Deformation of a nanocube with a single incoherent precipitate: role of precipitate size and dislocation looping

ABSTRACT

Precipitate hardening is a key strengthening mechanism in metallic alloys. Classical models for precipitate hardening are based on the average behaviour of an ensemble of precipitates, and fail to capture the complexity of dislocation-precipitate interactions that have recently been observed at individual precipitates in simulations and in-situ electron microscopy. In order to achieve tailored mechanical properties, detailed deformation mechanisms at specific precipitates that account for precipitate size, crystallography, and defect structure must be understood, but has been challenging to achieve experimentally. Here, in-situ scanning electron microscope mechanical testing is used to obtain the compressive stress–strain behaviour at an individual, incoherent Au precipitate within a Cu nanocube, and determine the influence of precipitate and cube size on yield strength and strain hardening. TEM imaging and strain mapping of the initial structure shows misfit dislocations at the Au precipitate, threading dislocations that traverse the Cu shell, and localised and anisotropic strain near the precipitate and threading dislocation. These nanocubes have yield strengths of 800–1000?MPa and strain hardening rate of 1–4?GPa. Yield strength is found to depend on the distance from the precipitate interface to the cube edge, while strain hardening depends on both cube size and precipitate size. An analytical model is developed to quantify the contribution of Orowan looping, Orowan stress, back stress and image stress to plasticity at the Au precipitate. Orowan stress is found to be the largest contributor, followed by back stress and image stress.     

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

The 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.     

Fatigue in precipitation hardened materials: a three-dimensional discrete dislocation dynamics modelling of the early cycles

Three-dimensional dislocation dynamics (DD) fatigue simulations in precipitation hardened metals is a major challenge in terms of numerical development. Several precipitate configurations have been investigated with an original treatment of precipitate–dislocation interactions and a parallelized DD code. In grains containing single-sized shearable particles (r _p?=?160?nm), strain is localized in clear bands where the precipitates are totally sheared-off. The fatigue behaviour involves an initial hardening followed by severe cyclic softening and significant surface slip irreversibility. In the presence of large single-sized particles (r _p?=?400?nm), the persistent slip band (PSB) structure is accompanied by highly reversible surface displacements. Slip dispersion originates from Orowan loops that have little effect on the mechanical response. The mechanical behaviour of a bimodal distribution is intermediate between the two above cases with the above microstructural features coexisting within the same grain. Unlike in the monomodal large-particle case, where all the particles retain their initial strength, some of the large particles of the bimodal distribution undergo a significant strength reduction.     

Influence of ageing on the low cycle fatigue behaviour of an Al–Mg–Si alloy

Abstract

The low cycle fatigue (LCF) performance of AA6063 Al–Mg–Si alloy at under-aged (UA), peak-aged (PA) and over-aged (OA) conditions has been examined to understand the micromechanism of fatigue and the associated dynamic structural changes in this alloy. The LCF behaviour of the differently aged AA6063 alloys has been studied at strain amplitudes ranging between 0.2 and 1.0% under strain control mode. The UA state exhibits pronounced cyclic hardening unlike the PA and the OA states at strain amplitudes greater than 0.4%. The PA and the OA states show hardening only for a few cycles followed by prolonged softening. Characterisations of the micro- and the sub-structural alterations due to LCF establish that the phenomenon of dynamic precipitation results in cyclic hardening the UA alloy. The softening of PA alloy occurs due to shearing of precipitates and that in the OA alloy takes place owing to reversibility of slip by the formation and annihilation of the Orowan loops around the β (Mg₂Si) precipitates. Analyses of the hysteresis loops reveal Masing, nearly-Masing and non-Masing behaviour in the UA, OA and PA states, respectively. Analyses of the asymmetry factor of the hysteresis loops assist to infer that the Masing behaviour in the UA alloy is due to dislocation–dislocation interactions, whereas the nearly-Masing behaviour in the OA alloy and the non-Masing behaviour in the PA alloy are the consequence of varying degrees of dislocation–precipitate interactions associated with inhomogeneous deformation.     

