Dislocation Multiplication Rate Research Articles

Crystal plasticity framework related to size effect: From single crystal parameters to polycrystalline mechanical properties

Size effect has a significant influence on the accuracy of two key factors of parameters and models in crystal plasticity simulation. This study introduces a parameter identification method that considers the indentation size effect, determining the initial slip resistance of IN625 alloy. Based on the identified parameters and utilizing the integral point traversal method, a grain boundary affected zone (GBAZ), whose strength field related to the distance to the grain boundary (GB) is introduced into the polycrystalline microstructure to represent the hindering effect of GBs on dislocations. This method effectively predicts the Hall-Petch effect and strain hardening behavior of IN625 alloy. The research reveals that dislocation pile-ups primarily concentrate in small grain clusters within the material. In fine-grained microstructures, a large volume fraction of GBs promotes dislocation pile-ups, reducing the mean free path of dislocations, leading to an increase in dislocation multiplication rate, and consequently, enhancing the strain hardening rate. An increase in GBAZ thickness results in a large stress level within the material, accompanied by a decrease in the homogeneity of stress distribution. However, the sensitivity of strain to GBAZ thickness is found to be low. The method proposed in this work holds significant applicative relevance in parameter calibration and prediction the mechanical properties of polycrystalline materials.

A new perspective on Lüders band formation in medium-Mn steels based on Lüders-strain-rate and dislocation evolution

Propagating Lüders bands with pronounced strain localization are often observed in medium-Mn transformation-induced plasticity (TRIP) steels, which adversely limits the application of such alloys in engineering structures. The present work aims to understand this phenomenon from a dislocation-based perspective, with a focus on the specific role of dislocation multiplication. The material studied is a typical dual-phase medium-Mn steel with a ferrite matrix and a second phase of retained austenite. A warm-rolling process was used as a pre-straining approach to adjust the microstructure of the material, such that materials with two different microstructural states can be obtained: as-received material and pre-strained material. They show distinct differences in initial dislocation density. Stress-controlled rather than conventional strain-controlled tensile testing was adopted, which allowed the Lüders band to develop in an unconstrained manner. In this way, the intrinsic Lüders-strain-rate can be obtained. The results show that the Lüders band-related mechanical parameters, including Lüders strain, Lüders-strain-rate and yield stress drop, all depend on the initial microstructure state and the dislocation evolution process during Lüders band formation. In particular, Lüders-strain-rate is a critical microstructure-sensitive factor. It is closely related to the dislocation multiplication in the formation of Lüders band, which can be characterized and quantified using scanning transmission electron microscope and synchrotron X-ray diffraction. Finally, a quantitative relationship between Lüders-strain-rate and dislocation multiplication rate is established, which allows providing a better understanding of the exceptional Lüders band phenomenon in medium-Mn steels.

Quasi-in-situ characterization of microstructure evolution in friction stir welding of aluminum alloy

The in-situ investigation of microstructure evolution during friction stir welding (FSW) can provide very important theoretical guidance to control the microstructure and mechanical properties of the FSW joint. In this study, a quasi-in-situ investigation method of the microstructure evolution in friction stir welding of AA1050 aluminum alloy was developed. The microstructure along the material flow path was characterized and analyzed by taking the strain, strain rate, and temperature into account simultaneously. The results show that the microstructure evolution during the FSW of aluminum alloy can be divided into four stages according to the material flow state and thermal history. Firstly, grain coarsening by static recovery and static recrystallization occurs at the static preparatory stage (or called the preheating stage). Secondly, grain refining by continuous dynamic recrystallization occurs at the acceleration stage, where the temperature gradually increases to nearly a constant. The grain size is mainly controlled by the accumulative total strain. The strain rate only affects the rate of dislocation generation and the type of β-fiber simple shear texture components. Thirdly, at the high-velocity flow stage, a dynamic equilibrium between plastic deformation and dynamic recrystallization is maintained, and the grain size only fluctuates within a small range. Finally, a second grain-coarsening process occurs through normal grain growth due to thermal activation at the deceleration stage. This process is inevitable because it occurs under the cover of the tool shoulder. The grain coarsening during the normal cooling stage was avoided in this study due to the rapid cooling used, which has been widely reported by published documents.

