Statistically Stored Dislocations Research Articles

Revealing the temperature-dependent hardening mechanisms of non-uniformly distributed defects for ion-irradiated metals: Experiments and modeling

In this work, an integrated approach including experimental examinations and theoretical modeling was employed to examine the temperature-dependent hardening of structural materials under ion irradiation. Experimental procedures involved the characterization of grain morphology and size distribution by electron backscatter diffraction (EBSD). Irradiation experiments were conducted utilizing high-energy Au-ions at elevated temperatures, with transmission electron microscopy (TEM) employed for observing irradiation-induced defects. Moreover, mechanical properties were assessed through high-temperature nano-indentation tests (HTNIT), revealing the concurrent occurrence of irradiation hardening and high-temperature softening in the considered materials. For theoretical modeling, a mechanistic model was developed to address the depth-dependent hardness. This model innovatively characterized the hardening mechanisms resulting from non-uniformly distributed defects in the irradiated layer while simultaneously incorporating the temperature effect. Calibration of the model demonstrated its capability to elucidate the hardness-depth relationships at different irradiation doses and testing temperatures. Further theoretical analyses indicated distinct evolution laws in irradiation hardening behavior with varying indentation depths, while the increment in temperature accelerated the expansion of the plastic zone, resulting in a moderate indentation size effect (ISE). With increasing indentation depth, the hardening contributions of geometrically necessary dislocations (GNDs) and irradiation-induced defects gradually diminished. At substantial indentation depths, the dominant hardening mechanism was then controlled by statistically stored dislocations (SSDs).

Insights into the deformation mechanisms of an Al1Mg0.4Si alloy at cryogenic temperature: An integration of experiments and crystal plasticity modeling

In this work, we investigated the mechanical properties and corresponding deformation mechanisms of an Al1Mg0.4Si alloy, which exhibited significantly higher strength and outstanding strain hardening capacity at 77 K compared to its counterparts at 298 K. The deformation mechanisms responsible for the excellent strength-ductility synergy and extraordinary strain hardening capacity at cryogenic temperature were elucidated through a combined experimental and simulation study. The results reveal the presence of numerous slip traces and microbands throughout grain surfaces during deformation at 298 K, whereas at 77 K, vague grain surfaces dominate, indicating the simultaneous operation of multiple slip systems. Transmission electron microscopy (TEM) analysis using the two-beam diffraction technique demonstrates the presence of dislocations with several different Burgers vectors inside a grain at cryogenic temperature, confirming the activation of multiple slip systems. The accumulation of dislocations facilitated by these multiple slip systems, combined with the high dislocation density, contributes to strain hardening and remarkable uniform elongation at 77 K. A modified dislocation density-based crystal plasticity model, incorporating the effect of grain boundary hardening (GBH) and temperature, was developed to gain a better understanding of the underlying mechanisms governing alloy's strength and plasticity. The GBH effect significantly enhances statistically stored dislocation (SSD) density and screw dislocation proportion, which promote homogeneous deformation and enhance strain hardening capacity at cryogenic temperature. These findings deepen the understanding of plastic deformation at cryogenic temperatures and pave the way for the development of ultrahigh-performance metallic materials for cryogenic applications.

Dislocation Hardening in a New Manufacturing Route of Ferritic Oxide Dispersion-Strengthened Fe-14Cr Cladding Tube.

The microstructure evolution associated with the cold forming sequence of an Fe-14Cr-1W-0.3Ti-0.3Y2O3 grade ferritic stainless steel strengthened by dispersion of nano oxides (ODS) was investigated. The material, initially hot extruded at 1100 °C and then shaped into cladding tube geometry via HPTR cold pilgering, shows a high microstructure stability that affects stress release heat treatment efficiency. Each step of the process was analyzed to better understand the microstructure stability of the material. Despite high levels of stored energy, heat treatments, up to 1350 °C, do not allow for recrystallization of the material. The Vickers hardness shows significant variations along the manufacturing steps. Thanks to a combination of EBSD and X-ray diffraction measurements, this study gives a new insight into the contribution of statistically stored dislocation (SSD) recovery on the hardness evolution during an ODS steel cold forming sequence. SSD density, close to 4.1015 m-2 after cold rolling, drops by only an order of magnitude during heat treatment, while geometrically necessary dislocation (GND) density, close to 1.1015 m-2, remains stable. Hardness decrease during heat treatments appears to be controlled only by the evolution of SSD.

