HMX subjected to different heating rates with a certain hydrostatic pressure were investigated based on the finite element software ABAQUS. The simulated results showed that with the thermal heating and cooling boundary conditions, the β ↔ δ phase transition state is reversible, but its path is irreversible. The path-dependence of the β ↔ δ phase transition is reflected by the residual strain and stress that comes into being in the absence of mechanical constraints for 1 mm size HMX single crystals during a temperature cycle. Moreover, the β → δ phase transition is inhibited by higher temperature gradients and hydrostatic pressure. As the β-phase of HMX crystal converts to the δ-phase, the crystal volume expands due to the larger expansion coefficients of δ-HMX so that the stress concentration can be found at the sample center.

Mesoscale cyclic crystal plasticity with dislocation substructures

Constitutive formulations have increasingly focused on physically-based approaches that are less phenomenological and incorporate information from multiple scales. Most dislocation-based plasticity approaches reflect many-body dislocation physics without considering the length scales introduced by the self-organization of dislocations into mesoscale structures. These structures promote internal stresses or back stresses that are heterogeneous and long-range in nature and play a critical intermediary role in distinguishing the stress at micro- and nano-scales under cyclic loading. We present a framework that explicitly incorporates length-scales and evolution laws associated with mesoscale dislocation substructures such as cells and persistent slip bands (PSBs) in metallic materials under cyclic loading. A physically-based formulation for the back stress based on the Eshelby inclusion formalism is introduced that explicitly depends on morphology of mesoscale dislocation structures. The approach employs material parameters that can be measured or computed at lower length scales to contrast the response of models and experiments for multiple single crystals orientation and polycrystals for a wide range of strains.

Three-dimensional phase-field model of dislocations for a heterogeneous face-centered cubic crystal

A central aim of current materials studies is to develop a predictive modeling that incorporates dislocation-based plastic activity and microstructural evolution. Phase-field method has emerged as a powerful tool for addressing this issue, providing us with a versatile variational framework able to describe the movement of dislocations in interaction with underlying microstructures. In this article, a three-dimensional phase-field model of dislocations (PFMD) is developed with a discretization scheme that explicitly captures the face-centered cubic (FCC) geometry. Within this framework, continuous fields are discretized in a way that allows to consider strongly heterogeneous materials and sharp interfaces (free surfaces, stiffer precipitates, pores...) without generating numerical artifacts. The PFMD exposed in this work reproduces dislocation activity in FCC geometry, their reactions, and a particular attention is devoted to the dislocation core behaviors in order to remove effects present in prior generic PFMDs that can appear to be spurious for micron-scale applications. This allows us to rigorously reproduce the dislocation’s velocity with respect to experimental friction coefficients. The model is discussed and illustrated by applications standing at different space-scales that show how dislocations operate with microstructural heterogeneities such as free-surfaces (cylindrical nanopillar) and voids (pore under isostatic pressure).

Well-posedness for the microcurl model in both single and polycrystal gradient plasticity

We consider the recently introduced microcurl model which is a variant of strain gradient plasticity in which the curl of the plastic distortion is coupled to an additional micromorphic-type field. For both single crystal and polycrystal cases, we formulate the model and show its well-posedness in the rate-independent case provided some local hardening (isotropic or linear kinematic) is taken into account. To this end, we use the functional analytical framework developed by Han-Reddy. We also compare the model to the relaxed micromorphic model as well as to a dislocation-based gradient plasticity model.

Dislocation-based plasticity and strengthening mechanisms in sub-20 nm lamellar structures in pearlitic steel wire

The tensile properties and the deformation microstructure of pearlitic steel (0.8 wt % C) have been quantified in wires drawn to strains in the range from 3.7 to 5.4, having a flow stress in the range from 3.5 to 4.5 GPa. With increasing strain the interlamellar spacing (ILS) decreases from about 20 to 10 nm and the thickness of the cementite lamellae decreases from about 2 nm to about 0.7 nm, representing a structure, which breaks up at large strains, decomposes and releases carbon to the ferrite lamellae. The dislocation density increases continuously with strain and reaches about 5 × 1016 m−2 at a strain of 5.4; the dislocations are stored as threading dislocations, as dislocation tangles and as cell boundaries with low to medium misorientation angles. An analysis of the evolution of microstructure and strength with increasing strain suggests that dislocation-based plasticity is a dominating mechanism in the wire and three strengthening mechanisms are applied: boundary strengthening, dislocation strengthening and solid solution hardening with their relative contributions to the total flow stress which change as the strain is increased. Based on linear additivity good correspondence between the calculated and the measured flow stress is observed over the strain range 0–5.4. However at large strains beyond 3.7 deviations are observed which are discussed in terms of the applied strength-structure relationships.

