Dislocation Mean Free Path Research Articles

Dislocation density based modeling of three-stage work hardening behaviour of type 316LN SS with varying nitrogen content and its finite element implementation for different notch radii

Dislocation density based modified Kocks-Mecking approach has been employed to understand the influence of nitrogen on kinetics of dislocation storage and annihilation processes during tensile deformation of type 316LN stainless steel at 300 K. As compared to original Kocks-Mecking approach, the modified version based on the evolution of forest dislocation density and mean free path of dislocations provides better description of three-stage hardening behaviour of the steel at all the nitrogen content. The effect of increase in nitrogen on work hardening behaviour is clearly reflected in systematic increase in flow stress, mobile and forest dislocation densities and decrease in mean free path at a given plastic strain. The predicted decrease in mean free path with increasing nitrogen has not only influenced the enhancement of dislocation-dislocation interactions leading to higher storage of dislocation but also provides a large driving force for higher dynamic recovery in the steel. The material model is implemented into finite element code via user-defined material subroutine using implicit algorithm to study the influence of notch radius on tensile properties of type 316LN stainless steel for different nitrogen content. Detailed analysis showed that notch-strengthening effect increases with increase in nitrogen and decrease in notch radius in the steel.

Dislocation dynamics during cyclic loading in copper single crystal

Crystalline plasticity can take place through numerous, small, uncorrelated dislocation motions (mild plasticity) or through collaborative events: dislocation avalanches (wild plasticity). Here, we study the correlation between dislocation patterning under cyclic loading and the nature of collective dislocation dynamics. The dislocation motion of a [110] oriented pure copper single crystal was dynamically followed using Acoustic Emission (AE) for different imposed stress amplitudes. The dislocation structure between each cyclic stress step was investigated using Electron BackScattered Diffraction (EBSD) and Rotational-Electron Channeling Contrast Imaging (R-ECCI) in a Scanning Electron Microscope (SEM). At low imposed stress, when the structure consists of dislocation cells, few dislocation avalanches are observed, while for a wall structure, at higher imposed stress, the contribution of avalanches is increased during the first cycles. For a given stress amplitude, the evolution of mild plasticity is synchronous with the plastic strain-rate, and rapidly vanishes after few cycles due to work hardening. The mean free path of the dislocations in this mild plasticity regime corresponds to the characteristic size of the dislocation structure (cell size, distance between walls). From one stress level to another, brutal rearrangements of the dislocation structure occur within a few numbers of cycles. Those rearrangements take place, at least partly, through dislocation avalanches. Upon reloading at a larger stress amplitude, dislocation avalanches can travel over distances much larger than the former dislocation mean free path. As the dislocation avalanches spread within the crystal, the memory of the previous dislocation structure is lost and a new dislocation structure emerges.

Anomalous work hardening behavior of Fe40Mn40Cr10Co10 high entropy alloy single crystals deformed by twinning and slip

The orientation dependence of tensile deformation in Fe40Mn40Co10Cr10 high entropy alloy (HEA) was investigated in [111], [001] and [123] oriented single crystals. Transmission electron microscopy investigations revealed three major mechanisms controlling the deformation stages, depending on the orientation: (i) deformation twinning, (ii) planar slip and (iii) dislocation wall/network formation. While twinning and planar slip were strongly orientation dependent, dislocation walls were observed in all orientations. Twinning was the dominant deformation mode in [111] crystals, while only multi-slip was observed in [001]. Both twins and planar slip were activated in [123] crystals. [111] crystals exhibited the highest strain hardening coefficients and ultimate tensile strength due to the strong twin-twin and twin-slip interactions where twin boundaries reduce the mean free path of dislocations, leading to dynamic Hall–Petch hardening. The decent ductility levels (∼45%) were attained in [111] due to nanoscale internal twins and tertiary twin system forming at the later stages of deformation and suppressing necking. In contrast, no twins or stacking faults were observed in [001] crystals, which is consistent with the Copley–Kear effect. [123] crystals had outstanding tensile ductility (∼65%), due to the activation of planar slip and twinning. Overall, in this off-stoichiometric HEA, we have determined the stacking faculty energy and critical resolved shear stresses for both twinning and slip, and demonstrated the formation of high dislocation density walls and wavy slip in [001], while the hardening stages of [123] and [111] are primarily governed by planar slip and twinning, which can be rationalized by the Copley–Kear effect.

