Dislocation Core Diffusion Research Articles

Effect of natural and artificial ageing on steel mechanical properties and fracture toughness

The operating conditions of welded structures of shipbuilding steels, including operation at northern latitudes, determine high requirements for their quality. Materials used for such structures should guarantee stable mechanical properties, good processability during hull fabrication and serviceability at subzero temperatures. Strain aging is due to the thermodynamic non-equilibrium of steel structure in its initial state and gradual transition to the equilibrium state provided the diffusion mobility of interstitial atoms is sufficient. In unfavorable conditions, this can lead to the degradation of properties during processing (cold straightening, bending, welding), operation or long-term storage. The paper studies the probability of natural and artificial ageing processes in steels of different chemical compositions due to bulk diffusion and carbon dislocation core diffusion (dislocation pipe diffusion). The effect of strain ageing on mechanical properties and the CTOD parameter value has been examined.

Inelastic Deformation of Copper Nanoparticle Based Joints and Bonds

Abstract The inelastic deformation properties of sintered metal nanoparticle joints are complicated by the inherent nanocrystalline and nanoporous structures, as well as by dislocation networks formed in sintering or under cyclic loading. Creep rates of sintered nanocopper structures were found to be dominated by the diffusion of individual atoms or vacancies, while dislocation motion remained negligible up to stresses far above those of practical interest. Rapid sintering of one material led to unstable structures with particularly narrow necks between Cu particles and a dense network of dislocations. Creep rates were dominated by dislocation core diffusion within the necks to the nearest open pore surfaces. Exposure to elevated temperatures led to coarsening of the necks and, importantly, annihilation of dislocations, which reduced the creep strongly. Longer sintering of another material led to wider necks without excess dislocations and thus more stable structures. Creep rates were dominated by grain boundary diffusion within the necks and could be strongly enhanced by subsequent work hardening in mild cycling.

Quantitative Analysis of the Recovery Process in Pure Iron Using X-ray Diffraction Line Profile Analysis.

We conducted quantitative analysis of the recovery process during pure iron annealing using the modified Williamson-Hall and Warren-Averbach methods. We prepared four types of specimens with different dislocation substructures. By increasing the annealing temperature, we confirmed a decrease in dislocation density. In particular, screw-dislocation density substantially decreased in the early stage of the recovery process, while edge-dislocation density gradually decreased as annealing temperature increased. Moreover, changes in hardness during the recovery process mainly depended on edge-dislocation density. Increases in annealing temperature weakly affected the dislocation arrangement parameter and crystallite size. Recovery-process modeling demonstrated that the decrease in screw-dislocation density during the recovery process was mainly dominated by glide and/or cross-slip with dislocation core diffusion. In contrast, the decrease in edge-dislocation density during the recovery process was governed by a climbing motion with both dislocation core diffusion and lattice self-diffusion. From the above results, we succeeded in quantitatively distinguishing between edge- and screw-dislocation density during the recovery process, which are difficult to distinguish using transmission electron microscope and electron backscatter diffraction.

An improved method to model dislocation self-climb

Dislocations can provide short circuit diffusion paths for atoms resulting in a dislocation climb motion referred to as self-climb. A variational principle is presented for the analysis of problems in which fast dislocation core diffusion is the dominant mechanism for material redistribution. The linear element based self-climb model, developed in our previous work [1] Liu, Cocks and Tarleton (2020 J. Mech. Phys. Solids 135 103783), is significantly accelerated here, by employing a new finite element discretisation method. The speed-up in computation enables us to use the self-climb model as an effective numerical technique to simulate emergent dislocation behaviour involving both self-climb and glide. The formation of prismatic loops from the break-up of different types of edge dislocation dipoles are investigated based on this new method. We demonstrate that edge dipoles sequentially pinch-off prismatic loops, rather than spontaneously breaking-up into a string of loops, to rapidly decrease the total dislocation energy.