A multiscale gradient-dependent plasticity model for size effects

The mechanical behaviour of polycrystalline material is closely correlated to grain size. In this study, we investigate the size-dependent phenomenon in multi-phase steels using a continuum dislocation dynamic model coupled with viscoplastic self-consistent model. We developed a dislocation-based strain gradient plasticity model and a stress gradient plasticity model, as well as a combined model, resulting in a theory that can predict size effect over a wide range of length scales. Results show that strain gradient plasticity and stress gradient plasticity are complementary rather than competing theories. The stress gradient model is dominant at the initial strain stage, and is much more effective for predicting yield strength than the strain gradient model. For larger deformations, the strain gradient model is dominant and more effective for predicting size-dependent hardening. The numerical results are compared with experimental data and it is found that they have the same trend for the yield stress. Furthermore, the effect of dislocation density at different strain stages is investigated, and the findings show that the Hall–Petch relation holds for the initial strain stage and breaks down for higher strain levels. Finally, a power law to describe the size effect and the transition zone between the strain gradient and stress gradient dominated regions is developed.

Interplay of dislocation-based plasticity and phase transformation during Si nanoindentation

Nanoindentation into single-crystalline Si is modeled by molecular dynamics simulation using a modified Tersoff potential. We observe that the high stress produced during indentation leads to three processes occurring consecutively in the substrate: (i) phase transformation of the original cubic diamond (cd) to the bct5 phase; (ii) generation of dislocations; and (iii) amorphization. The bct5 phase develops along {111} planes of the cd phase; when these meet, the enclosed volume of cd phase transforms to bct5. The particular role played by a stable tetrahedral structure formed by bct5 {111} planes and {111} intrinsic stacking faults in the cd structure is highlighted. The phase transformation to bct5 is partially reversed when dislocations nucleate in the cd phase and locally relieve stresses. The generation and reactions of the uncommon dislocations 14〈111〉 and 13〈112〉 are discussed.

Comparative study of high-temperature grain boundary engineering of two powder-processed low stacking-fault energy Ni-base superalloys

Results of high-temperature grain boundary engineering of an experimental, low stacking-fault energy (LSF) Ni-base superalloy were compared to a commercially available superalloy RR1000. Deformation mechanism maps for thermal-mechanical processing were compared along with the resulting length fractions of Σ3 boundaries following sub-solvus and super-solvus annealing. Compared to the hot deformation processing characteristics of RR1000, lowering the stacking-fault energy reduces dislocation mobility and expands the range of temperatures and strain rates over which dislocation-based plastic flow mechanisms were operative in the LSF alloy. For both alloys, processing conditions conducive to dislocation-based plasticity allowed for the storage of strain energy within the microstructure that was utilised for strain-induced boundary migration (SIBM) and the formation of Σ3 boundaries upon annealing. Based on the results of this study, alloying changes that serve to reduce the stacking-fault energy of Ni-base superalloys also make the alloys more amenable for grain boundary engineering techniques that utilised hot deformation.

Analysis of strain bursts during nanoindentation creep of high-density polyethylene

Nanoindentation creep experiments on polyethylene were carried out in order to investigate dislocation-based plastic deformation mechanisms. Similarly to that reported in a recent paper (Li J and Ngan AHW, Scr Mater 62:488–491 (2010)), discrete deformation processes occur during nanoindentation creep tests which again seem to arise from the break-off of dislocation avalanches. That interpretation is supported from systematic studies of the effect of variations of the loading rate and of the applied load on the number and the height of bursts. © 2015 Society of Chemical Industry

On dislocation pileups and stress-gradient dependent plastic flow

In strain-gradient plasticity, the length scale controlling size effect has been attributed to so-called geometrically necessary dislocations. This size dependency in plasticity can also be attributed to dislocation pileups in source-obstacle configurations. This has led to the development of stress-gradient plasticity models in the presence of stress gradients. In this work, we re-examine this pileup problem by investigating the double pileup of dislocations emitted from two sources in an inhomogeneous state of stress using both discrete dislocation dynamics and a continuum method. We developed a generalized solution for dislocation distribution with higher-order stress gradients, based on a continuum method using the Hilbert transform. We qualitatively verified the analytical solution for the spatial distribution of dislocations using the discrete dislocation dynamic. Based on these results, we developed a dislocation-based stress-gradient plasticity model, leading to an explicit expression for flow stress. Findings show that this expression depends on obstacle spacing, as in the Hall–Petch effect, as well as higher-order stress gradients. Finally, we compared the model with recently developed models and experimental results in the literature to assess the utility of this method.