Surface strengthening phenomenon and mechanism of 6061 solid solution alloy after ultrasonic stress relief

The evolution of residual stress, microstructure and mechanical properties, and their correlations of supersaturated 6061 solid solution alloy were investigated after ultrasonic stress relief. It is found that following ultrasonic stress relief, the residual stress of 6061 solid solution aluminum alloy is gradually released with the hardness of the alloy rising first to a peak and then decreasing gradually to a stable value. After ultrasonic stress relief, the peak hardness of the alloy is capable of reaching 81.8 ± 1.95HV, which is about 45% higher than 56HV of the initial state. When the residual stress was released by about 80%, the hardness of the alloy came to a stable value of 63.75 ± 1.65HV. It is proved that the ultrasonic stress relief could not induce a precipitation of the strengthening phase in the supersaturated 6061 solid solution alloy. The hardening of the alloy was mainly caused by the evolution of dislocation during the residual stress relief process. The superposition of ultrasonic dynamic stress and the internal residual stress in the alloy first prompted the multiplication and entanglement of dislocation, and consequently increase the hardness of the alloy. With further relief of the residual stress, the dislocation multiplication rate slows down and the annihilation rate accelerates, and then the corresponding dislocation density and entanglement are obviously reduced, resulting in a decrease in the hardness of the alloy to a constant.

Role of lattice resistance in the shock dynamics of fcc-structured high entropy alloy

The shock response of high entropy alloys (HEAs) would be important for their performance under extreme conditions. However, it is still difficult to obtain the shock response data at the atomic scale over the wide range of loading conditions. Here, the shock compression response of fcc-structured modeled HEAs and pure metals with different degrees of lattice resistance and stacking fault energy has been studied using the molecular dynamics simulations in the terms of the Hugoniot stress, atomic structure, and dislocation density. The results show that the HEA with low lattice resistance exhibits a significantly low shock compression strength in comparison with pure metal. In contrast to pure metal, Shockley partial dislocations and stacking faults with high density were found in HEA with low lattice resistance. Interestingly, during the shock wave propagation in HEA with high lattice resistance to dislocation glide, the crystalline to amorphous phase transformation has been observed to occur behind the shock front. The high lattice resistance slows down the movement of dislocations in HEA, and then promotes the amorphization process. This trend gives an effective toughening mechanism in shock loading of HEAs. In addition, the microstructure-based physical model suggests the obvious effect of lattice resistance on the working hardening of the HEAs after shock compression. It indicates that the lattice resistance of intrinsic chemically disordered structures dominates the rate of dislocation generation and the shock compression strength. The current study provides an important atomic insight for understanding the dynamic mechanical behaviors of HEAs. • Shock compression response of HEAs and pure metals was studied. • HEA with low lattice resistance exhibit low strength in comparison to pure metals. • Amorphization occurred behind the shock front of HEA with high lattice resistance.

Micromechanical response of pure magnesium at different strain rate and temperature conditions: twin to slip and slip to twin transitions

The strain rate (ε˙) and temperature (T) dependent mechanical response of single crystal magnesium (Mg) micropillars compressed along the [2¯110] direction (a-axis) is investigated from room temperature to 573 K and from 10-3 to 100 s-1. The loading direction was chosen to disfavour basal slip activation by a low Schmid factor, allowing the investigation of the rate-sensitivities of extension twinning and prismatic slip. For T ≤ 423 K, the plasticity was governed by extension twinning for the entire range of the applied strain rates. At T > 423 K and for ε˙ ≤ 10 s-1, extension twinning did not occur and a continuous plastic flow induced by prismatic dislocation mediated plasticity was observed: the twin to slip transition takes place due to the decrease of the critical resolved shear stress of non-basal slip. For ε˙ > 10 s-1, however, the accommodation of the plastic deformation by activation of prismatic slip is not enough to match the applied deformation rate, favouring again deformation twinning. The first part of this work provides a complete overview of the mutual effects of T and ε˙ on the transition points of deformation modes in Mg at the microscale. In a second stage, the influence of thermal and kinetic contributions on the evolution of the flow stress leading to the slip to twin transition at 573 K has been assessed in more detail. Within the slip-dominated plasticity regime, this work provides a quantitative assessment of the increases in the saturation stress (stage III) with ε˙ at high temperature, showing how the strain rate dependency of the dislocation generation rate in the pillar and escape rate at the free surfaces of the structure controls the stress evolution in Mg microcrystals.