A new method to model dislocation self-climb dominated by core diffusion

The mobility of atoms in dislocation core regions is many orders of magnitude faster than in the surrounding lattice. This rapid atomic transport along dislocation cores plays a significant role in the kinetics of many material processes, including low-temperature creep and post-irradiation annealing. In the present work, a finite element based analysis of the dislocation core diffusion process is presented; based on a variational principle for the evolution of microstructure. A dislocation self-climb model is then developed by incorporating this finite element core diffusion formulation within the nodal based three-dimensional discrete dislocation dynamics framework. The behaviour of an isolated loop in bcc iron is briefly reviewed, and simulations are extended to include the loop coarsening processes of both parallel and non-parallel loops by self-climb plus glide mechanisms, in which the huge time scale separation between climb and glide is bridged by an adaptive time stepping scheme. Excellent agreement is obtained between the numerical simulation, the theoretical solution of rigid prismatic loops and published experimental results. The coarsening process of a population of loops is simulated to investigate the mechanisms of the accumulative interactions and large-scale-patterning in bcc materials.

Effects of Thermal Cycling on Creep of SnAgCu Solder Joints

The long-term life of properly optimized high-end microelectronics assemblies is commonly limited by fatigue of the solder joints. The most credible assessments of this rely on modeling-based extrapolation and generalization of accelerated test results. As the validity of extrapolations to long-term service can rarely if ever be verified experimentally, there is a strong need for mechanistically justified models. The models all rely on predictions of stresses, strains, and perhaps functions of those versus time and temperature in cycling. Finite-element-based predictions of these require the assumption of relatively complex constitutive relations capable of predicting inelastic strain rates under continuously varying stresses and temperatures. These are usually extracted from a series of creep or stress relaxation experiments and generalized under the implicit assumption that the inelastic deformation is dominated by dislocation creep. However, the resulting constitutive relations were recently shown to be strongly misleading. It was suggested that this is a result of the inelastic deformation at the stresses and temperatures of primary concern actually being dominated by dislocation core diffusion. This paper lends further support for this picture, showing additional contributions from diffusion on cycling induced dislocation structures to make for ongoing, usually nonmonotonic, variations in deformation rates from cycle to cycle. These effects are certain to have major consequences for modeling. In fact, it has been argued that the combination of wrong constitutive relations with a wrong damage function has led to a partial cancellation of errors across a limited parameter range, but that this cannot be counted on for more detailed predictions of accelerated test results and does not allow for interpretation of such results in terms of even qualitative trends in service.

Effects of Zr and Si addition on high-temperature mechanical properties and microstructure in Ti-10Al-2Nb-based alloys

The solid-solution strengthening effect for the single and simultaneous addition of Zr and Si on the compression strength and the creep property in Ti-10Al-2Nb based alloys (at%) with an equiaxed α phase designed by us, was investigated. The compression strengths of these alloys were investigated at temperatures between room temperature and 650 °C. The largest solid-solution strengthening effect was obtained for the alloys with Zr and Si simultaneously added, followed by alloys with the single addition of 2Zr or 0.5Si. For the same amounts of addition elements, the solid-solution strengthening effect of Si was larger than that of Zr. This was attributed to the larger atomic size misfit between Ti and Si than that of between Ti and Zr. A creep test was conducted for Ti-10Al-2Nb-2Zr and Ti-10Al-2Nb-2Zr-0.5Si within a temperature range of 550–650 °C under an applied stress between 137 and 240 MPa. The alloy with Si exhibited a longer creep life for all tested conditions due to a large solid-solution strengthening effect and high compression strength.The deformation mechanisms of the compressive deformation and tensile creep deformation were analyzed using an Arrhenius-type equation. Considering the stress exponent and activation energy, the deformation mechanism of the compressive deformation was identified as low-temperature power-law creep controlled by dislocation core diffusion. While, the deformation mechanism of the creep deformation was identified as high-temperature power-law creep controlled through lattice diffusion.

Trading off between dynamic strain aging and substructure evolution in κ-carbide-free lightweight steel at room temperature

The previous proposed models to describe the room temperature dynamic strain aging of twinning-induced-plasticity steels appear to be theoretically invalid in the case of lightweight grades. The proposed theory in the present work accentuates the high capability of the experimented dilute solid solution in progressive formation and refinement of the cell structures. The higher dislocation population in the cell-walls in comparison to that of cell-interiors is viable enough to increase the stress assisted drift and stimulate the sub-boundaries preferred sites to accommodate the solutes. The short-range dislocation core diffusion enables the cell-walls to assist the strain aging to occur.