Bulk texture evolution of nanolamellar Zr–Nb composites processed via accumulative roll bonding

It was recently demonstrated that bulk two-phase 50/50 Zr–Nb nanolayered composites with 90nm individual layers can be fabricated from an initial coarse-layered composite with 1mm layers via the severe plastic deformation process of accumulative roll bonding. During the deformation, the Zr phase retained its hcp crystal structure and the Zr–Nb interface remained sharp. Here we use a combination of neutron diffraction and dislocation-based polycrystal plasticity constitutive modeling to assess the evolution of texture and deformation mechanisms over a four order-of-magnitude range in layer thickness. The phase textures in the nanocomposite strongly deviate from that of Zr or Nb rolled in monolithic form, becoming highly peaked and intense. The model suggests that texture development in the Nb phase is associated with multiple slip and contributions from both {112}〈110〉 slip and {110}〈110〉 slip. In the Zr phase the model suggests that the texture develops due to a predominance of prismatic 〈a〉 and basal 〈a〉 slip.

Mechanical strain mediated carrier scattering and its role in charge and thermal transport in freestanding nanocrystalline aluminum thin films

In bulk metals, mechanical strain is known not to influence electrical and thermal transport. However, fundamentally different deformation mechanisms and strain localization at the grain boundaries may influence electron or phonon scattering in nanocrystalline materials. To investigate this hypothesis, the authors developed an experimental approach, where the authors performed thermal and electrical conductivity measurements on 100 nm thick freestanding nanocrystalline aluminum films with average grain size of 50 nm in situ inside a transmission electron microscope (TEM). The authors present experimental evidence of decrease in thermal conductivity and increase in electrical resistivity as a function of uniaxial tensile strain. In-situ TEM observations suggest that grain rotation induced by grain boundary diffusion, and not dislocation-based plasticity, is the dominant deformation mechanism in these thin films. The authors propose that diffusion causes rise in oxygen concentration resulting in increased defects at grain boundaries. Presence of oxygen only at the grain boundaries is confirmed by energy dispersive spectroscopy. Increased defect concentration by mechanical strain at grain boundary causes the change in thermal and charge transport.

Microstructural Stability and Hot Deformation of γ–γ′–δ Ni-Base Superalloys

Nickel-base superalloys exhibit excellent high-temperature mechanical and physical properties and remain the first choice for structural components in advanced gas turbine engines for the aerospace propulsion and power generation applications. In response to the increasing demand for more efficient solutions and tighter requirements linked to gas turbine technologies, the properties of nickel-base superalloys can be improved by modification of their thermo-mechanical and/or compositional attributes. Recent investigations have revealed the potential use of ternary eutectic γ–γ′–δ Ni-base superalloys in advanced gas turbines due to high temperature mechanical properties that are comparable to state-of-the-art polycrystalline Ni-base superalloys. With properties largely dependent on microstructural strengthening mechanisms, both the composition and thermo-mechanical processing parameters of this novel class of alloys need to be optimized concurrently. The hot deformation characteristics of four γ–γ′–δ Ni-base superalloys with varying levels of Nb were evaluated at temperatures and strain rates between 1353 K and 1433 K (1080 °C and 1160 °C) and 0.01 to 0.001/s, respectively. Evidence of dislocation-based plasticity was observed following deformation at low temperatures and high strain rates, while high temperatures and low strain rates promoted superplasticity in these alloys. The extent of the microstructural changes and the magnitude of the cavitation damage which occurred during deformation was found to vary as a function of the alloy composition.

Universal mechanisms of Al metallization ageing in power MOSFET devices

Power MOSFET devices are extensively used in the automotive industry, but their modes of ageing are still poorly understood. Here we focus on the physical degradation mechanisms that occur in the upper Al-based metallization layer (source). This layer undergoes thermo-mechanical structural modifications due to the combination of electrical pulses and differences between the various coefficients of thermal expansion. Using electronic and ionic microscopy, we show that ageing can be divided in 2 phases where dislocation-based plasticity and then grain boundary diffusion become predominant. As a result, grain boundary grooving and surface roughening follows a partial division of the later in disconnected Al grains. Such a degradation of the metallization has been widely observed in various devices. It may lead to the observed augmentation of resistivity and also to the focusing of the various current paths, promoting hot spots and subsequent failure.