Microstructure and high-temperature tribological properties of Ti–6Al–4V alloy treated by laser shock peening

The high-temperature wear resistance plays an important role for Ti–6Al–4V alloy components working in extreme environments, especially vital for avoiding unexpected failure. However, the reasonable method of surface modification should meet the requirement of improving in wear resistance and less decreasing in mechanical properties simultaneously, which brings a great challenge. In the present research, the laser shock peening (LSP) technique was applied to optimize the superficial layer of Ti–6Al–4V alloy by different processing. The microstructure, elastic modulus, nano-hardness and high-temperature tribology properties of the LSP processed Ti–6Al–4V were investigated to reveal the improving effect. The results demonstrate the LSP processing transforms the dual-size grain structure to relative homogeneous grain structure and forms the gradient nano-structure in superficial layer. With the increasing of LSP processing numbers, the density of geometrically necessary dislocation (GND) decreases obviously, but the density of statistically stored dislocation (SSD) rises significantly, which promotes the increase of total dislocation density compared with the as-received (AR) alloy. Due to the crystal evolution, the Ti–6Al–4V alloy with three-times LSP processing has the lowest wear rate which is less than half of the as-received state. The observations on worn surface and adjacent cross-sectional microstructure reveal the severe scratching and many inner microcracks in the AR sample but the slight scraping and few inner microcracks in the three-times LSP processed sample. Considering the elevated nano-hardness and elastic modulus, the improved tribological properties should be mainly attributed to the optimized microstructure and dislocation state by LSP processing. The present research provides a more reasonable method to improve the high-temperature wear properties of Ti–6Al–4V alloy.

The synergy between texture evolution and grain refinement in a BCC steel

ABSTRACT This work investigates the synergy between texture evolution and grain refinement in ultra-low carbon body-centred cubic (BCC) ferritic steel. In this regard, experiments and polycrystal plasticity for ambient compressive deformation in low (up to ϵ≈0.22) and moderate (ϵ≈0.22−0.69) strain regimes were carried out. The tests were interrupted at intermediate strains for microstructure and texture characterisation. It was observed that the change in texture to γ -fibre ( { 111 } ∥ Compression direction ( CD ) ) and the formation of θ -fibre ( { 100 } ∥ CD ) up to ϵ ≈ 0.22 contributes towards lattice bending, resulting in grain size reduction from ∼ 104 ( 23 ) μ m to ∼ 23 ( 6 ) μ m . Simultaneously, crystallite size decreases, and statistically stored dislocations (SSD) and geometrically necessary boundaries (GNB) increase rapidly. Thus, resulting in an abrupt decrease in strain hardening rate (SHR). From ϵ ≈ 0.22 − 0.69 , the γ and θ -fibre broadens and θ -fibre intensity increases. The low GNB density increase indicates insignificant deformation-induced lattice curvature formation within grains, resulting in SSD intensification. Thus, leading to elongated grains with sluggish grain size decrease to ∼ 17 ( 4 ) μ m and a lesser decrease in SHR. The α -fibre could not evolve due to the dispersion of 110 axes along the axisymmetric radial direction due to axial deformation. The polycrystal model could appropriately simulate strain-hardening behaviour and texture evolution.

Microstructure Characteristics of Porous NiTi Shape Memory Alloy Synthesized by Powder Metallurgy during Compressive Deformation at Room Temperature

Porous NiTi shape memory alloys (SMAs) possess compatible mechanical properties with human bones and can effectively reduce the risk of stress shielding and stress concentration; therefore, they have been termed promising candidates for orthopedic implants. However, microstructure characteristics of porous NiTi SMAs during plastic deformation have rarely been investigated. The present study aims to specifically investigate microstructure characteristics and the corresponding underlying mechanisms of fabricated porous NiTi SMAs via a conventional sintering (CS) process with NaCl space holder during compressive deformation at room temperature. To realize the aforementioned target, X-ray diffraction (XRD), scanning electron microscope (SEM), electron backscattered diffraction (EBSD), transmission electron microscopy (TEM), and high-resolution transmission electron microscopy (HRTEM) are applied in the present study. The results show that the fabricated porous NiTi SMA is 51.8% for porosity, 181.65 μm for the average pore size, and 0.78 μm for the average grain size. Many Ni4Ti3 and NiTi2 phases are formed in the mixed matrix with dominant B2 (NiTi) and some B19′ (NiTi). Severe inhomogeneous deformation happens within compressed specimens, leading to the occurrence of tangled dislocation and shear bands. Microcracks occur within fabricated porous NiTi SMAs at a deformation degree of 9.2%; then, they extend quickly to form macrocracks, which finally results in the failure of regions between pores. The observed nanocrystallization and amorphization around microcrack tips within the 12.5%-deformed sample can be attributed to the relatively small grain size and the grain segmentation effect via statistically stored dislocation (SSD) and geometrically necessary dislocation (GND).

