Mean Slip Distance Research Articles

Calculating the grain size effect during strain hardening through a probabilistic analysis of the mean slip distance in polycrystals

Grain refinement is an important mechanism to produce stronger alloys. Strain hardening is an essential phenomenon in metal forming processes. The interaction between grain size and strain hardening is evident: a decrease in grain size (dg)causes an increase in ultimate tensile strength but a decrease in uniform elongation. The Kocks-Mecking (KM) model for strain hardening is based on the relationship between shear strain and the path length for dislocation slip. It provides good general estimates for stress-strain curves, and empirical modifications have been made to include dg. Here, the empirical approach is substituted by theoretical probability calculations, accounting for the fact that the grain size imposes a bound on the mean slip distance, while strain compatibility defines a relationship between grain boundary-dislocation interaction and bulk storage and annihilation. The resulting differential only uses the two parameters inherent to KM. Fitting to published tensile curves for Al, Cu, and Ni produces excellent results. The fitting parameters allow to predict the tensile strength as a function of dgto good approximation, for dg>1μm. Below this limit, fundamental changes in dislocation statistics impose the activation of grain boundary dislocation sources and may induce dislocation density gradients, which seem to determine the flow stress in the sub-μm range.

Grain-size effect on dislocation source-limited hardening and ductilization in bulk pure Ni

Dislocation source-limited hardening and ductilization is an effective strategy to obtain superior strength-ductility synergy in some engineering structural metals. Recent works demonstrated that the synergy could be enhanced by grain-size reduction. However, the mechanism of grain-size dependence is still a mystery. In this work, bulk pure Ni produced by electrodeposition and subsequent annealing, with grain sizes ranging from ∼20 nm to ∼20 µm, were methodically investigated to unravel the mechanism of the grain-size effect on dislocation source-limited hardening and ductilization. The high-density nano-twinning in the as-electrodeposited nanograined specimens exhibited better thermodynamic stability than the peers with random high-angle grain boundaries, leading to fine recrystallized grains with low-density dislocations. The low dislocation density enabled extra hardening beyond grain boundary strengthening via yield-point behavior with grain sizes ranging from ∼110 nm to ∼10 µm and extra ductilization over ∼500 nm. This work demonstrated that the prerequisite for dislocation source-limited hardening was that the dislocation density of the specimen should be lower than the size-dependent critical value of ((1.1 × 107/d) m–2, d is the grain size in unit of the meter) where a transition from forest-dominated hardening to dislocation source-limited hardening could occur. On the other hand, dislocation source-limited ductilization only worked when the grain size was comparable to/larger than the theoretical dislocation mean slip distance. Dislocation source-limited ductilization resulted from more room in grains for accumulation of dislocations and deformation nano-stacking faults enabling the higher work hardening rate. This work offered an altogether new avenue to obtain stronger and more ductile metallic materials through utilizing grain-size dependent dislocation source-limited hardening and ductilization.

High strain rate deformation behavior of 2195 Al-Li alloy: Constitutive behavior and grain fragmentation

The high-speed forming process is a promising method for the preparation of high-performance Al-Li alloy components. However, the high-strain rate deformation behavior of the material is complex and difficult to accurately predict, which significantly restricts its development. In this paper, using the split Hopkinson pressure bar apparatus, the constitutive behavior and microstructure evolution of as-annealed and solution treated 2195 Al-Li alloy during high strain rate deformation was studied. As the strain rate increases, the flow stress first decreases and then increases for both two-state materials, showing a local strain rate softening behavior. Based on the Johnson-Cook model, a modified constitutive model is proposed, in which a correction term for the C value related to strain rate and strain is introduced. The modified Johnson-Cook model can accurately capture the abnormal strain rate sensitivity behavior observed in the experiment. In addition, it was found that the heat treatment state has a significant effect on the microstructural evolution behavior of 2195 Al-Li alloy. The as-annealed material shows the deformation behavior based on the evolution of dislocation cells. In addition to dislocation cells, there is also deformation behavior based on the evolution of submicron lath deformation bands for solution treated material. Dislocation cross slip is suppressed in the solution treated material, and its slip mode tends to be the plane slip. Through the analysis of dislocation density, mean slip distance of dislocation slip, and the interaction between solid atoms and dislocation, the mechanism of the abnormal deformation behavior of the solution treated material is revealed.