Effect of Graphitic Carbon Nitride Nanosheets Addition on the Microstructure and Mechanical Properties of Sn-3.5Ag-0.5Cu Solder Alloy

The microstructure and mechanical properties of Sn-3.5Ag-0.5Cu (SAC355) solder alloy reinforced with different amounts of graphitic carbon nitride nanosheets (GCNNs) are assessed. The as-synthesized GCNNs were examined by a scanning electron microscope and X-ray diffraction techniques. A set of composite solders were fabricated by adding GCNNs with different concentrations (0 wt.%, 0.25 wt.%, 0.5 wt.%, and 1.0 wt.%) to SAC355 solder alloy. After a solution heat treatment, samples were immediately aged at temperatures ranging from 343 K to 403 K for 2 h followed by water quenching at 273 K. The mechanical properties of the composite solders were assessed using the indentation hardness test. The experimental results showed that the minimum creep rate values estimated from hardness data increased progressively with increasing weight percentage of GCNNs and/or aging temperature. The homogeneous distribution of GCNNs in the composite solders allows microscopic defects such as cracks to develop throughout the solders leading to higher creep rate values. The calculated values of the stress exponent and the activation energy for the creep process indicated that the creep rate controlling process depends on dislocation core diffusion in the tin matrix.

Investigation of microstructure and mechanical properties of Sn-xCu solder alloys

The microstructure and mechanical properties of five binary pre-aged Sn-Cu alloys with varying Cu contents were investigated. The Cu compositions examined varied from 1 wt% to 5 wt%. Serial aging heat treatment processes were performed at 373, 393, 413 and 433 K with a holding time of 2 h at each temperature. The microstructural characteristics of the tested alloys have been investigated using scanning electron microscope (SEM) and X-rays diffraction (XRD). Typical indentation creep curves were derived from hardness values. The minimum creep rate is increased as the Cu content increased up to 4 wt%, but above this level the trend is reversed. Moreover, increasing aging temperature resulted in an increase in the minimum creep rate for the all tested alloys. The mean values of energy activating the creep process are in agreement with that quoted for dislocation core diffusion mechanism.

Effect of creep on the Bauschinger effect in a polycrystalline austenitic stainless steel

A combined thermodynamic/kinetic approach is adopted to derive the climb-controlled recovery of dislocation junctions on individual slip planes in a material during creep when dislocation core diffusion is the rate controlling kinetic process. The model is used in an integrated multi-scale crystal plasticity/creep self-consistent framework to evaluate the effect of creep pre-strain on the Bauschinger effect in a polycrystalline austenitic stainless steel. The model predictions are in good agreement with experimental findings of the effect of tensile creep on the subsequent low temperature response in tension and compression and on the development of residual stresses determined from neutron diffraction studies.

Residual stresses in high temperature corrosion of pure zirconium using elasto-viscoplastic model: Application to the deflection test in monofacial oxidation

The paper is devoted to modeling residual stresses and strains in an oxide film formed during high temperature oxidation. It describes the deflection test in isothermal high-temperature monofacial oxidation (DTMO) of pure zirconium. The model incorporates kinetics and mechanism of oxidation and takes into account elastic, viscoplastic, growth and chemical strains. Different growth strains models are considered, namely, isotropic growth strains given by Pilling–Bedworth ratio, anisotropic growth strains defined by Parise and co-authors and physically based model for growth strain proposed by Clarke. Creep mechanisms based on dislocation slip and core diffusion, are used. A mechanism responsible for through thickness normal stress gradient in the oxide film is proposed. The material parameters are identified using deflection tests under 400°C, 500°C and 600°C. The effect of temperature on creep and stress relaxation is analyzed. Numerical sensitivity study of the DTMO experiment is proposed in order to investigate the effects of the initial foil thickness and platinum coating on the deflection curves.