Ion-irradiation induced hardening behavior of zirconium alloys: A combination of experimental and theoretical study

This study aimed to investigate the microstructure information and mechanical behavior of ion-irradiated zirconium (Zr) alloys through a combination of experimental measurements and theoretical analysis. Experimental procedures involved Au3+ irradiation of Zr-1.5Sn-0.2Fe-0.1Cr and Zr-1.0Sn-1.0Nb-0.1Fe at 3 displacements per atom (dpa) and 30 dpa. Transmission electron microscopy analysis revealed the formation of precipitates such as Zr(Fe, Cr)2 in Zr-1.5Sn-0.2Fe-0.1Cr, as well as β-Nb and Zr(Nb, Fe)2 in Zr-1.0Sn-1.0Nb-0.1Fe. These precipitates exhibited a transformation from crystalline state to partial or complete amorphization after ion-irradiation. Furthermore, macroscopic mechanical properties of the Zr alloys were characterized by nano-indentation tests, which revealed a significant indentation size effect (ISE) and irradiation hardening behavior. To provide a theoretical understanding of the depth-dependent hardness observed in ion-irradiated Zr alloys, a mechanistic model was developed to address the different expansion rates of the plastic zone in the irradiated and unirradiated region. The results indicated that the ISE phenomenon could be attributed to the reduction in the density of geometrically necessary dislocations (GNDs) caused by the expansion of the plastic zone. In addition, the irradiation hardening behavior primarily resulted from the contribution of irradiation-induced defects. With increasing indentation depth, the dominant hardening mechanisms changed from the contribution of irradiation-induced defects, GNDs and statistically stored dislocations (SSDs) in the irradiated region to SSDs in the unirradiated substrate.

Model for the hardness-depth relationships of ion-irradiated nanocrystalline metals

In this work, a mechanistic model is proposed for ion-irradiated nanocrystalline (NC) metals to characterize the evolution of hardness as a function of the indentation depth at room temperature and under quasi-static loading condition. At the grain level, grain interiors (GIs) and grain boundaries (GBs)-dominated hardening are addressed simultaneously in the developed model, which is able to effectively characterize the contribution of geometrically necessary dislocations (GNDs), statistically stored dislocations (SSDs), irradiation-induced defects, Hall-Petch effect and the intrinsic strength of GBs. Thereinto, the GIs-dominated hardening mechanisms are systematically analyzed by considering the evolution of microstructures, which include the average density of dislocations and irradiation-induced defects within the plastic zone, and are noticed to be affected by the high ratio of GBs. Main attentions are focused on the description of GBs influence that covers dislocation hardening and defect hardening. The rationality and accuracy of the proposed model are validated by comparing the theoretical results with corresponding experimental data under different irradiation conditions. The proposed model offers a promising way to analyze the irradiation hardening mechanisms of NC metals.

Electrical-thermal-mechanical coupled modeling and simulation on deformation behaviors of Ti6554 alloy in electrically-assisted micro-tension

