Slip Transmission Research Articles

Molecular dynamics simulations of plastic deformation in Nb/NbC multilayers

Experimental studies show that metal–ceramic multilayers can have high strength, high strain hardening and measurable plasticity when the ceramic layer is a few nanometers thick. Using molecular dynamics simulations we studied deformation mechanisms in metal–ceramic multilayers and the role of interface structure and layer thickness on mechanical behavior. NbC/Nb multilayers were investigated numerically using the molecular dynamics (MD) method with empirical interatomic potentials. The interface dislocation structure was characterized by combining MD simulations and atomically informed Frank–Bilby theory. Two sets of pure edge misfit dislocations have been identified. Plastic deformation in NbC/Nb multilayers commences first in the metal layers by nucleation and glide of lattice dislocations initiating from interface misfit dislocations. These dislocations glide in the Nb layer and are deposited at the interface. The deposited dislocations facilitate slip transmission from the Nb layer to the NbC layer. The critical strain corresponding to dislocation nucleation is insensitive to layer thickness but depends on interface dislocation structure. The strain hardening and the peak flow strength of NbC/Nb multilayers are associated with the slip transmission from Nb to NbC, and are correlated to the interfacial dislocations, Nb layer thickness, and NbC layer thickness. The flow strength decreases with increasing Nb layer thickness and decreasing the NbC layer thickness.

Atomistic observation of a crack tip approaching coherent twin boundaries

Coherent twin boundaries (CTBs) in nano-twinned materials could improve crack resistance. However, the role of the CTBs during crack penetration has never been explored at atomic scale. Our in situ observation on nano-twinned Ag under a high resolution transmission electron microscope (HRTEM) reveals the dynamic processes of a crack penetration across the CTBs, which involve alternated crack tip blunting, crack deflection, twinning/detwinning and slip transmission across the CTBs. The alternated blunting processes are related to the emission of different types of dislocations at the crack tip and vary with the distance of the crack tip from the CTBs.

Strain localization at dislocation channel–grain boundary intersections in irradiated stainless steel

The interaction of dislocation channels with grain boundaries in irradiated stainless steel was observed on multiple length scales using scanning electron microscopy (SEM) digital image correlation (DIC) and confocal microscopy (micro-scale), in situ straining and transmission electron microscopy (TEM) (nano-scale), and atomistic modeling (atomic scale). Interactions were divided into three classifications; slip transmission, discontinuous slip, and discontinuous slip that induced grain boundary slip. DIC and confocal microscopy were used to quantify the plastic strain at dislocation channel–GB intersections. In situ TEM was used to image dislocations inside of channels as they interacted with the grain boundary. Slip in the dislocation channels, as observed by TEM, was found to involve cross slip between different slip planes, as well as the possibility of different slip systems activated on parallel slip planes. Atomistic simulations agreed well with experiments on the nature of channel-grain boundary interactions and also showed elevated levels of elastic stress at DC–GB intersections where slip was discontinuous with no slip transmission. The two distinct classifications of discontinuous slip are significant, suggesting two possible cracking mechanisms that both lead to the rupture of the oxide over the grain boundary.

Influence of irradiation damage on slip transfer across grain boundaries

The interaction of lattice dislocations with grain boundaries in proton- and ion-irradiated austenitic stainless steels is investigated. At the macroscale, interactions of dislocation channels with grain boundaries result in slip blockage, slip transmission and slip along the grain boundary with an associated in-plane displacement. At the dislocation level, slip transmission prediction is governed by the strain energy density minimization. However, the importance of the local resolved shear stress increases, in the sense that it must be of sufficient magnitude to propagate the dislocations through the damaged matrix. If this condition is not satisfied, the grain boundary will activate an alternative mechanism to relieve the strain accumulated from accommodation of lattice dislocations and the stress concentration associated with the formation of a dislocation pile-up. One observed relief mechanism involves the nucleation and propagation of a crack along the grain boundary, which is accompanied by an out-of-plane displacement of the boundary.