Advanced method for structure-strength-ductility assessment of dispersion-strengthened FCC metals using activation work, mean slip distance and constitutive relation analyses: Decoding the Haasen plot

The role of cross-slip activation on controlling dislocation mechanisms and deformation debris creation in a dispersion-strengthened matrix (DSM) face-centred cubic metal, GlidCop®, has been elucidated using experimental measurement of the strain rate sensitivity, S, the mean slip distance, λ, and constitutive relation analyses (CRA) from 78 to 473 K. If the stress for cross-slip activation is larger than that of DSM yield stress, geometrically necessary prismatic loops (GNPL) are generated, but the rate controlling kinetics is that of vacancy-drag for cube-textured copper wire-specimens. With increasing temperature, percolation continues to occur by Orowan looping. However, upon yielding, GNPL formation is replaced by various types of dipole loop creation due to dislocation intersections from multiple slip. Loops that convert to stacking fault tetrahedra are measurable, but opposite sign dipoles are dynamically annihilated by pipe diffusion reducing debris retention. The rate controlling mechanisms are identified in the temperature range in which S is constant and the activation energy to overcome the obstacle becomes identical to the measurable activation work. This study shows that cross-slip activation stress determined by CRA, when superposed on the yield stress versus temperature plot of DSM alloys, can identify the mechanism-change temperatures. Subsequent S versus temperature profiles, determined from a new method of Haasen plot analysis of up- and down-strain-rate change tests, can delineate the prime rate-controlling mechanisms, characterize the stored debris and determine whether non-shearing or shearing of particles had occurred. Hence, an advanced method to characterize plastic behavior of DSM alloys has been developed.

Forensic analyses of microstructure evolution of stage II & III: New assimilated model for work-hardening in FCC metals

From the beginning of crystal plasticity studies, the cause for the small percentage of expended work retained as stored work has been a quandary. From forensic analyses of plastic deformation studies, it was deduced that coplanar annihilation of dislocations occur since slip takes place in small slip-patch areas of mean slip distance squared. A simple model predicts that the athermal annihilation factor A between expended and stored energy is about 20 comparable to the observed 5% for stored work. The derived A ranged from 19 at 20 K to 25 at 300 K for copper. Using the functional constitutive relation which can replicate the stress-strain diagram, analyses invoking the imposed shear strain to assess the height between coplanar slip planes indicate that structure evolution due to monopole dislocations result in the principle of similitude. However, the break-down of this Stage II structure occurs when cross-slip and the accompanying double cross-slip is incurred resulting in increasing height between slip planes. The consequences of these bypass mechanisms are the change of the random array of dislocations to that of clustered patterns with the increase in mean slip distance leading to cell structure formation. This evolution can be examined using the shear flow stress versus the inverse mean slip distance plot. Hence the bases for decoding work-hardening of face-centred cubic metals using constitutive relations have become possible.

Decoding stress-strain diagrams to identify the evolution of crystal defects and their obstacle strengths using constitutive relations analyses

Recent advances in microstructural characterization from the mesoscopic and microscopic scales to the nanometric and atomic scale have revealed precise details regarding the formation of nanoparticles responsible for increased strength of alloys. The size and distribution of such features have been modelled ad hoc with limited success to replicate the work-hardening behaviour. The missing issue is that of including also the evolution of the crystal defects that arise as a result of plastic flow, such as the volume fraction of nano-voids and rotated lattice structures as observed by small angle X-ray scattering (SAXS). The constitutive relation analyses (CRA) approach assumes that all shape change is due to dislocation motion, and through use of the Taylor slip model, a functional relation has been formulated to replicate the measured curve in terms of shear stress and shear strain. The CRA parameters can be correlated to the evolving deformation products by quantitatively deriving a relation for the obstacle strength factor, α, using the strain dependence of the mean slip distance, λ. Hence, the evolution of different crystal defects as straining proceeds can be assessed.

Constitutive Relations Analyses of Plastic Flow in Dual-Phase Steels to Elucidate Structure–Strength–Ductility Correlations

The structure–strength characterization is typically performed by correlating the structure with x-ray, electron, or atomic imaging devices to the bulk mechanical tensile parameters of yield stress and the plastic yielding response. The problem is that structure parameters embedded in the stress–strain data cannot be revealed without an analyzable constitutive relation. New functional slip-based constitutive formulation with precise digital fitting parameters can replicate the measured data with at least two loci. Thus, this study examines the possibility of identifying the mechanical response as a result of the various microstructure components. The key parameter, the mean slip distance, can be calibrated from the initial work-hardening slope at 0.2% strain from which all the fit parameters can be determined. In this process, a newly derived friction stress is defined to separate the yield phenomenon from the plastic strains beyond yield-point elongation. This methodology has been applied to dual-phase steel specimens that resulted in excellent predictive correlations with prior structure-strength characterization. Hence, the structure–strength–ductility changes resulting from processing conditions can be more precisely surmised from mechanical testing. Thus, a method to delineate the nanostructure evolution with deformation using mesoscopic mechanical parameters has been introduced.