The electrically assisted forming (EAF) technology can reduce the load & stress and improve the formability of difficult-to-deform alloys due to its coupled thermal and athermal effects. To decouple the two effects and to elucidate each mechanism for deeply understanding and optimizing the EAF processing, we developed an electrothermalmechanical (ETM) macro-meso multiscale model by combing a modified Johnson-Cook (JC) constitutive model with the dislocation density based crystal plasticity finite element (DD-CPFE). The modified JC was used to describe the macroscopic electro-assisted deformation, while the meso-scale DD-CPFE was used to deal with the thermal and athermal effects on the slip rate. Statistically stored dislocations (SSDs) were introduced into the Orowan rate equation to explain the thermal effect part, and the athermal part was reflected through the effect of free energy change on the dislocation motion in the rate equation, due to the collision between free electrons and metallic ions. The simulated results show that the equivalent stress, strain, and dislocation densities are distributed heterogeneously in a meso-scale and sensitive to the current density. Local thermal effect due to geometrically necessary dislocations (GND) exerts no effect on the temperature gradient because of rapid heat conduction between grains. The thermal effect is dominated by the thermal expansion obviously reducing the flow stress in the single-phase and two-phase fields (0 to 70 A/mm2), while the athermal effect is effective in the two-phase field (corresponding to the current density range of 0 to 20 A/mm2) in reducing the flow stress, which is reasonably explained by the change of bonding strength in defect zones, such as grain boundaries, of the HCP structure via the first principle calculations.

Effect of pre-strain on springback behavior after bending in AA 6016-T4: Experiments and crystal plasticity modeling

Modeling springback in sheet materials is challenging in aluminum alloys, especially when a complex strain path is applied. This paper presents results from pure bending experiments on AA 6016-T4 sheet material, where various plastic pre-strains were first applied prior to bending. A crystal plasticity based elasto-plastic self-consistent (EPSC) model that includes the effect of backstress in the hardening law was used to predict final part shape after unloading. The backstress term in the model was calibrated using geometrically necessary dislocation (GND) content, measured experimentally by high resolution electron backscattered diffraction (HREBSD). The EPSC model predicted springforward angles for unstrained 1 mm AA 6016-T4 sheet with an error of 0.4% (0.3°) in the worst case, while the J2 plasticity isotropic model overpredicted springforward angles by as much as 2.4% (2°). For cases where uniaxial, plane-strain, and biaxial pre-strains were first imparted to the sheets before bending, the EPSC model with backstress accurately predicted the transition from springforward to springback, while the EPSC model without backstress did not. Backstress influence on model accuracy, which increased with greater pre-strain levels, appears to be correlated to the statistically stored dislocation (SSD) density computed by the model at the end of each pre-strain step.

Inconsistent nanoindentation test hardness using different Berkovich indenters

When testing the nanoindentation hardness of the same sample with different Berkovich indenters, inconsistencies arise even when the frame stiffness and indenter tip area functions are regularly calibrated. This phenomenon has not been fully understood, making it challenging to accurately test and compare material hardness data from different laboratories. To address this issue, incremental test hardness caused by indenter tip defects and indentation size effects (ISE) is quantified. The ISE correction method proposed in this study is based on the Nix-Gao model for nanoindentation load-indentation depth (P-h) curves, and an area function equivalent modeling method is used to reproduce the geometry of Berkovich indenters in finite element (FE) analysis. Although the test hardness using different Berkovich indenters is inconsistent, their intrinsic hardness remains consistent. The proposed ISE correction method is validated by FE simulation results for A508-3 and 316 L steel that match perfectly with the ISE-corrected experimental P-h curves. The analysis of load increments shows that tip defects affect the test result through statistically stored dislocation (SSD) and geometrically necessary dislocation (GND). Indenter tip defects mainly affect the nanoindentation test results through GND. The smaller the indenter tip radius, the higher the GNDs, and the higher the test hardness. The different effects of indenter tip defects on GND lead to inconsistent hardness measurements using different Berkovich indenters.

Crystal plasticity evaluation of the effect of grain morphology on compressive deformation behavior of AA2099 Al–Li alloy

The strip-like grain shape is one of three important factors (the strip-like grain shape, strong crystallographic texture and plate-like T1 precipitate) influencing the mechanical properties of the third-generation Al–Li alloys. However, studies on its effect have seldom been investigated to date. In the present study, an extended crystal plasticity finite element (CPFE) framework considering the strain gradient effect via incorporating the geometrically necessary dislocation (GND) density is constructed to investigate the compressive deformation behavior of studied AA2099 Al–Li alloy with strip-like grain shape. Good consistency with respect to the true stress-strain curve and texture characteristics between experimental and predicted results confirms the validity of constructed CPFE framework, as well as these fitted material parameters. Simulation results show the occurrence of aggregation for GND density not only near grain boundaries but also at grain interiors, which benefits in blocking the motion of the statistically stored dislocation (SSD) and the occurrence of obvious stress concentration in the constructed polycrystalline model. This demonstrates that the strip-like grain shape could exsert a nonnegligible influence on the mechanical response of studied AA2099 Al–Li alloy. Moreover, the difference between the predicted orientation distribution functions (ODFs) and the difference about the evolution of accumulative shear strain in 12 slip modes collectedly confirm that the strip-like grain shape does exert some influence on slip activities of studied AA2099 Al–Li alloy.