A New View of Incipient Plastic Instability during Nanoindentation

Whether the dislocation nucleation or the sudden dislocation multiplication dominates the incipient plastic instability during the nanoindentation of initial defect-free single crystal still remains unclear. In this work, the dislocation mechanism corresponding to the incipient plastic instability is numerically investigated by coupling discrete dislocation dynamics with the finite element method. The coupling model naturally introduces the dislocation nucleation and accurately captures the heterogeneous stress field during nanoindentation. The simulation results show that the first dislocation nucleation induces the initial pop-in event when the indenter is small, while for larger indenters, the incipient plastic instability is ascribed to the cooperation between dislocation nucleation and multiplication. Interestingly, the local dislocation densities for both cases are almost the same when the sudden load drop occurs. Thus it is inferred that the adequate dislocations generated by either nucleation or multiplication, or both, are the requirement for the trigger of incipient plastic instability. A unified dislocation-based mechanism is proposed to interpret the precipitate incipient plastic instability.     

The effect of size on dislocation cell formation and strain hardening in aluminium

The formation of dislocation cells has a significant impact on the strain hardening behaviour of metals. Dislocation cells can form in metals with a characteristic size defined by three-dimensional tangles of dislocations that serve as “walls” and less dense internal regions. It has been proposed that inhibiting the formation of dislocation cells could improve the strain hardening behaviour of metals such as Al. Here we employ in situ scanning electron microscope compression testing of pure Al single crystal pillars with physical dimensions larger, close to and smaller than the reported cell size in Al, respectively, to investigate the possible size effect on the formation of dislocation cell and the consequent change of mechanical properties. We observed that the formation of dislocation cells is inhibited as the pillar size decreases to a critical value and simultaneously both the strength and the strain hardening behaviour become strongly enhanced. This phenomenon is discussed in terms of the effect of dimensional restriction on the formation of dislocation cells. The reported mechanism could be applied in polycrystalline Al where the tunable physical dimension could be grain size instead of sample size, providing insight into Al alloy design.     

Aberration-corrected HAADF-STEM investigations of precipitate structures in Al–Mg–Si alloys with low Cu additions

Precipitates in a lean Al–Mg–Si alloy with low Cu addition (~0.10 wt.%) were investigated by aberration-corrected high angle annular dark field scanning transmission electron microscopy (HAADF-STEM). Most precipitates were found to be disordered on the generally ordered network of Si atomic columns which is common for the metastable precipitate structures. Fragments of known metastable precipitates in the Al–Mg–Si–(Cu) alloy system are found in the disordered precipitates. It was revealed that the disordered precipitates arise as a consequence of coexistence of the Si-network. Cu atomic columns are observed to either in-between the Si-network or replacing a Si-network column. In both cases, Cu is the center in a three-fold rotational symmetry on the Si-network. Parts of unit cells of Q′ phase were observed in the ends of a string-type precipitates known to extend along dislocation lines. It is suggested that the string-types form by a growth as extension of the B′/Q′ precipitates initially nucleated along dislocation lines. Alternating Mg and Si columns form a well-ordered interface structure in the disordered Q′ precipitate. It is identical to the interface of the Q′ parts in the string-type precipitate.     

A crystal plasticity finite element model for flow stress anomalies in Ni3Al single crystals

This paper presents a dislocation density-based non-Schmid constitutive model to address the anomalous thermo-mechanical behaviour of the L1₂ intermetallic single-crystal Ni₃Al. Ni₃Al is used as a strengthening precipitate (γ′ phase) in Ni-based superalloys. Addressing such anomalous behaviour by accounting for temperature-dependent flow stress and hardening evolution, as well as orientation-dependent tension–compression asymmetry, is necessary for modelling superalloys across a range of temperatures. While hardening in cube-slip systems results from statistically stored dislocations (SSDs), hardening in octahedral slip systems is due to both SSDs and cross-slip dislocations (CSDs). The constitutive model incorporates hardening evolution due to SSDs and CSDs. Experimental data for Ni₃Al-type single crystals, available in the literature, are used to calibrate material parameters. Subsequently, results of crystal plasticity FEM simulations are compared with experimental data for several orientations under constant strain rate and creep loading conditions for a wide range of temperatures. The model is able to correctly predict the response of L1₂ intermetallic single crystals including features of anomalous flow stress and non-Schmid yield behaviour.     