Flow stress and work-hardening behaviour of Al–Mg binary alloys

Analysis of the flow stress and work hardening behaviour has been carried out in series of Al–Mg solid solutions between 4K and 298K. The results reveal that the yield stress decreases linearly with the temperature and increases approximately linearly with the Mg content in the solution. The thermomechanical and Portevin–Le Chatelier instabilities dominate the flow stress behaviour of alloys at 4K and 298K. Dynamics of these instabilities increases with the solute content. It is argued that neither PLC nor adiabatic instabilities contribute to the premature failure of the samples. The work-hardening can be reproduced by the Voce type scaling law in a broad range of temperatures. The mean slip distance obtained from the macroscopic model of work hardening is correlated to the scale of the referenced microstructure; Λmin is interpreted as a transition from cell-like to micro shear band microstructure. The failure is discussed in terms of a critical point in a transition form unsaturated to saturated with defects dislocation substructure.

Intermittent plastic flow of single crystals: central problems in plasticity: a review

The relationships between microstructure and plastic flow properties of copper single crystals deformed at low temperatures are reviewed based on the analysis of experimental results of mechanical, structural and electrical resistivity characterisation. Electrical resistivity measurements suggest that the flow stress correlates with the average density of defects accumulated in the microstructure. The characteristic microstructural length scale that determines the flow stress corresponds closely to the size of dislocation free channels and/or cells produced during plastic flow. The correspondence between micro- and macroscopic approaches to the plastic flow has been analysed based on the behaviour of dislocation mean free path and mean slip distance and their relationship to the microstructure. Production and annihilation of nanoscale debris and point defects and their role in plastic flow and questions pertinent to the influence of microstructural instabilities on the flow stress, workhardening, storage and annihilation of lattice defects have been discussed.

A new analysis of yielding and work hardening in AA1100 and AA5754 at low temperatures

Microstructural evolution determined by mechanical testing is usually modelled from perceived mechanisms of work hardening during dislocation passage and storage in complex arrays. The predicted stress–strain behaviour is then compared with the measured one. Recently a new functional constitutive relation was derived by Saimoto and Van Houtte based on Taylor slip analysis that is optimally fitted to replicate the measured data. The curve fitting parameters arise from the incremental strain Δγ producing a mean slip distance λ and the retained dislocation density ρ assessed from the flow stress τ. A method has been derived to precisely determine λ from the measured data. Moreover, the yield stress determined from the optimum curve fitting is derived from strains beyond the yield point and, hence, has the capacity to separate the solid solution and grain size effects from that of the yield phenomenon. Typically two fit curves are required, the intersection of which defines τ3, γ3 and λ3, akin to the stage II to stage III transition in single crystals. A tabulation of these parameters permits reproduction of the mechanical curves. Furthermore, a plot of flow stress τ vs. 1/λ results in a description of work hardening evolution onto which the inverse cell size 1/dC can be superimposed. Using the results from standard materials testing practice the temperature dependence and evolution of the pertinent parameters show that point defect drag effects are prominent below 273K for AA1100 but not for AA5754.

Characterization of work-hardening evolution in hexagonal metals using mean slip distance normalized with inter-obstacle spacing

Abstract The quantitative determination of the mean slip distance is the basis for the new constitutive relation that encompass slip-based parameters which are determined by precise fitting the functional form to the measured work-hardening evolution. This replicating procedure appears to apply to cases where non-monotonic work-hardening is evident but in such cases more than two fit-loci are required. The extrapolation of such loci to define the matrix strength for the composite structure involving mechanical twins can predict the upper-limit volume fraction of twins present. Comparison with other means of microstructural determinations directly correlates the observed mechanistic changes with the mechanical response. Normalization of the mean slip distance with the inter-obstacle spacing is found to be independent of the strength of obstacle and the evolving texture. Hence its plot can delineate the critical strain locations and supplement this data with quantitative values with respect to volume fraction of twinning.

Constitutive relation based on Taylor slip analysis to replicate work-hardening evolution

A constitutive relation based on crystal plasticity was derived by equating the energy of dislocations required to generate the imposed incremental strain with that which was stored as determined from the flow stress. The dynamic annihilation of created dislocations was accounted for by using a factor to balance the equation. The specific case of Taylor’s parabolic relation was reproduced and microstructure-based parameters were explicitly formulated in the proportionality constant usually attributed as empirical in the Hollomon relation. The nearly precise replication of the stress–strain relation using at least two curve-fits for aluminum and its alloys validates the quantitative determination of the mean slip distance. The intersection of the two fits appears to be analogous to Stage II to III transition, which was confirmed by analysis of [1 1 1] and [1 0 0] single-crystal studies taken from the literature. The correlation of the flow stress with inverse mean slip distance and deformation cell size, together with the measured stored work, permitted an insight into this Stage II to III transition. The analysis suggests that dynamic-recovery effect in Stage III may be attributed to the change in mean slip distance pattern due to the evolution of cells.