Explanation of the size effect on the flow stress of thin sheet based on the size of dislocation cell

By constructing the relation between the dislocation mean free path (L) and mean size of dislocation cell (dDC), the effects of the grain size (d) on the evolution of the dDC, dislocation mean cell size in surface (dDCS) and interior (dDCI) parts of a sample are investigated in the present work. The values of 1/dDCI and 1/dDCS increase linearly with increasing 1/d. When d approaches the sheet thickness (t), the value of dDC approaches dDCS. With d decreases, 1/dDC increases rapidly when t/d is less than the critical value of ∼4.

Effect of Annealing on the Microstructure, Texture and Tensile Deformation Properties of Cu–3 wt%Ag–0.5 wt%Zr Thin Sheets Rolled at Room and Cryogenic Temperature

The Cu–3 wt%Ag–0.5 wt%Zr are rolled with the same reduction process at room (RT) and cryogenic (CT) temperature, respectively. The electron backscatter diffraction and transmission electron microscope are used to analyze and compare the evolutions of material microstructure and texture. The results show that the stability of as-rolled CT sheets is different from that of the RT samples, which can be verified by the lower temperature for the occurrence of recrystallization and Ag-base particles precipitation. Besides the Brass, Copper and S textures which are exhibited in the two kinds of as-rolled sheets, there are also Q and P texture components in the as-rolled CT sheets. The constitutive equation basing on evolution of dislocation mean free path (L) and dislocation cell size (dDC) with plastic strain indicates that the initial values of L, dDC and mobile dislocation density (ρm) are associated with annealing condition closely. Furthermore, the strain ranges of the stable and instable plastic deformation are related to the degree of recovery and recrystallization.

Tensile deformation and fracture behaviours of cold rolled Cu-3wt.%Ag-0.5wt.%Zr thin sheets with different annealed microstructures

Analyses of the microstructures, plastic deformation behaviours and fracture behaviours with respect to annealing conditions are presented for Cu-3wt.%Ag-0.5wt.%Zr sheets rolled to achieve a 90% overall thickness reduction at room temperature. The results show that the starting temperatures of recovery and recrystallization are approximately 200 °C and 400 °C, respectively. The microstructural evolution manifests as the lamellar boundaries disappearing and sub-grains (SGs) coarsening during recovery. The average size of the dislocation cell (dDC) is clearly elevated during recrystallization. By constructing relationships among mobile dislocation density (ρm), dislocation mean free path (L) and dDC, a constitutive equation is built for describing plastic deformation behaviour. The parameters of the simplified Kubin-Estrin (KE) and new model describing mobile dislocation multiplication, mutual annihilation, dynamic recovery, L and dDC are related to the annealing conditions. A microstructure with a larger dDC value possesses a higher strain-hardening capacity, which leads to a large unstable plastic deformation stage and a large shear dimple region on the fracture surface.

Grain boundary strengthening of FCC polycrystals

Abstract

Implementation of Internal-State-Variable Based Model into Finite Element Code and its Applicability to Study the Tensile Behaviour of Type 316LN SS With Different Notch Radii

An attempt has been made towards the implementation of two-internal-variable model based on the evolution of forest dislocation density and mean free path with the plastic strain into finite element code via user-defined material subroutine using implicit Euler backward algorithm with radial-return scheme. The rate independent two-internal-variable model considers isotropic hardening and the parameters associated with the model are optimised by fitting uniaxial true stress-true plastic strain data. Applicability of the implemented scheme has been examined by simulating the tensile behaviour of type 316LN austenitic stainless steel with different U-notch radii as 1.25, 2.5 and 5 mm at 300 K. Good agreement between the predicted and experimental data has been observed. Detailed analysis showed notch-strengthening effect increases with decrease in notch radius at 300 K.

Microstructural Evolution and Strain-Hardening in TWIP Ti Alloys

A multiscale dislocation-based model was built to describe, for the first time, the microstructural evolution and strain-hardening of {332} TWIP (twinning-induced plasticity) Ti alloys. This model not only incorporates the reduced dislocation mean free path by emerging twin obstacles, but also quantifies the internal stress fields present at β-matrix/twininterfaces. The model was validated with the novel Ti-11Mo-5Sn-5Nb alloy (wt.%), as well as an extensive series of alloys undergoing {332} twinning at various deformation conditions. The quantitative model revealed that solid solution hardening is main contributorto the yield stress, where multicomponent alloys or alloys containing eutectoid β-stabilisers exhibited higher yield strength. The evolution of twinning volume fraction, intertwin spacing, dislocation density and flow stress were successfully described. Particular attentionwas devoted to investigate the effect of strain rate on the twinning kinetics and dislocation annihilation. The modelling results clarified the role of each strengthening mechanism and established the influence of phase stability on twinning enhanced strain-hardening. The origin of strain-hardening is owing to the formation of twin obstacles in early stages, whereas the internal stress fields provide a long-lasting strengthening effect throughout the plastic deformation. A tool for alloy design by controlling TWIP is presented.