Origins of strengthening and toughening effects in twinned nanocrystalline alloys of low stacking fault energy with heterogeneous grain structure

Low stacking-fault energy (SFE) nanocrystalline alloys with pre-existing nanotwins (PNTs) and heterogeneous grain structure (HGS) exhibit exceptional strength-ductility combinations. This has been mainly ascribed to the multiple concurrent deformation mechanisms promoted by the low SFE, and back stress hardening from the strain gradient imposed by PNTs and HGS via activities of geometric necessary dislocations (GNDs). However, the influence of PNTs on dislocation configurations, and the role of intragranular statistically stored dislocations (SSDs) in the mechanical response are still unclear. Here, we uncover the origins of strengthening and toughening effects in a prototype low SFE multicomponent CoCrNi alloy with PNTs and HGS via atomistic simulations. The results show that HGS leads to significant strain partitioning between the smaller- and larger-grain domains and promotes the strain localization, while PNTs alleviate the strain localization and facilitate homogeneous deformation for better toughness. Moreover, PNTs efficiently block intragranular mobile Shockley partials and enhance the dislocation reaction probability, increasing the densities of sessile SSDs. The strengthening effects from both, dynamically increased sessile structures and plastic resistance induced by localized dislocations, are revealed by quantitative analysis on dislocation distributions. This indicates that the dislocation configurations correlated with strain localization are fortified owing to the presence of PNTs and HGS, which further enhance the flow stress on deformation. The present study demonstrates that, PNTs can enable efficient controlling of dislocation configurations upon deformation, while the strengthening and toughening effects of alloys with heterostructures are achieved by both GNDs correlated with localized strains and SSDs generated via dislocation reactions.

Void size, shape, and orientation effects in shear-dominated void coalescence across scales

In a stress state dominated by shear, pre-existing voids rotate, elongate, and close up to form micro-cracks, which interact through void coalescence and eventually may cause a complete loss of load-carrying capacity. The mechanism sets apart void coalescence in shear from that under tensile-dominated stress states, and the present work demonstrates that gradient strengthening affects the macroscopic strain at the onset of plastic flow localization leading to coalescence. Despite that zero or limited void growth develop in shear, a severe heterogeneous plastic straining develops near the void, which generates large plastic strain gradients accompanied by densities of Geometrically Necessary Dislocations (GNDs) in addition to the Statistically Stored Dislocations (SSDs) that controls conventional strain hardening. The GNDs lead to additional micron scale strengthening, and the present work investigates their effect on the plastic flow localization leading to void coalescence in shear by modeling voids embedded in a gradient-enhanced matrix material, thus revisiting the early work by Tvergaard (2008), which was carried out in a conventional scale independent setting. The Fleck–Willis gradient theory is assumed to govern the matrix surrounding the voids such that a material length parameter enters the analysis. Increasing the length parameters while keeping the void volume fraction and intervoid distance constant corresponds to diminishing the material microstructure. The results show that (i) voids with the minor axis in the direction of the shear (denoted “prolate”), give the highest ductility mainly due to the larger intervoid ligament; (ii) both the initial relative void size and the initial void orientation have strong effects on material ductility across the scales; (iii) the initial void orientation plays a fundamental part in the void deformation mechanism and the plastic field that develops prior to coalescence; (iv) the ductility increases substantially when down-scaling the microstructure where the gradient strengthening intensifies (corresponding to increasing the material length parameter). Throughout, fitting functions for the average shear angle at the onset of plastic flow localization are suggested, with respect to the relative void size, the initial void orientation, and the intrinsic material length parameter, to bring out the dependencies and facilitate using the unit cell results in continuum models.

