Dislocation Mean Free Path Research Articles

Crystal Plasticity Analysis of Mechanical Response and Size Effect in Two Phase Alloys with Dispersion of Fine Particles

Plastic deformation and dislocations accumulation in a steel alloy dispersed with vanadium carbide particles is numerically analyzed by a crystal plasticity finite element technique and work hardening characteristics are discussed. Increment of dislocation density that contributes to work hardening is calculated from the mean free path of dislocations. The mean free path is defined by the spacing of forest dislocations and the average spacing of dispersed particles. Obtained yield stress and work hardening characteristics was close to that of experimental result, except that the value of work hardening rate was higher than that of experimental one.

A constitutive model of the deformation behaviour of twinning induced plasticity (TWIP) steel at different temperatures

The mechanical behaviour of Fe–18Mn–0.6C–1Al (wt%) TWIP steel was modelled in the temperature range from room temperature to 400°C. The proposed constitutive model was based on the Kocks–Mecking–Estrin (KME) model. The model parameters were determined using extensive experimental measurements of the physical parameters such as the dislocation mean free path and the volume fraction of twinned grains. More than 100 grains with a total area of ~300μm2 were examined at different strain levels over the entire stress–strain curve. Uniaxial tensile deformation of the TWIP steel was modelled for different deformation temperatures using a modelling approach which considers two distinct populations of grains: twinned and twin-free ones. A key point of the work was a meticulous experimental determination of the evolution of the volume fraction of twinned grains during uniaxial tensile deformation. This information was implemented in a phase-mixture model that yielded a very good agreement with the experimental tensile behaviour for the tested range of deformation temperatures.

Dislocation evolution during tensile deformation in ferritic–martensitic steels revealed by high-energy X-rays

Deformation processes in Grade 91 (Fe–9%Cr–1%Mo–V,Nb) and Grade 92 (Fe–9%Cr–0.5%Mo–2%W–V,Nb) ferritic–martensitic steels were investigated at temperatures between 20 and 650°C using high-energy synchrotron X-ray diffraction with in situ thermal–mechanical loading. The change of the dislocation density with strain was quantified by X-ray diffraction line profile analysis complemented by transmission electron microscopy measurements. The relationship between dislocation density and strain during uniform deformation was described by a dislocation model, and two critical materials parameters, namely dislocation mean free path and dynamic recovery coefficient, were determined as a function of temperature. Effects of alloy chemistry, thermal–mechanical treatment and temperature on the tensile deformation process in Grade 91 and Grade 92 steels can be well understood by the dislocation evolution behavior.

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.

Hardening and softening mechanisms of pearlitic steel wire under torsion

The mechanical behaviors and microstructure evolution of pearlitic steel wires under monotonic shear deformation have been investigated by a torsion test and a number of electron microscopy techniques including scanning electron microscopy (SEM) and transmission electron microscopy (TEM), with an aim to reveal the softening and hardening mechanisms of a randomly oriented pearlitic structure during a monotonic stain path. Significantly different from the remarkable strain hardening in cold wire drawing, the strain hardening rate during torsion drops to zero quickly after a short hardening stage. The microstructure observations indicate that the inter-lamellar spacing (ILS) decreases and the dislocations accumulate with strain, which leads to hardening of the material. Meanwhile, when the strain is larger than 0.154, the enhancement of dynamic recovery, shear bands (SBs) and cementite fragmentations results in the softening and balances the strain hardening. A microstructure based analytical flow stress model with considering the influence of ILS on the mean free path of dislocations and the softening caused by SBs and cementite fragmentations, has been established and the predicted flow shear curve meets well with the measured curve in the torsion test.

A microstructure-based model for describing the material properties of Al–Zn alloys during high pressure torsion

In this work, super saturated solid solution Al–30wt%Zn alloy was subjected to high pressure torsion (HPT). The material properties and microstructural evolution were experimentally studied. Despite strong grain refinement during HPT, the process of softening is observed. Such a material behavior is captured by a proposed model (MBWG) that takes into consideration the effects of solid solution hardening, Orowan looping and evolution of the dislocation density. Namely, the softening process occurred during HPT is attributed to decomposition of super saturated solid solution and evolution of the dislocation mean free path with plastic strain. Our simulation shows that the proposed model describes well the softening and saturation processes, and the decomposition of solid solution plays a significant role during the HPT process.