Assessment of the time-dependent behavior of dislocation multiplication under shock loading

In this study, we proposed a method, which is a combination of qualitative analysis and quantitative analysis, to establish dislocation-based plasticity model, and assessed the time-dependent behavior of dislocation multiplication under shock loading. First, the dimensional analysis method is applied to generate the governing equation of dislocation multiplication rate, and ten potential governing equations are derived. Second, through the theoretical analysis of the mechanical response on the shock front, each time-dependent governing equation is directly integrated on the shock front, and the explicit expression of dislocation density with respect to the applied stress is derived, which is further quantitatively connected to the power scaling characteristics of the plastic front. It's found that only three of the ten equations, including two common equations and one newly derived equation via the dimensional analysis method, can predict the appropriate scaling coefficient of the plastic front. Third, three common equations and the newly derived equation are implemented into a dislocation-based constitutive model, and we compared results, including the velocity profiles and dislocation densities, calculated using the model associated with each equation and experimental results to evaluate the accuracy and efficiency of each equation. Through the comparison of the quantitative relation of the power scaling characteristics of the plastic front, and the elastic precursor decay, it's concluded that the newly derived stress-dependent governing equation is more suitable for shock-loading process than the commonly used equations by previous constitutive models.

Effect of rolling temperature on microstructure evolution and mechanical properties of high carbon high manganese steel

The effects of rolling temperature ranging from −55 to 300 °C on dislocation density, twinning behavior and correlative tensile properties of a high carbon high manganese steel were investigated. Results showed that the twinning behavior was enhanced at −55 °C but suppressed at 300 °C. The twin thickness and spacing increase with the rolling temperature. At low rolling reduction of 10%, the dislocation multiplication rate decreased with the increase in rolling temperature. However, the dislocation multiplication rate maintained high level when rolled at high rolling reduction and high temperature. At a given rolling reduction, the samples rolled at −55 °C possessed higher work hardening rate. Especially, the strength of −55°C-rolled-20% sample was higher than that of 300°C-rolled-30% sample and was equivalent to room temperature (RT)-rolled-30% sample. Concurrently, the elongation of the −55°C-rolled-20% sample was higher than the other two. The contributions of dislocation strengthening and twin strengthening to the yield strength of high carbon high manganese steel after rolling at different conditions were calculated by the parameter model. The dislocation strengthening effect played a dominant role under various deformation conditions. Twin strengthening effect showed a temperature sensitivity in the temperature range selected in the present study. Lower rolling temperature showed greater contribution of twin strengthening, whereas the dislocation strengthening effect was insensitive to temperature.

Strain hardening versus softening: Anisotropic response of strain hardening-softening transition in a polycrystalline zirconium alloy at room temperature from dislocation viewpoint

The anisotropic response of strain hardening-softening transition behavior in Zr–Sn–Nb–Fe–Mo alloys was investigated. Dynamic recovery via dislocation annihilation could occur during the strain-softening process. Samples possessed promoted strain hardening capability along rolling direction than transverse direction, originating from the different rate of dislocation multiplication and annihilation along the two directions.