Anomalous recovery of work hardening rate in Cu-Mn alloys with high stacking fault energies under uniaxial compression

The work hardening behavior and deformation microstructures of pure Cu and Cu-Mn alloys were systemically investigated under uniaxial compression. An anomalous phenomenon of work hardening rate recovery was observed in the present Cu-Mn alloys with high stacking fault energies (SFEs). Such a phenomenon is dramatically distinctive from those observed in previous studies on high-SFE metals, whose work hardening rate monotonically decreases with the increase of strain. Microstructural examinations demonstrate that the occurrence of work hardening rate recovery should be attributed to the transformation from wavy slip to planar slip by increasing Mn content, since these planar slip dislocation structures effectively inhibit dynamic recovery and reduce the dislocation mean free path. Therefore, the possible influencing parameters such as SFE, friction stress, and short-range ordering (SRO) are analyzed. It is suggested that the existence of SRO in Cu-Mn alloys is the main reason causing planar slip. Furthermore, the effect of SRO on the multi-stage work hardening behavior is discussed based on the analyses of dislocation density evolution during deformation. This study enriches a fundamental knowledge of how to improve the work hardening capacity of alloys with high SFEs.

On the onset of necking instability in tempered martensitic 9% Cr steels

Considère criterion accounting for necking instability has been examined in terms of dislocation density based approach for tempered martensitic 9% Cr steels. The critical dislocation density as well as the critical strain at which instability sets-in has been predicted from the dislocation dynamics approach. The parameters associated with the approach such as mean free path of dislocations and dynamic recovery have been the key for developing microstructural based necking instability criterion. The interrelationship between true uniform plastic strain and dynamic recovery parameter has been established from the present formulation for tempered martensitic 9% Cr steels. The increase in dynamic recovery with decreasing mean free path and increasing temperature strongly influences the work hardening ability of tempered martensitic 9% Cr steels.

Origin of strengthening-softening trade-off in gradient nanostructured body-centred cubic alloys

The gradient nanograined metals have the unexpected combination of high strength and high ductility. However, the detailed dynamic and continuous process of deformation mechanism at nanoscale need to be further understood. Herein, we report the deformation behavior and microstructure evolution of gradient-nanograined body-centred cubic alloys using molecular dynamics simulations. An analytical model is also established to predict the strength for nanograined alloys. The results show that the alloying can soften the gradient-grained and random-nanograined Fe-based alloys. With the increasing Ni concentration, dislocation density decreases, due to the fact that the Ni solute increases stacking fault energy and the deformation twinning acts as a strong obstacle to suppress dislocation motion. The gradient distributions of strain and stress in gradient-nanograined metals occur due to the plastic incompatibilities, resulting in the inhomogeneous deformation of gradient-nanograined Fe and alloys. In addition, the inverse gradient-nanograined distribution, including large grain in the top surface and small grain in the central region, generates in random-nanograined alloys. It is owing to the grain growth in surface layer, resulting in the gradient strain and stress. Interestingly, the nucleated dislocation network and the deformation twinning considered as a reduction of dislocation mean free path decline rapidly with the increasing grain size for gradient-nanograined structure. The theoretical modeling determines the total strength derived from the individual contributions of different strengthening mechanisms, revealing that the grain boundaries dominate the yield strength and the back stress contributes the most to the straining hardening in nanograined materials.

Microstructural effects on strain rate and dwell sensitivity in dual-phase titanium alloys

In this study, stress relaxation tests are performed to determine and compare the strain rate sensitivity of different α−β titanium alloy microstructures using discrete dislocation plasticity (DDP) and crystal plasticity finite element (CPFE) simulations. The anisotropic α and β phase properties of alloy Ti-6242 are explicitly included in both the thermally-activated DDP and CPFE models together with direct dislocation penetration across material-interfaces in the DDP model. Equiaxed pure α, colony, Widmanstatten and basketweave microstructures are simulated together with an analysis of the effect of α grain size and dislocation penetration on rate sensitivity. It is demonstrated that alloy morphology and texture significantly influence microstructural material rate sensitivity in agreement with experimental evidence in the literature, whereas dislocation penetration is found not to be as significant as previously considered for small deformations. The mechanistic cause of these effects is argued to be changes in dislocation mean free path and the total propensity for plastic slip in the specimen. Comparing DDP results with corresponding CPFE simulations, it is shown that discrete aspects of slip and hardening mechanisms have to be accounted for to capture experimentally observed rate sensitivity. Finally, the dwell sensitivity in a polycrystalline dual-phase titanium alloy specimen is shown to be strongly dependent on its microstructure.