Combination between Voce formalism and improved Kocks–Mecking approach to model small strains of flow curves at high temperatures

Tensile test curves of an austenitic stainless steel (AISI 316L) are described through the Voce equation in combination with the kinetic approach to strain hardening analysis proposed by Kocks and Mecking (KM) at temperatures ranging from 700 to 1000°C with strain rates between 10−2 and 10−5s−1. The KM approach to strain hardening analysis is used to find the Voce parameters (saturation stress σV, relaxation strain εC, back-extrapolated flow stress to zero strain σo) from the strain hardening rate dσ/dε vs. the flow stress σ. The obtained Voce equations can well describe the flow curves only at large strains in Stage III of strain hardening, while a significant discrepancy occurs at small strains. In order to reduce this discrepancy an improved KM approach is here proposed. The original KM approach assumes that in Stage III of strain hardening the mean free path of mobile dislocations Λ is defined as β/ρ with β constant and ρ the total dislocation density. Λ, and in turn β, are linked to the dislocation cell-pattern typical of Stage III. The proposed improvement of the KM approach consists of assuming that β is not constant at small strains, where dislocations are not organised in cell-pattern, but homogeneously distributed in the material. Based on TEM observations reporting dislocation distributions at small and at high strains, it is proposed that β varies from an initial value at small strains to achieve at high strains the equilibrium value predicted by the original KM approach in Stage III of strain hardening. This assumption provides very good modelling flow curves also at small strains.

Comparisons between homogeneous boundaries and heterophase interfaces in plastic deformation: Nanostructured Cu micropillars vs. nanolayered Cu-based micropillars

Both the homogeneous boundaries and the heterophase interfaces play important roles in crystalline plasticity as they often serve as obstacles for dislocation motion, as well as dislocation sources/sinks. In this work, microcompression tests were carefully performed to explicitly identify the relevant plasticity mechanisms of nanostructured micropillars with five distinct nanostructures: (i) Cu nanotwinned multicrystalline micropillars; (ii) Cu nanocrystalline multicrystalline micropillars; (iii) Cu/X (X=Cr, Zr) nanotwinned nanolayered micropillars; (iv) Cu/X nanocrystalline nanolayered micropillars; and (v) Cu/Cu–Zr crystalline/amorphous nanolayered micropillars. By characterizing their stress–strain response and evolution of strain-rate sensitivity (SRS) with strain, our findings elucidate the effects of homogeneous boundaries, heterophase interfaces and their coupling effects on the plastic yield, and reveal the fundamentally different roles these perform in the rate-limiting process of nanomaterials. In sharp contrast to the normal strain-dependent SRS in nanostructured Cu micropillars with homogeneous boundaries that monotonically decreases with increasing strain, nanolayered Cu-based micropillars with heterophase interfaces exhibit inverse strain-dependent SRS that monotonically increases with increasing strain. These expected (normal) and unexpected (inverse) SRSs are quantitatively explained by a dislocation model in terms of the strain-related dislocation mean free path. These findings provide valuable insights into our understanding of the fundamental roles that homogeneous boundaries and heterophase interfaces play in plastic deformation.

Nonadiabatic spin-dependent transitions in iron clusters as a possible cause of the magnetoplastic effect in NaCl : Fe

A model of nonadiabatic transitions initiated by elastic fields of stresses of moving dislocation in Fe2+ ion pairs has been considered. The transitions are spin-forbidden in the absence of magnetic field. The forbidding is removed in magnetic field. Nonmonotonic dependence of dislocation mean free paths under action of a short (100 μs) magnetic field pulse on the pulse amplitude in NaCl : Fe crystals is explained in the framework of the model of nonadiabatic transitions in Fe2+-Fe2+ pairs.

The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high-entropy alloy

An equiatomic CoCrFeMnNi high-entropy alloy, which crystallizes in the face-centered cubic (fcc) crystal structure, was produced by arc melting and drop casting. The drop-cast ingots were homogenized, cold rolled and recrystallized to obtain single-phase microstructures with three different grain sizes in the range 4–160μm. Quasi-static tensile tests at an engineering strain rate of 10−3s−1 were then performed at temperatures between 77 and 1073K. Yield strength, ultimate tensile strength and elongation to fracture all increased with decreasing temperature. During the initial stages of plasticity (up to ∼2% strain), deformation occurs by planar dislocation glide on the normal fcc slip system, {111}〈110〉, at all the temperatures and grain sizes investigated. Undissociated 1/2〈110〉 dislocations were observed, as were numerous stacking faults, which imply the dissociation of several of these dislocations into 1/6〈112〉 Shockley partials. At later stages (∼20% strain), nanoscale deformation twins were observed after interrupted tests at 77K, but not in specimens tested at room temperature, where plasticity occurred exclusively by the aforementioned dislocations which organized into cells. Deformation twinning, by continually introducing new interfaces and decreasing the mean free path of dislocations during tensile testing (“dynamic Hall–Petch”), produces a high degree of work hardening and a significant increase in the ultimate tensile strength. This increased work hardening prevents the early onset of necking instability and is a reason for the enhanced ductility observed at 77K. A second reason is that twinning can provide an additional deformation mode to accommodate plasticity. However, twinning cannot explain the increase in yield strength with decreasing temperature in our high-entropy alloy since it was not observed in the early stages of plastic deformation. Since strong temperature dependencies of yield strength are also seen in binary fcc solid solution alloys, it may be an inherent solute effect, which needs further study.