High temperature mechanical behavior of alumina dispersion strengthened copper alloy with high content of alumina

The microstructure and its effects on the high temperature mechanical behavior of Cu–2.7%Al2O3 (volume fraction) dispersion strengthened copper (ADSC) alloy were investigated. The results indicate that fine alumina particles are uniformly distributed in the copper matrix, while a few coarse ones are distributed on the grain boundaries. Tensile tests results show that Hall-Petch mechanism is the main contribution to the yield strength of ADSC alloy at room temperature. Its high temperature strength is attributed to the strong pinning effects of alumina particles on the grain and sub-grain boundaries with dislocations. The ultimate tensile strength can reach 237 MPa and the corresponding yield strength reaches 226 MPa at 700 °C. Tensile fracture morphology indicates that the ADSC alloy shows brittleness at elevated temperatures. Creep tests results demonstrate that the steady state creep rates at 400 °C are lower than those at 700 °C. The stress exponents at 400 °C and 700 °C are 7 and 5, respectively, and the creep strain rates of the ADSC alloy are controlled by dislocation core diffusion and lattice diffusion.

Supper strong nanostructured TWIP steels for automotive applications

A ductile and super strong nanostructured twinning-induced plasticity (TWIP) steels were fabricated by cold rolling and recovery treatment. This strong and ductile nanostructured alloy can be used for the anti-intrusion part of body-in-white. Cold rolling was used to produce intensive nano-twins so that the microstructure was greatly refined. Recovery is employed to anneal dislocations for improving the ductility. A physical model is proposed to describe the relationship between the yield stress and the twin density. Furthermore, the present work also found that the activation energy for recovery is ~160J/mol, which implies that the recovery mechanism is governed by dislocation core diffusion.

Highly-enhanced reflow characteristics of sputter deposited Cu interconnections of large scale integrated devices by optimizing sputtering conditions

Improving the reflow characteristics of sputtered Cu films was attempted by optimizing the sputtering conditions. The reflow characteristics of films deposited under various sputtering conditions were evaluated by measuring their filling level in via holes. It was found that the reflow characteristics of the Cu films are strongly influenced by the deposition parameters. Deposition at low temperatures and the addition of H2 or N2 to the Ar sputtering gas had a significant influence on the reflow characteristics. Imperfections in the Cu films before and after the high-temperature, high-pressure treatments were investigated by positron annihilation spectroscopy. The results showed that low temperature and the addition of H2 or N2 led to films containing a large number of mono-vacancies, which accelerate atomic diffusion creep and dislocation core diffusion creep, improving the reflow characteristics of the Cu films.

“Conjugate Channeling” Effect in Dislocation Core Diffusion: Carbon Transport in Dislocated BCC Iron

Dislocation pipe diffusion seems to be a well-established phenomenon. Here we demonstrate an unexpected effect, that the migration of interstitials such as carbon in iron may be accelerated not in the dislocation line direction , but in a conjugate diffusion direction. This accelerated random walk arises from a simple crystallographic channeling effect. is a function of the Burgers vector b, but not , thus a dislocation loop possesses the same everywhere. Using molecular dynamics and accelerated dynamics simulations, we further show that such dislocation-core-coupled carbon diffusion in iron has temperature-dependent activation enthalpy like a fragile glass. The 71° mixed dislocation is the only case in which we see straightforward pipe diffusion that does not depend on dislocation mobility.

Numerical simulation of NbC precipitation in microalloyed steel

This work describes with the investigation of the precipitation kinetics of NbC in microalloyed steel. Using the thermo-kinetic software MatCalc, computer simulations of NbC precipitation are carried out and compared with several independent experimental results, measured in austenite and ferrite. The selected experiments involve a variety of different dislocation densities originating from distinct thermo-mechanical treatments. Two separate populations of NbC precipitates are accounted for in the simulations, representing precipitates on grain boundaries as well as dislocations. Furthermore, three different diffusion mechanisms are taken into account, which are bulk diffusion in the undisturbed crystal, accelerated diffusion along the dislocation core and fast diffusion along grain boundaries. It is demonstrated that deformation-induced dislocation densities higher than 1013 m−2 lead to prominent diffusion along dislocation networks. Therefore, in such cases, the precipitation kinetics of NbC is dominated by the pipe diffusion mechanism, and the precipitation process is several orders of magnitude faster compared with NbC precipitation in unstrained, well-annealed microstructures.