Dynamic Evaluation of Strength-Structure Properties by the Determination of Activation Volume and Mean Slip Distance

Measurements of the activation volume and mean slip distance were used in the dynamic dislocation-defect analysis to reveal the dislocation-obstacle evolution with strain. Due to the large effect of point defect mobility above 250 K on the strain rate sensitivity, fine-grained Al specimens with the grain-boundaries sealed and unsealed as vacancy sinks were tested at 300 K as the reference behaviour. The activation distance diagrams revealed that the artificially aged products in AA6111 and naturally aged extruded AA6063 can be used to examine the effect of chopping-up of particles on the ductility of the samples. Thus a means to examine strength-structure-ductility of specific products have been devised.

Dynamic dislocation–defect analysis

The dynamic internal variables which control plastic flow can only be assessed by dynamic materials testing at any given instance. The testing method championned by our studies has been precision strain rate sensitivity (PSRS) whereby the change in flow stress due to a set change in strain rate is taken to be an operational measure of the activation volume and its product with the flow stress gives rise to the operational activation work. Also, from the work hardening slope, a modelled parameter proportional to the mean slip distance (λ) is simultaneously determined. The deviation from the linear Cottrell–Stokes relation as determined with the Haasen plot indicates the evolution of secondary defects other than monopole dislocations. Hence PSRS can assess the theoretical predictions of the activation distance (d) and work as a function of temperature, resulting in quantitative values that are in accord with dislocation theory at temperatures below that where point defects become mobile. A method to calibrate λ using Stage II slope θII shows that λ/ℓ, where ℓ is the mean forest dislocation spacing, is inversely proportional to θ, the work hardening coefficient. This analysis has led to a new plot of θII/θ versus b 2λ/ν where b is the Burgers vector and its slope is directly proportional to d. An example using an alumina-dispersed high conductivity copper shows that geometrically necessary punched out loops are continuously generated. The role of point defect mobility is dramatically illustrated by load drops in [001] aluminium crystals with the formation of slip clusters.

Characterization of Ageing Products in AA6111 Using Dynamic Dislocation-Defect Analysis

In dynamic dislocation-defect analysis, the thermodynamic deformation-mode signatures are examined as the ageing proceeds. In this method, the activation volume (ν) and the mean slip distance (λ) is simultaneously determined with the flow stress (τ) such that the inverse workhardening slope (1/θ) can be plotted versus b2λ/ν where b is the Burgers vector. The slope of this almost linear locus is directly proportional to the activation distance (d). Calibration with a model alumina-dispersed high conductivity copper reveals that punched-out loops are produced up to failure and is represented by a linear locus from 0.1 to 11 % strain. Artificial ageing of AA6111 at 180°C follows this pattern but the naturally-aged specimen manifest a distinctly different signature which shows a transition as the GP zone-type precipitates are sheared. Furthermore by selecting a suitable tensile-test temperature below 250K, the particle size and volume fraction can be determined if particle shearing does not take place. The optimum size and volume fraction necessary for sufficient strength and ductility can be assessed using this method.

Recovery of Tensile Properties of AA5182 after Cold Rolling

An experimental AA5182 sheet was cold rolled 80%, and tensile specimens removed with orientations 0, 45 and 90 degrees to the rolling direction. Room temperature monotonic tensile tests were performed on the specimens in different recovered states obtained by isothermal annealing at 230°C from 0.1 to 10h. The tests were instrumented to measure instantaneous plastic strain ratio, and unloaded just after incipient necking, but before failure if possible. With annealing the flow curves are characterized by lower strains to the onset of jerky flow, the reappearance of yield point elongation, decrease in work hardening, and increasing ductility. The recovery in substructure was described using a constitutive parameter proportional to the mean slip distance.

The Characterization of the Plastic Potential of Aluminum Alloys Using Internal Variables of Strain Rate Sensitivity, Mean Slip Distance and Mean Slip Velocity

The Characterization of the Plastic Potential of Aluminum Alloys Using Internal Variables of Strain Rate Sensitivity, Mean Slip Distance and Mean Slip Velocity

The Determination of Evolving Microstructure Using Constitutive Relationships

AbstractThe evolution of the constitutive parameter, the mean slip distance, λ, is monitored during tensile deformation of 3.2 μm grain size aluminum at 200 K. Transmission electron microscopy (TEM) confirms that the grain size, D, sets an upper limit to λ.

Measurement of Mean Slip Distance in Aluminum and its Correlation to Ductility

Measurement of Mean Slip Distance in Aluminum and its Correlation to Ductility

Strengthening in low carbon pearlitic steels

The microstructure-flow stress relationship has been examined in two simple ferrite-pearlite steels. As in fully pearlite steels, a Hall-Petch equation was shown to be applicable, when care is taken in obtaining the appropriate mean slip distance in ferrite for each microstructure.