Transient Negative Strain Hardening during Severe Plastic Deformation of Al-30wt%Zn Alloys

In this work we propose a new model (SOFTMAR) to describe the transient softening observed during severe plastic deformation of Al-30wt%Zn alloys. The model is divided in two main parts. The first one describes the softening process based on the evolution law of the mean free path of dislocations (L) with plastic strain . In the second part of the model emphazis is given to the relationship between the grain size and strain rate that in turn depends on diffusion-driven grain-boundary sliding.

Mechanism of twinning-induced plasticity in β-type Ti–15Mo alloy

The mechanism of {3 3 2}〈1 1 3〉 twinning-induced plasticity in a Ti–15Mo alloy was investigated through quantitative evaluation of twinning structure evolution at various tensile strains. A linear relationship between the inverse square root of the dislocation mean free path and the true stress was obtained at strains up to 0.12, indicating that strain hardening was due to dynamic microstructural refinement induced by twinning. Further strain hardening at strains up to 0.24 was mainly brought about by a rapid increase in dislocation density.

A microstructure-based model for describing strain softening during compression of Al-30%wt Zn alloy

A microstructural-based model, describing the plastic behavior of Al-30wt% Zn alloy, is proposed and the effect of solid solution decomposition, Orowan looping, twinning and grain refinement is analyzed. It is assumed that the plastic deformation process is dominated by strain-induced solute diffusion and dislocation motion. To capture the essential physics, a law describing the evolution of the mean free path of dislocations with plastic strain is proposed which reproduces the experimentally observed strain softening.

Influence of the transverse size of samples with micro- and nano-grained structures on the yield and flow stresses

The effects of reduction in the strength and deviation from the Hall-Petch relationship under plastic deformation of specimens with micro- and nano-grained structures with decreasing size of their cross section have been considered theoretically. The analysis is based on the kinetic equation for the dislocation density, which takes into account that the surface of the specimen serves as both the source and the sink for dislocations, whereas the grain boundaries are barriers limiting the mean free path of dislocations. It has been found that, when the ratio of the transverse size of the specimen D to the grain size d becomes less than 3, in the dependence of the yield stress on the size of the specimen there appears a minimum as a result of the increase in the number of near-surface grains that exhibit a weak resistance to plastic deformation due to the withdrawal of dislocations through the external surface of the fine-dimensional specimen. The minimum of the strength in the range d < D < 3d is a consequence of the competition and nonlinear interaction of the size factors D and d.

Scale effects in necking

Geometrically similar specimens spanning a scale range of 100:1 are tested quasi-statically to failure. Images of neck development are acquired using optical means for large specimens, and in-situ scanning electron microscope testing for small specimens, to examine the dependence of neck geometry on a broad range of specimen sizes. Size effects typically arise when the smallest specimen dimension is on the order of a microstructural length (e.g. grain size, dislocation mean free path, etc.), or in the presence of significant plastic strain gradients, which increase the density of geometrically necessary dislocations. This study was carried out for the purpose of investigating scale dependence in models used for predicting dynamic deformation and damage to very high strains for ballistic impact applications, such as the Goldthorpe path-dependent failure model, which includes temperature and strain-rate dependence but does not account for specimen size or a dependence on microstructural lengths. Although the experiments show that neck geometry does not exhibit a clear dependence on specimen size across the range of length scales tested, the statistical variation due to microstructural variations was found to increase monotonically with decreasing size, becoming significant for the smallest (0.35 mm diameter) size, allowing a limit to be identified for reliable model calibration.

Orientation dependence of twinning and strain hardening behaviour of a high manganese twinning induced plasticity steel with polycrystalline structure

The twinning induced plasticity steel 0.6 C–18 Mn–1.5 Al (wt.%) employed in this study exhibited a strength of about 1GPa, combined with a large uniform elongation of over 60% at moderate strain rates. This excellent combination of tensile mechanical properties was shown to be a result of complex dynamic strain-induced microstructural reactions, including dislocation glide, dislocation dissociation, stacking fault formation, dynamic recovery, mechanical twinning and dynamic strain ageing. The contribution of each of these processes was discussed with respect to the strain hardening behaviour. An important observation was that the propensity for mechanical twinning in a particular grain strongly depends on its crystallographic orientation and is clearly correlated with the magnitude of the corresponding Taylor factor. The current results reveal that the development of partial dislocations and stacking faults at an early stage of straining and the consequent interaction of gliding dislocations with stacking fault interfaces enhances the strain hardening rate. Subsequent or concurrent initiation of mechanical twins also contributes to strain hardening through a dynamic Hall–Petch effect limiting the dislocation mean free path and consequently enhancing dislocation storage. Dynamic strain ageing (DSA) took place at a late stage of deformation, adding to strain hardening. DSA is a factor reducing ductility by promoting strain localization.