A Practical Meso-Scale Polycrystal Model to Predict Dislocation Densities and the Hall–Petch Effect

A practical SuperDislocation Model (SDM) has been developed and implemented to predict dislocation density distributions in a plastically deforming polycrystal and thereby the Hall­Petch effect. The model is composed of two stepwise simulation scales; the first scale is a finite element model of a polycrystal using a novel single-crystal constitutive equation and the second scale redistributes the mobile part of the dislocation density within grains consistent with the plastic strain distribution, and enforces slip transmission criteria at grain boundaries that depend on local grain and boundary properties. In this work, deformation of Fe­3% Si tensile specimen is simulated using SDM to compare dislocation densities obtained from the highresolution electron backscatter diffraction (HR-EBSD). The model accurately predicts the measured dislocation density at 10% deformation. In addition, size-dependent simulations show that the model qualitatively predicts Hall­Petch slope as well as the grain boundary strength of Fe­ 3% Si. [doi:10.2320/matertrans.MA201305]

Effect of retained beta layer on slip transmission in Ti–6Al–2Zr–1Mo–1V near alpha titanium alloy during tensile deformation at room temperature

Slip is the main plastic deformation mechanism in titanium alloys at room temperature. This is especially so for near alpha titanium alloy like Ti–6Al–2Zr–1Mo–1V, which contains low beta stabilizing and high aluminum (alpha stabilizing) element additions. The effects of retained beta layers on slip transmission across α/β interfaces in Ti–6Al–2Zr–1Mo–1V during tensile deformation have been studied in the current work. High resolution scanning electron microscopy (HR-SEM) and electron backscatter diffraction (EBSD) techniques were used to study the deformation microstructure. The results indicate that the full Burgers crystal orientation relationship (OR) between the α and the thin retained β phase layers facilitates slip transition but is not the necessary requirement/restriction. Some novel slip trace morphologies that are characterized by deflection and bifurcation (fork-like morphology) are revealed in the retained β layers between two abutting α grains. The possible reasons for these different slip transmission patterns are analyzed by EBSD results and a schematic model is proposed.

Slip transmission in bcc FeCr polycrystal

Grain boundaries induce heterogeneities in the deformation response of polycrystals. Studying these local variations in response, measured through high resolution strain measurement techniques, is important and can improve our understanding of fatigue damage initiation in the vicinity of grain boundaries and material hardening. In this work, strain fields across grain boundaries were measured using advanced digital image correlation techniques. In conjunction with strain measurements, grain orientations from electron back-scattered diffraction were used to establish the dislocation reactions at each boundary, providing the corresponding residual Burgers vectors due to slip transmission across the interfaces. A close correlation was found between the magnitude of the residual Burgers vector and the local strain change across the boundary. When the residual Burgers vector magnitude (with respect to the lattice spacing) exceeds 1.0, the high strains on one side of the boundary are paired with low strains across the boundary, indicating the difficulties for slip dislocations to penetrate the grain interfaces. When the residual Burgers vector approaches zero, the strain fields vary smoothly across the boundary due to limited resistance to slip transmission. The results suggest that the residual Burgers vector magnitude, which relates to the GB (Grain Boundary) resistance to slip transmission, enables a quantitative analysis of the accumulation of strain at the microstructural level and the development of strain heterogeneities across grain boundaries. The results are presented for FeCr bcc alloy which exhibits single slip per grain making the measurements and dislocation reactions rather straightforward. The work points to the need to incorporate details of slip dislocation–grain boundary interaction (slip transmission) in modeling research.

On Decision Aided Carrier Phase and Frequency Offset Estimation in Coherent Optical Receivers

We investigate carrier estimation (CE) for coherent optical receivers where the received signal is impaired by additive white Gaussian noise, laser phase noise, and frequency offset. Best practical 4-, 8-, and 16-point constellations are identified. A generalized differential encoding rule for signal constellations is presented. Performance of our complex-weighted decision-aided maximum-likelihood (CW-DA-ML) phase noise and frequency offset estimator is analyzed at low signal-to-noise ratio (SNR) and the optimal filter lengths are found. CW-DA-ML CE is put in perspective with respect to two fundamental estimators in the literature: (i) differential frequency estimator followed by block <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th power phase estimator (DiffFE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th CE), and (ii) fast Fourier transform based frequency estimator followed by block <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th power phase estimator (FFTbE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th CE), in terms of laser linewidth tolerance, frequency estimation range and speed, SNR threshold, and cycle slip probability. CW-DA-ML CE is 2.5 and 10.5 times faster than DiffFE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th CE in 4 phase-shift keying and 16 quadrature amplitude modulation signals, respectively, at a 1-dB system penalty for a bit-error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . Our CE has lower cycle slip probability and transmission overhead than DiffFE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th and FFTbE- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th CE. Hence, our CE is shown to be favourable in pilot-assisted (PA) systems. A PA CW-DA-ML CE is introduced and shown to be robust against time-varying frequency offset with minimal training overhead. Analog-to-digital convertor quantization error on our CE performance is also addressed.