Variant selection and morphology by the different cooling rates in Zr-xNb-0.4Mo alloys

Although many efforts have been made on understanding the variant selection rules, the interplay of these rules and their combined effects on variant selection have not been well addressed. In this work, variant selection and morphology by the different cooling rates in Zr-xNb-0.4Mo (x=0.2, 0.6 and 1.0 wt.%) alloys are characterized using scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) technique. The results show that the variation of variant selection and morphology is attributed to the Nb content, the parent β grain size, the cooling rate, the β grain boundary (GB) characteristics and the interplay among them. The Nb addition (Nb≤0.6 wt.%) decreases the average grain size of parent β grains, and the smaller parent β grain size generally results in the larger degree of variant selection (DVS) values in the individual parent β grain due to their resistance to the uniform nucleation and growth of α-variants. The slow cooling rate promotes the diffusional transformation and favors the formation of special β GBs and the β GBs with high dislocation density, which usually lead to a stronger DVS in the individual parent β grains. The very large weighted area percentage of α-variant in the individual parent β grains, which accounts for the stronger DVS in the individual parent β grains, is due to the special β GBs, the β GBs with high dislocation density and the incomplete martensitic transformation (martensitic-diffusional mixed transformation). The β GB with high dislocation density has a larger contribution to the strong DVS of individual parent β grains than the special β GB. In addition, the result shows that the low density of statistically stored dislocations (SSDs) can inhibit the nucleation and growth of the α-variant produced by the special β GB.

Role of particles and lattice rotation in tension–compression asymmetry of aluminium alloys

Plastic deformation of aluminium alloy AA6061 under tension and compression is investigated using a strain gradient crystal plasticity model implemented with the finite element method. This approach takes into account the microstructure as determined experimentally by electron backscatter diffraction (EBSD). The asymmetry of stress strain curves in loading of tension and compression (TC) is revealed for the FCC crystal structure. Plastic slip on activated slip systems leads to lattice rotation of crystal matrix and particles towards specific orientations, resulting in variation of moduli. The evolution of two different types of dislocations, statistically stored dislocations (SSD) and geometrically necessary dislocations (GND), is investigated to reveal the TC asymmetry due to slip resistance. It is found that the TC asymmetry at the yield strain is caused by lattice rotation of both crystal matrix and particles. When strain increases, the TC asymmetry is due to a combination of lattice rotation of crystal matrix and particle and variation of the GND density. As particle content increases, the TC asymmetry is mainly attributed to lattice rotation of particles at large strain.

Manipulating the strength and tensile ductility of a PM near α titanium alloy by adjusting the morphologies and volume fractions of α and βt domains

Powder metallurgy (PM) near α Ti−6Al−2Sn−4Zr−2Mo−0.1Si−0.5Y (wt.%) alloy with a low oxygen content and fabricated by thermomechanical powder consolidation of an elemental powder blend with a trace amount of Y addition was subjected to two heat treatments to obtain different microstructures which were free of grain boundary α (αGB) layers. One heat treatment (960°C/1h/AC, AC = air cooling) led to the formation of an α/βt microstructure consisting of 75.3 vol% primary α (αp) domains with globular and platelike morphologies, 21.5 vol% β transformed structure (βt) domains comprising ultrafine secondary α (αs) lamellae in a β matrix and 3.2 vol% thin β strips. The other heat treatment (960°C/1h/WQ+580°C/6h/AC, WQ = water quenching) led to the formation of a microstructure consisting of 38.2 vol% isolated αp plates, slabs, and globules dispersed in a βt matrix comprising nanometer-sized αs lamellae and residual β strips. The first microstructure rendered the alloy with high tensile strength of 1128 MPa and excellent tensile ductility of 15.6%, thanks to the activation of abundant <a> and <c+a> slips in all α grains and tensile twinning in the “hard” <0001> micro-textured α grains with the c-axis parallel to the tensile force direction which mitigated the strain localization and enhanced strain hardening. On the other hand, the harder nanostructure of the βt matrix in the second microstructure resulted in a significantly increased tensile strength of 1351 MPa while maintaining an excellent tensile ductility of 10.5%. This can be attributed to the activation of abundant <a> and <c+a> slips in thin α plates and a limited degree of tensile twinning in the “hard” α domains, as well as a large number of statistically stored dislocations (SSDs) within the micron-scaled α slabs/globules. Both microstructures rendered the alloy with favorable ductile fracture.