Grain Boundary Behavior in an Ultrafine-Grained Aluminum Alloy

The low-angle grain boundary (LAGB) stability in an ultrafine-grained (UFG) Al alloy during monotonic loading was investigated by orientation imaging microscopy (OIM). The experiments show that boundaries with misorientation below ~2.5 deg are stable, while boundaries with misorientation between 2.5 and 15 deg are unstable. Similar results were observed during cyclic loading of UFG Al alloy. This behavior was rationalized using the nonequilibrium thermodynamics concept. On the other hand, it is postulated that the grain boundary behavior in microcrystalline alloy is different because of the larger dislocation mean free path.

Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals

The miniaturization of metallic samples has been proved to deeply affect their mechanical properties leading to a softening or a hardening effect depending on the order of the dimension reduction. The objective of this work is to provide new numerical results which explain the softening mechanisms on the mechanical behavior for nickel polycrystals which have been experimentally characterized by the authors in a previous published paper ( Keller et al., 2011). Based on a strain gradient crystalline plasticity model identified for nickel, simulations of tensile tests were performed for samples with different thicknesses and grain sizes. The simulations correctly reproduce the softening effect linked to a decrease in the thickness and in the number of grains across the thickness. The analysis of the plasticity mechanisms shows that the softening is due to surface effects which are discussed in terms of grain orientations, dislocation mean free path and long-range back-stress. The model also predicts a hardening mechanism for further dimension reduction if the samples have only grain boundaries perpendicular to the tensile direction. In this case, the modification of the mechanical behavior is due to strain gradients formation.

Dislocation and twin substructure evolution during strain hardening of an Fe–22 wt.% Mn–0.6 wt.% C TWIP steel observed by electron channeling contrast imaging

We study the kinetics of the substructure evolution and its correspondence to the strain hardening evolution of an Fe–22wt.% Mn–0.6wt.% C TWIP steel during tensile deformation by means of electron channeling contrast imaging (ECCI) combined with electron backscatter diffraction (EBSD). The contribution of twin and dislocation substructures to strain hardening is evaluated in terms of a dislocation mean free path approach involving several microstructure parameters, such as the characteristic average twin spacing and the dislocation substructure size. The analysis reveals that at the early stages of deformation (strain below 0.1 true strain) the dislocation substructure provides a high strain hardening rate with hardening coefficients of about G/40 (G is the shear modulus). At intermediate strains (below 0.3 true strain), the dislocation mean free path refinement due to deformation twinning results in a high strain rate with a hardening coefficient of about G/30. Finally, at high strains (above 0.4 true strain), the limited further refinement of the dislocation and twin substructures reduces the capability for trapping more dislocations inside the microstructure and, hence, the strain hardening decreases. Grains forming dislocation cells develop a self-organized and dynamically refined dislocation cell structure which follows the similitude principle but with a smaller similitude constant than that found in medium to high stacking fault energy alloys. We attribute this difference to the influence of the stacking fault energy on the mechanism of cell formation.

Micro–macro investigations about the fatigue behavior of pre-hardened 304L steel

In this work, the effect of cyclic pre-hardening (CPH) and monotonic pre-hardening (MPH), on the Cyclic Stress–Strain Curve (CSSC) and fatigue are considered. New tension-compression tests on two types of 304L alloys used in nuclear power plants are carried out under the following conditions: (i) strain or stress control near endurance limit; (ii) zero or positive mean stress; (iii) virgin, CPH or MPH specimens. Macroscopic results show a detrimental effect of pre-hardening in strain control and a beneficial one in stress control. Some macroscopic considerations are given to explain this result and the effects of an applied mean stress which differ under stress and strain control. Relations between macroscopic results and microstructures at failure are investigated using SEM and TEM. SEM is used for analysis of fatigue striation space.TEM analyses suggest that cyclic pre-hardening mainly promotes wavy slip during subsequent fatigue testing, while monotonous pre-loading favors planar slip. For CPH case it seems that primary cells which are preserved and refined for the most part during fatigue testing, constitute the hard stable structure. After MPH and subsequent fatigue testing, a hard structure is constituted by embedding of three kinds of microstructures, small twins, small cells, crossing twin systems. The formation of a hard structure creates an important internal stress. Observation shows that in pre-hardened specimens, softening arrays as veins and PSBs are frequent under strain control and rather scarce under stress control. It can be so deduced that the increase of fatigue life by pre-hardening in stress control is related to reduced mean free path of mobile dislocations due to internal stress.The obtained results may help to understand some aspects about linear versus non linear fatigue damage accumulation.