Dislocation multiplication and dynamics in an aluminium alloy

ABSTRACT A mechanism of dislocation multiplication is introduced. The surface of the Al20Cu2Mn3 phase in an Al alloy can act as a barrier to impede dislocation movement. When two dislocations with opposite Burgers vectors approach each other, dislocations can annihilate if the pair remains at a distance less than the critical distance for annihilation. A dislocation loop is then formed around the Al20Cu2Mn3 phase or dislocations interact with the loop forming a dislocation tangle, which can promote dislocation multiplication. The driving force for dislocation reproduction, the dislocation glide velocity and the rate of dislocation multiplication are discussed.

Effect of δ-ferrite on the low-cycle fatigue behavior of the 0Cr17Ni10Mn5Mo2 steel

In the present paper, a 0Cr17Ni10Mn5Mo2 steel was treated with different hot extrusion processes to obtain three different microstructures, namely, single austenite, austenite with thin-striped shaped δ-ferrite, and austenite with thin-sheet shaped δ-ferrite. Cyclic deformation tests were conducted on the test steel with microstructures described above. Cyclic deformation microstructures were characterized by optical microscope, electron backscatter diffraction technique and transmission electron microscopy. Results showed that the fatigue lives of the test steels containing δ-ferrite were longer than that with single austenite. At the total strain amplitude of 0.8%, cyclic hardening followed by softening occurred in the test steel containing δ-ferrite at the initial stage of cyclic deformation. Secondary hardening was observed in the subsequent cyclic deformation in the test steel containing thin-sheet shaped δ-ferrite. The hard lamellae of δ-ferrite and fine austenite grains reduced the plastic strain amplitude and dislocation multiplication rate in the test steel. Therefore, cyclic softening behavior was induced. With the increase of size and quantity of δ-ferrite and adjacent grains, the plastic strain amplitude and dislocation multiplication rate were elevated, leading to increased cyclic stress and secondary hardening behavior.

On the assessment of creep damage evolution in nickel-based superalloys through correlative HR-EBSD and cECCI studies

The evolution of dislocation density with creep strain in single-crystal superalloys is studied quantitatively using high-resolution electron backscatter diffraction (HR-EBSD) and electron channelling contrast imaging under controlled diffraction conditions (cECCI). Data regarding dislocation density/structure is measured for deformation at 900 °C and 450 MPa up to ≈ 1% plastic strain. Effects of chemical composition are elucidated via three purpose-designed superalloys of differing rhenium and ruthenium contents. The evidence indicates that dislocation avalanching is already prevalent at plastic strains of ≈ 0.1%; thereafter, an exponential decay in the dislocation multiplication rate is indicative of self-hardening due to dislocation constriction within the matrix channels, as confirmed by the imaging. The results are rationalised using discrete dislocation dynamics modelling: a universal dislocation evolution law emerges, which will be useful for alloy design efforts.

Dislocation structure evolution under electroplastic effect

In this study, the effect of high current density electropulsing (103 A/mm2 for 150 μs) on the residual stress of quenched steel was investigated with the objective of determining the electroplastic effect on plastic strain and dislocation evolution. The residual stress and dislocation density, which were closely related to the plastic strain, were significantly reduced through electropulsing. The direct effect of drift electrons on the dislocation motion, instead of side effects such as skin, pinch, instantaneous thermal expansion stress, and Joule heating, primarily contributes to the plastic strain. Employing the thermally activated plastic flow concept, the drift electrons were also found to have an effect on the thermally activated dislocation motion in addition to the force exerted on the dislocations by an electron wind. Under the action of drift electrons, the movement of vacancies and dislocations were enhanced, which accelerated the dislocation annihilation. In contrast, affected by the electron wind force, Frank-Read source failed to produce a large amount of dislocations, thereby simultaneously decreasing the dislocation multiplication rate. Finally, the dislocation density decreased and the dislocation structure was rearranged parallel to the direction of motion of the drift electrons.

Unique defect evolution during the plastic deformation of a metal matrix composite

During the plastic deformation of a metal matrix composite (MMC) containing non-deformable particles, high dislocation density and strong back stresses are expected because the particles help with blocking and accumulating dislocations. Here we report that the MMC has lower, instead of higher, dislocation density than the corresponding monolithic matrix material when they are deformed to high plastic strains, because smaller sub-grains in the MMC lowered dislocation generation rate and meanwhile promoted the dislocation interaction and annihilation in the matrix. This unique defect density evolution is a hitherto unknown but important factor affecting the mechanical properties of MMCs.