On the first direct observation of de-twinning in a twinning-induced plasticity steel

Electron back-scattering diffraction was used to track the microstructure evolution of a fully annealed Fe-24Mn-3Al-2Si-1Ni-0.06C TWinning Induced Plasticity (TWIP) steel during interrupted reverse (tension-compression) loading. Direct observation of the same selected area revealed that all deformation twins formed during forward tension loading (0.128 true strain) were removed upon subsequent reverse compression loading (0.031 true strain). Consequently, the present study provides the first unambiguous experimental evidence of de-twinning during the reverse loading of a polycrystalline TWIP steel. The reverse loading behaviour was simulated by a dislocation-based hardening model embedded in the Visco-Plastic Self-Consistent (VPSC) polycrystal framework taking into account the accumulation and annihilation of dislocations and back-stress effects. The model has been extended to account for the processes of twinning and de-twinning, as well as the twin barrier effect under load reversal. A new formulation based on the changes in the dislocation mean free path is proposed to track twin lamellae generation/annihilation throughout deformation along with its associated effect on hardening.

A new model for the description of creep behaviour of aluminium-based composites reinforced with nanosized particles

A basic model developed to describe the creep response of fcc metals has been used to obtain a new constitutive equation valid for alloys and composites reinforced with a dispersion of nanosized particles. The new model gives an excellent description of the minimum strain rate dependence of applied stress and temperature, and gives reason for the reduced creep rate observed in these composites when compared with conventional alloys. The reason for the different behaviour is that the dislocation mean free path becomes equivalent to the distance between nanosized particles. The volume fraction and size of the nanosized particulate thus assumes a key-role in determining the creep response of these materials. In addition, the strengthening effect due to the interaction between particles and dislocation has been described by introducing a back stress, which is in general proportional to the Orowan stress and has the nature of a true threshold stress.

A unified constitutive model based on dislocation density for an Al-Zn-Mg-Cu alloy at time-variant hot deformation conditions

In order to study the flow behaviors of an Al-Zn-Mg-Cu alloy at elevated temperatures, uniaxial tensile tests were carried out in wide deformation temperature and strain rate ranges. The flow stress rapidly increases to a peak value and then slightly decreases with the increased strain, and the dynamic recovery (DRV) is the primary softening mechanism. A unified constitutive model based on dislocation density was developed. An iterative procedure was implemented into the developed model to describe the flow behaviors at time-variant deformation conditions (e.g. the strain rate is changed during hot deformation). The predicted flow stresses were in accord with the experimental results, suggesting that the flow behaviors of the studied Al alloy at elevated temperatures can be well reproduced by the developed model. Meanwhile, the variations of the product of the instantaneous work hardening (WH) rate and stress caused by dislocation evolution, the dislocation density changing rate, as well as the dislocation mean free path, were given to analyze the WH and DRV mechanisms of Al-Zn-Mg-Cu alloy.

Effect of strain path on the evolution of microstructure, texture and tensile properties of WE43 alloy

Hot rolling of extruded and solutionized WE43 alloy was carried out at 400°C through different strain paths such as unidirectional rolling (UDR) and multistep cross rolling (MSCR). The effect of strain path on the evolution of microstructure and texture was investigated. The grain size was ∼ 7µm and 18µm after hot rolling of UDR and MSCR samples, respectively. A strong basal texture was observed during rolling which is independent of the strain path of the samples and the recrystallization mechanism was identified to be continuous dynamic recovery and recrystallization type. Further, the texture of the deformed and recrystallized grains was observed to be same. Hence, the texture was simulated successfully using visco-plastic self-consistent (VPSC) simulation. The VPSC simulation of UDR sample showed the dominant activity of basal and prismatic slip system up to a true strain of ∼ 0.5 and after that pyramidal < c + a > activity dominants, whereas MSCR sample showed the combined activity of basal and pyramidal < c + a > up to a true strain of ∼ 0.5 and later on basal activity dominants on further deformation. The room temperature tensile testing showed that the yield strength of MSCR sample was greater than UDR sample except along RD of UDR sample and the tensile strength was more for MSCR compared to UDR sample which suggests that higher volume fraction of metastable precipitates in MSCR than UDR sample during high temperature rolling. The higher volume fraction of metastable precipitates was attributed to lower dislocation activity on prismatic planes of MSCR compared to UDR sample during hot rolling. The current VPSC simulation showed that the prismatic slip activity was four times higher in UDR than MSCR sample. A decrease in mean free path of dislocations by the presence of metastable precipitates led to higher tensile strength of MSCR compared to UDR sample. The mean free path of dislocations increased from RD to TD and hence, results in a decrease in tensile strength from RD to TD of both the samples.