Characterization of hot deformation behaviors of wrought and P/M oxygen free coppers (OFCs) using processing maps

Wrought and powder sintered (P/M) oxygen free coppers (OFC) were subjected to hot deformation testing over the range of strain rates (0.01–10.0s−1) and temperatures (200–800°C). Processing maps of both materials have exhibited different deterministic domains representing dynamic recrystallization (DRX), which occurs in the following temperature and strain rate ranges: for wrought copper, 400–600°C and 0.01–0.1s−1, 600–800°C and 0.01–10.0s−1; for P/M one, 600–800°C and 0.01–1.0s−1. The domain for wrought copper has higher efficiency of power dissipation with increasing temperature and decreasing strain rate. For P/M OFC, the region at temperature of 600°C and strain rate of 10−2s−1showed peak efficiency. The results on processing maps have well correlated with those obtained from kinetic analysis. The apparent activation energies estimated in the DRX domains are 146.04 and 190.67kJ/mol for wrought and P/M OFCs, respectively, which suggest that dislocation core diffusion and lattice self-diffusion are the rate controlling mechanism each. In all domains, the average grain diameter varies linearly with Zener–Holloman parameter.

Creep Mechanisms in a Fine-Grained Al-5356 Alloy at Low Stress and High Temperature

Monotonic creep tests were carried out on fine-grained Al-5356 alloy with grain size dg ¼ 5 � 0:5 mm by the helicoid spring specimen technique at homologous temperatures ranging from 0.63 to 0.74 and applied stresses of 0.13 to 1.42 MPa. At stresses lower than about 0.50 MPa, Bingham-type viscous creep with activation energy Q ¼ 80 � 25 kJ/mol, characterized by a threshold stress which decreases with increasing temperature, was predominant. At a stress above about 0.50 MPa, grain boundary sliding with a stress exponent n ¼ 2 and Q ¼ 85 � 25 kJ/mol obviously contributed to the measured creep data. Stress redistribution was evaluated, and it did not greatly influence the stress exponent. The creep mechanisms were elucidated with respect to standard creep models supported by the substructures studied by transmission electron microscopy. Viscous creep (n ¼ 1) was identical to be Harper-Dorn creep controlled by dislocation core diffusion. The motion of jogs on edge dislocations dependent on dislocation core diffusion was observed to control the creep. Grain boundary sliding accommodated by slip with n ¼ 2 was noted, while hardening and the recovery of dislocations at grain boundaries were suggested to control the creep. Microstructural observations along with a determination of parametric variations in the creep rates were useful for identifying the underlying deformation mechanisms. [doi:10.2320/matertrans.M2011143]

Materials modeling and finite element simulation of isothermal forging of electrolytic copper

Isothermal forging of electrolytic copper is modeled using finite element simulation and materials models involving kinetic analysis and processing maps with a view to validate their predictions. Forging experiments were conducted on a rib–web (cup) shape in the temperature range of 300–800°C and at speeds of 0.01–10mms−1. The processing map for hot working of electrolytic copper revealed two domains in the temperature and strain ranges of (1) 400–600°C and 0.001–0.01s−1, (2) 650–950°C and 0.3–30s−1, where dislocation core diffusion and lattice self-diffusion are the rate-controlling mechanisms, respectively. Finite element simulation using the relevant experimental constitutive equations, predicted load–stroke curves that correlated well with the experimental data. The simulation has shown that there is a strain variation from about 0.4 to 4 in the web and rib regions of the forged component, although the dynamically recrystallized grain structure is fairly uniform, suggesting that dynamic recrystallization (DRX) is not sensitive to strain once the steady state flow is reached. The DRX grain size in the component is linearly dependent on Z and is similar to that predicted by the materials model after discounting for the longer time taken for the component removal.