Kinetics of dislocation ensembles in deformable irradiated materials

The development of plastic instability in the initial deformation stages of irradiated materials is studied. The dependence of the fraction of dislocations which overcome obstacles in the dynamic regime (dislocation “channeling”) on the degree of radiation hardening (irradiation dose) and the dislocation velocity is analyzed. It is shown that this effect plays a role in radiation embrittlement of reactor materials. Fiz. Tverd. Tela (St. Petersburg) 40, 1631–1634 (September 1998)     

Atomistic simulation of the stacking fault energy and grain shape on strain hardening behaviours of FCC nanocrystalline metals

ABSTRACT

Ultra-fine grained copper with nanotwins is found to be both strong and ductile. It is expected that nanocrystalline metals with lamella grains will have strain hardening behaviour. The main unsolved issues on strain hardening behaviour of nanocrystalline metals include the effect of stacking fault energy, grain shape, temperature, strain rate, second phase particles, alloy elements, etc. Strain hardening makes strong nanocrystalline metals ductile. The stacking fault energy effects on the strain hardening behaviour are studied by molecular dynamics simulation to investigate the uniaxial tensile deformation of the layer-grained and equiaxed models for metallic materials at 300?K. The results show that the strain hardening is observed during the plastic deformation of the layer-grained models, while strain softening is found in the equiaxed models. The strain hardening index values of the layer-grained models decrease with the decrease of stacking fault energy, which is attributed to the distinct stacking fault width and dislocation density. Forest dislocations are observed in the layer-grained models due to the high dislocation density. The formation of sessile dislocations, such as Lomer–Cottrell dislocation locks and stair-rod dislocations, causes the strain hardening behaviour. The dislocation density in layer-grained models is higher than that in the equiaxed models. Grain morphology affects dislocation density by influencing the dislocation motion distance in grain interior.     

The role of dislocations in radiation strenghtening of alkali halide crystals

The dependence of activation volume and dislocation start stress in sodium and calcium chloride crystals on-radiation dosage (in the range 10⁴–10⁹rad) is studied. It is established that these functions indicate that the hardening of crystals subjected to radiation is of a dislocation nature. Analysis of data from the literature leads to the conclusion that in the medium and high radiation dose region planar precipitates and surrounding dislocations formed by halogen molecules are responsible for hardening.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 99–103, June, 1976.     

Specific features in the generation and motion of dislocations in heat-treated silicon wafers

The specific features in the generation and motion of dislocations in silicon single-crystal wafers after different heat treatments are investigated by the four-point bending technique. It is demonstrated that annealing of silicon single-crystal wafers at a temperature of 450°C leads to their substantial hardening as compared to the postgrowth state. The oxygen-containing precipitates and precipitate dislocation pileups formed in the silicon wafer bulk during multistage heat treatment are efficient heterogeneous nucleation sites of dislocations under the action of thermal or mechanical stresses. It is found that the multistage heat treatment of the silicon wafers under conditions providing the formation of an internal getter within their bulk results in considerable disordering of the wafer structure. The inference is made that the formation of the defect state in the crystal lattice of silicon and the strength characteristics of silicon wafers substantially depend on the temperature-time schedules of the low-temperature stage of multistage heat treatment.     

Size effects under plastic deformation of microcrystals and nanocrystals

A theoretical analysis of size effects in plastically deformed crystals with transverse sizes in micro and nanometer ranges has been performed in the framework of the dislocation-kinetic approach. The analysis is based on the evolution equation of the dislocation density in these crystals and takes into account the generation of dislocations from surface dislocation sources and the escape of dislocations from the crystal through the crystal surface. It has been established that the generation of dislocations from the sources leads to a strong strain hardening of the crystal and that the escape of dislocations through the crystal surface results in a fast equilibration of these two kinetic processes. As a result, there occurs a strong “exhaustion” of strain hardening of thin crystals at the early stage of their plastic deformation in accordance with experiments. According to the theory, the flow stresses σ and transverse sizes D of microcrystals and nanocrystals are related by the expressions σ ∼ D ⁻ⁿ (n = 0.625–1.0), which are in agreement with the experiment.     