Modeling and Crystal Plasticity Analysis of Multiple Slip Deformation in the Microstructure of Particle Dispersed Alloy and Its Macroscopic Strain Hardening Characteristics

Multiple slip deformation in dispersion hardening steels are numerically analyzed by a crystal plasticity finite element technique and macroscopic strain hardening characteristics are discussed. The critical resolved shear stress (CRSS) for slip system is given by the extended expression of the Bailey-Hirsch type model which include contributions from lattice friction, Taylor hardening and also the Orowan stress to give a size effect from microstructure. Strain hardening of slip systems are estimated by the density of statistically stored dislocations (SSDs) through the Taylor term. Increment of the SSD density is evaluated by slip strain and the dislocation mean free path. Models for the CRSS and dislocation mean free path for the primary and secondary slip systems are discussed. Analysis results show that macroscopic yield stress agrees well with experimental one but strain hardening ratio is overestimated when the CRSS and dislocation mean free paths for secondary systems are given the same characteristics of scale dependency to that for the primary one. Some new models for the CRSS and mean free path for secondary systems are studied and analysis results with these models show to agree well not only for the yield stress but also for the strain hardening behavior.

Effects of strain rate on mechanical properties and deformation behavior of an austenitic Fe-25Mn-3Al-3Si TWIP-TRIP steel

The effects of quasi-static and low-dynamic strain rate (ε̇ = 10−4 /s to ε̇ = 102 /s) on tensile properties and deformation mechanisms were studied in a Fe-25Mn-3Al-3Si (wt%) twinning and transformation-induced plasticity [TWIP-TRIP] steel. The fully austenitic microstructure deforms primarily by dislocation glide but due to the room temperature stacking fault energy [SFE] of 21 ± 3mJ/m2 for this alloy, secondary deformation mechanisms such as mechanical twinning (TWIP) and epsilon martensite formation (TRIP) also play an important role in the deformation behavior. The mechanical twins and epsilon-martensite platelets act as planar obstacles to subsequent dislocation motion on non-coplanar glide planes and reduce the dislocation mean free path. A high-speed thermal camera was used to measure the increase in specimen temperature as a function of strain, which enabled the use of a thermodynamic model to predict the increase in SFE. The influence of strain rate and strain on microstructural parameters such as the thickness and spacing of mechanical twins and epsilon-martensite laths was quantified using dark field transmission electron microscopy, electron channeling contrast imaging, and electron backscattered diffraction. The effect of sheet thickness on mechanical properties was also investigated. Increasing the tensile specimen thickness increased the product of ultimate tensile strength and total elongation, but had no significant effect on uniform elongation or yield strength. The yield strength exhibited a significant increase with increasing strain rate, indicating that dislocation glide becomes more difficult with increasing strain rate due to thermally-activated short-range barriers. A modest increase in ultimate tensile strength and minimal decrease in uniform elongation were noted at higher strain rates, suggesting adiabatic heating, slight changes in strain-hardening rate and observed strain localizations as root causes, rather than a significant change in the underlying TWIP-TRIP mechanisms at low values of strain.

Impact of coherent and incoherent twin boundaries on the microhardness of annealed nanocrystalline Ni–W alloys

The microstructural evolution of nanocrystalline Ni–W alloys with annealing temperature and more specifically grain boundary (GB) character is investigated through several techniques and correlated with the hardening behaviour. It is shown that two distinct regions can be identified in relation to the annealing temperature and the microstructural evolution. At temperatures below 550 °C (Regime I), a small increase in grain size is observed and is accompanied by a significant hardening and an increase in the fraction of Σ3 incoherent twin boundaries. At temperatures above 550 °C (Regime II), the thermal stability is overcome and important grain growth occurs with a decrease in both the volumic fraction of GBs and the microhardness. It is suggested that the microhardness evolution during heat treatment is influenced by two opposing processes: an increase in the fraction of incoherent twin boundaries (hardening effect) and grain growth (softening effect). Both aspects are directly associated with the mean free path of mobile dislocations.