An efficient and minimalist scheme for continuum dislocation dynamics

Continuum dislocation dynamics methods have received considerable interests for simulating dislocation microstructures at the meso-scale, serving as potential tools for bridging the gap between micro- and macro-scale models for the plastic behaviours of crystalline materials. Recently, an exact evolution equation for the “all-dislocation” density that represents dislocation quantities over both space and dislocation-character domains has been developed by one of the present authors. The “all-dislocation” representation is superior to representations based on the Nye tensor or geometrically necessary dislocations (GND), since the statistically stored dislocation (SSD) contents will be preserved. In this paper, a numerical scheme is presented to solve the dynamics of the “all-dislocation” density efficiently, with long-range elastic interaction between dislocations accounted for via Mura's formula after singularity removal. The proposed simulation scheme is demonstrated by simulation examples in the multi-scale hierarchy, from intensive microstructures of individual dislocations including Frank-Read source and Orowan looping, to extensive microstructures of coarse-grained dislocation densities in single- and multi-slip in the face-centred cubic crystal structure.

The dependency of work hardening on dislocation statistics in cold rolled 1050 aluminum alloy

In this contribution, the phenomenon of work hardening is studied as a function of the nature of dislocation evolution with change in the level of deformation for commercially available 1050 Al alloy. To investigate the nature of dislocations in the cold-rolled aluminum alloy, total dislocation density was calculated using the indentation technique as well as by implementing two numerical approaches. For estimation of a statistically representative value of geometrically necessary dislocations (GND), electron backscattering diffraction measurements were performed over a large area (~ 0.5 mm2). The GND density of deformed samples was quantified by the implementation of a modified kernel average misorientation technique as well as by using Nye's dislocation density tensor for corresponding lattice curvature. The values of statistically stored dislocations (SSD) are obtained based on the assessment of the total dislocation density and GND values after different straining levels. The study provides both qualitative and quantitative illustrations of the mechanism of dislocation multiplication as thickness reduction increases, thereby, increasing the hardness of the samples. The results obtained reveal that the hardening of rolled materials is majorly governed by the SSD density at lower deformation. However, as the deformation level approaches the value of ~0.4, the density of GNDs rises and its contribution becomes significantly accountable for the strain hardening of the material. On the other hand, it has been observed that at lower straining levels the generated GNDs are trapped at grain boundaries and have a high contribution towards forest dislocations but with an increase of strain, the GNDs have a tendency to contribute nearly equally to mobile and forest dislocations. The estimated stored energies for samples subjected to rolling reduction ranging between 5.3 and 76% tend to change between the 5.6 kJ/m3 and 343.3 kJ/m3.

Temperature-dependent hardening of zirconium alloys under heavy ion-irradiation: Experimental observation and theoretical analysis

In this work, microstructure observation and thermo-mechanical property characterization of ion-irradiated Zr-0.5Sn-0.5Nb-0.3Fe-0.015Si alloys were addressed by both experimental measurements and theoretical analyses. In experiments, 6 MeV Au3+ irradiation was carried out for Zr alloys with the irradiation dose up to 30 displacements per atoms (dpa). Transmission electron microscopy (TEM) indicated the addition of solute elements could facilitate the formation of second phase particles (SPPs) like (Zr, Nb)2Fe, Zr(Nb, Fe)2 and Zr-Nb-Fe-Si precipitates in the unirradiated matrix, which were then transformed from the crystalline to amorphous state during the irradiation process. Moreover, it was indicated that there existed microband structures with different orientations inside the grains, and the actual irradiation depth had exceeded the value predicted by the SRIM simulation. The influence of irradiation-induced defects on the macroscopic mechanical behaviors of Zr alloys was characterized by both nano-indentation test (NIT) at 298 K and high-temperature nano-indentation test (HTNIT) at 573 K and 673 K. To theoretically address the hardness-indentation depth relations of ion-irradiated Zr alloys at elevated temperatures, a mechanistic model considering the underlying hardening mechanisms was developed. It was revealed that the irradiation hardening behavior was attributed to the contribution of irradiation-induced defects, while the decrease of hardness at elevated temperatures was ascribed to the weakening of all hardening mechanisms. In addition, with increasing indentation depth, the dominant hardening mechanisms changed from the contribution of irradiation-induced defects and geometrically necessary dislocations (GNDs) to those of statistically stored dislocations (SSDs).