Modelling the yield point phenomena during deformation at elevated temperatures: case study on Inconel 600

ABSTRACTThe discontinuous yield behaviour (DYB) of Inconel 600 was studied during hot compression tests at temperatures in range of 850–1150°C and strain rates of 0.001–1 s−1. The yield point phenomena were observed in the temperature range of 850–1000°C and strain rates of 0.001–0.1 s−1. The DYB was modelled by considering the evolution of dislocation density at the early stages of yielding. The opposite effects of dislocation multiplication, dislocation interaction (work hardening) and dynamic recovery (DRV) were considered. It was shown that the dislocation multiplication and DRV result in flow softening, while the dislocation interaction leads to work hardening. The model was established in a way to consider the effects of various microstructural evolutions on the σ(ε) function. The discontinuous flow curves were fitted by the developed model with acceptable precision. The variations of material constants with temperature and strain rate were found physically meaningful. The dislocation multiplication parameter was determined at various temperatures and strain rates. It was concluded that the rate of dislocation multiplication increases as temperature rises or strain rate declines. Accelerated dislocation multiplication leads to less drop in yield stress between the upper and lower yield points.

Analysis of nonlinear elastic aspects of precursor attenuation in shock-compressed metallic crystals

Unsteady characteristics of shock waves in metals, for example elastic precursor decay, have often eluded a complete model description. Historic continuum elastic-plastic theories tend to require excessive initial dislocation densities in order to match experimental observations. Studies incorporating superposition of linear elastodynamic solutions for dislocations, either in analytical solutions or in discrete numerical simulations, omit nonlinear elastic effects and only consider effects of defects immediately at the elastic shock front. Prior analytical treatments of hydrodynamic attenuation consider nonlinearity manifesting as effects of stress gradients or particle velocity gradients immediately behind the front. The present analysis seeks to augment the predictive precursor decay equation from linear elastodynamics to account for elastic nonlinearity and dislocation nucleation in the wake of the precursor shock. A complete solution for the precursor magnitude at a material point is shown to require consideration of the prior history of dislocation generation and the entire flow field behind the elastic shock up to that material point. However, introduction of reasonable simplifying assumptions and basic models for dislocation generation and glide resistance enable derivation of a mathematically tractable relation for precursor decay. This relation is a nonlinear first-order ordinary differential equation that, in non-dimensional form, contains only one scalar parameter controlling the rate of dislocation generation behind the shock. Model predictions that include nonlinear effects are shown to provide a better match to experimental data for three metals. Effects of nonlinearity are shown to emerge early, but not immediately, in the shock attenuation process, and these effects increase in prominence with increasing impact stress.

Creep behaviors and mechanisms of Inconel718 and Allvac718plus

To investigate creep mechanisms of Inconel718 and Allvac718Plus, creep behaviors of two alloys are studied under the temperature of 700°C and three applied stresses (560MPa, 650MPa and 720MPa) by using multiple microstructural analysis methods, including scanning electron microscope (SEM), emission scanning electron microscope (FSEM) and transmission electron microscopy (TEM). Result shows that steady-state region is not observed in these two alloys. Creep curves of two alloys are composed of primary region and tertiary region. Tertiary region occupies a dominant position. Ductile dimples are observed on creep fracture surface, indicating creep mechanisms of two alloys are the formation of creep voids. In this study, the formation of creep voids is found to be correlated with three factors which are dislocation multiplication, dislocation motion and dislocation obstacles. Inconel718 has higher dislocation multiplication rate, larger dislocation motion rate, more δ phases and less bands than Allvac718Plus. Therefore, Inconel718 has higher creep voids rate than Allvac718Plus, leading to the result that Inconel718 has shorter creep life than Allvac718Plus.