From dislocation junctions to forest hardening

The mechanisms of dislocation intersection and strain hardening in fcc crystals are examined with emphasis on the process of junction formation and destruction. Large-scale 3D simulations of dislocation dynamics were performed yielding access for the first time to statistically averaged quantities. These simulations provide a parameter-free estimate of the dislocation microstructure strength and of its scaling law. It is shown that forest hardening is dominated by short-range elastic processes and is insensitive to the detail of the dislocation core structure.     

Evidence for a transition in deformation mechanism in nanocrystalline pure titanium processed by high-pressure torsion

Nanocrystalline titanium with an average grain size of about 60–70 nm was prepared by high-pressure torsion. The results of hardness and structural evolutions indicate that a strain-induced hardening–softening–hardening–softening behaviour occurs. For coarse-grained titanium, 〈a〉-type dislocation multiplication, twinning and a high pressure-induced α-to-ω phase transformation play major roles to accommodate deformation, leading to a significant strain hardening. As deformation proceeds, dynamic recrystallisation leads to a decrease in dislocation density, especially for 〈a〉-type dislocations, leading to a slight strain softening. The 〈c〉-component dislocation multiplication dominates the deformation when the grain size decreases to 100 nm and 〈c〉-component dislocation multiplication, grain refinement and the α-to-ω phase transformation contribute to the second strain hardening. The following strain softening is attributed to dynamic recovery.     

Work hardening of alloys with short range order of atoms

The study presents analysis of the experimental flow curves for polycrystals of fcc concentrated solid solutions Ni-Cr and Ni-Mn. It was demonstrated that the flow curves of these alloys can be divided into a number of stages of work hardening, and stage II bisects into two substages: with parabolic, and linear hardening. It was demonstrated that the shape of the curves of work hardening is determined by the type of dependence L = f(σ), where L is the average path length of the motion of the dislocation;σ is flow stress. Some possible critical stresses of transition from stage to stage are discussed.     

Experimental and theoretical investigation of formation of the oxygen-containing precipitate-dislocation loop system in silicon

A model of coherent and incoherent oxygen-containing precipitates formed in an anisotropic silicon crystal due to the decomposition of a supersaturated oxygen solid solution has been considered. The stresses acting inside and outside the precipitate have been determined in the framework of the classical Eshelby’s approach. A criterion has been proposed for the generation of the misfit dislocation and the onset of motion of the perfect interstitial dislocation loop lying in the precipitate plane. The proposed precipitate model and criterion have been used for determining the dependence of the precipitate radius that corresponds to the formation of the misfit dislocation and the onset of motion of the perfect interstitial dislocation loop when an external load is applied to the sample. The results obtained are compared with the available experimental data.     

Modeling of motion of dislocation train through dislocation forest

Modeling methods were used to analyze tie motions of a train of dislocations through a dislocation forest. Differences were found in this motion in the basal plane of hep crystals and in the {11} plane in crystals of the NaCl type. It was established that the process of formation of dislocation loops when dislocations pass through a dislocation forest may be responsible for considerable strain hardening.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 97–103, December, 1979.     

Radiation hardening in Zircaloy-2

Annealed Zircaloy-2 was exposed to fast neutron fluences in the range 0.46 to 6.71 × 10¹⁹ nvt, E > 1 MeV, at temperatures of up to 450°C. The level of radiation hardening, as measured by the change in yield stress after irradiation, increased with irradiation temperature at least up to 380°C.

Post-irradiation annealing treatments showed that radiation anneal hardening occurred after irradiation at temperatures up to 325°C. After irradiation at 375°C, annealing treatments did not produce a further increase in the yield stress above that produced by the irradiation, however the radiation hardening persisted to 450°C. The uniform strain tended to decrease as the amount of radiation anneal hardening increased and as the fast neutron fluence increased above ～5 × 10¹⁸ nvt, E > 1 MeV.

The effects of irradiation temperature and post-irradiation annealing on the yield stress and on uniform strain are explained in terms of the strengthening of radiation damage defect clusters and their increased effectiveness to impede dislocation movement.