Micromechanical modeling of hardening mechanisms in commercially pure α-titanium in tensile condition

Tensile tests on commercially pure α-titanium show a three-stage behavior giving rise to a well on the strain dependence of the work hardening. An opposite strain rate effect on the well depth is found whether specimens are elongated along the rolling or the transverse direction. Slip lines analysis reveals an initial predominance of prismatic slip, particularly pronounced in specimens strained along the rolling direction. The relative activity of prismatic slip is then observed to decrease with the samples deformation. These results provide grounds for elaboration of an elasto-viscoplastic self-consistent model based on the translated field method and an affine linearization of the viscoplastic flow rule, and capable of explaining such peculiar work hardening behavior. The model considers crystal plasticity and deals separately with mobile dislocation density and dislocation velocity. It assumes lower strain rate sensitivity as well as higher dislocation multiplication rate for prismatic systems. Based on these assumptions, the model reproduces correctly the stress–strain curves and gives sound estimates of Lankford coefficients, prismatic slip activity and textures evolution. Most importantly, the opposite effect of strain rate on the well depth with regard to the orientation of the tensile axis is qualitatively retrieved, which allows putting forward an explanation of the observed phenomena.

High temperature dislocation structure and NbC precipitation in three Ni–Fe–Nb–C model alloys

In this original work, the dislocation structure and NbC precipitation were investigated in three Ni-based alloys (70Ni–Fe–0.331Nb–0.040C, 70Ni–Fe–0.851Nb–0.114C and 70Ni–Fe–1.420Nb–0.157C, wt%) thermomechanically processed in the temperature range of 1250–1075 °C. The dislocation structure inhomogeneity (dislocation networks and cell walls), which we observed in the middle and high Nb+C alloys, resulted from the dislocation pile-ups in the vicinity of >200 nm NbC particles. The dislocation density around >200 nm particles exceeded the average values by 5–7 times, and that in the cell walls might exceed the average values by 10 times. Twins and stacking faults were observed in all alloys after solution treatment at 1250 °C, however, they were not observed after 1.2 strain at 1075 °C. The dislocation generation rate during deformation at 1075 °C varied with alloy composition and increased with an increase in the <20 nm particle number density. During cooling in the temperature range of 1250–1075 °C, the majority of particles were growing in the high Nb+C alloy, the <20 nm particles were growing in the middle Nb+C alloy and all the particles were dissolving in the low Nb+C alloy. Deformation to 1.2 strain at 1075 °C resulted in strain-induced precipitation in all alloys and <20 nm particle growth in the high and middle Nb+C alloys.

Effects of directional grain structure on impact properties and dislocation substructure of 6061-T6 aluminium alloy

The effects of the grain structure direction on the impact properties and dislocation substructure of 6061-T6 aluminium alloy are investigated under room temperature conditions and strain rates of 1×103, 3×103 and 5×103 s−1 using a split-Hopkinson pressure bar system. The impact tests are performed using specimens machined from rolled 6061-T6 plates in the longitudinal, transverse and through thickness directions respectively. The results show that for all specimens, the flow stress increases with increasing strain rate. Furthermore, for all strain rates, the highest flow stress occurs in the transverse specimen. For strain rates of 1×103 and 3×103 s−1, the flow stress in the through thickness specimen is greater than that in the longitudinal specimen. However, at a strain rate of 5×103 s−1, the flow stress in the longitudinal specimen is higher than that in the through thickness specimen due to a greater dislocation multiplication rate. For all three grain structure directions, the strain rate sensitivity increases with increasing strain rate, but decreases with increasing true strain. The highest strain rate sensitivity is observed in the longitudinal specimen at strain rates of 3×103 to 5×103 s−1. The dislocation density increases markedly with increasing strain rate. Moreover, the square root of the dislocation density varies as a linear function of the flow stress in accordance with the Bailey–Hirsch relationship. The strengthening effect produced by the increased dislocation density is particularly evident in the transverse specimen, followed by the longitudinal specimen and the through thickness specimen.