Transmission performance improvement in digital coherent system by suppressing cycle slip using statistical analysis algorithm

Cycle slip adversely affects transmission performance in digital coherent systems. Proposed is an algorithm using statistical analysis for suppressing cycle slip in a digital coherent system. The cycle slip suppression effect, transmission performance, and nonlinear tolerance of the proposed algorithm were numerically investigated. The proposed algorithm enables cycle-slip-free wavelength division multiplex transmission under the presence of nonlinear optical effect and improves transmission performance.

Influence of boundary structure and near neighbor crystallographic orientation on the dynamic damage evolution during shock loading

The role of crystallographic orientation on damage evolution in ductile metals during shock loading has been investigated. By utilizing large-grained copper specimens, it has been shown that the development of intragranular damage, in the form of void growth and coalescence, is influenced by the grain orientation with respect to the applied load. Additionally, strain incompatibility and the inability to promote transmission or activation of secondary dislocation slip across a grain boundary, are proposed as the likely cause for intergranular failure. Finally, the free surface velocity profiles of each grain, specifically the decay of the oscillations after the pull-back, correlated well with the amount of damage measured within the respective grain.

Plastic strain localization and fatigue micro-crack formation in Hastelloy X

In polycrystalline metals, local deformation heterogeneities induced by the microstructure influence fatigue crack initiation and micro-crack propagation. The localization in plastic strains associated with heterogeneous deformation has been described as a necessary condition and a precursor for the nucleation of fatigue cracks. However, a clear and quantitative assessment of the correlation between strain localization and fatigue micro-crack lengths requires further investigation. In this work, during interrupted loading experiments, high resolution deformation measurements using digital image correlation are made on polycrystalline Hastelloy X subjected to fatigue loading. The sub-grain level strain measurements are made prior to the formation of micro-cracks. The correlation between the localization of plastic strains very early on during the loading (e.g., less than 1000 cycles) and the micro-cracks which are detected later in the life of the sample (e.g., around 10,000) is discussed in this paper. Particular focus is given to the difference in grain boundary response, either blocking or transmitting slip, and the associated fatigue micro-crack lengths generated in the vicinity of these boundaries. The results show a clear correlation between both the locations and lengths of fatigue micro-cracks, which form later in loading, and the localization of plastic strains very early in the loading process. For the same number of cycles, the transmission of slip across grain boundaries resulted in longer transgranular cracks compared to cracks near grains surrounded by blocking grain boundaries which were shorter cracks and confined within single grains.

Quasi-four-dimensional analysis of dislocation interactions with grain boundaries in 304 stainless steel

The application of diffraction contrast electron tomography to dynamic experiments involving dislocation interactions with grain boundaries is demonstrated for the first time. Two applications are shown: the first is concerned with post-mortem analysis of dislocation interactions with grain boundaries and illustrates the usefulness of the tomography technique for defect analysis; the second is in conjunction with in situ straining experiments in which the dynamics of dislocation interactions with grain boundaries are observed directly and the resulting structure visualized three-dimensionally. The in situ straining experiments were conducted at room and elevated temperatures to determine the influence, if any, of thermal processes on the slip transfer mechanism. It was found that increasing the temperature lowers the barrier for dislocation absorption and emission from the boundary and increases the complexity of the interactions, but does not change the fundamental mechanisms governing slip transmission. Previous experimentally determined criteria for slip transmission across boundaries were extended to interactions involving partial dislocations, where it was found that the reaction continues to be governed predominately by reduction of the Burgers vector of the residual grain boundary dislocation left after slip transfer.

Transmission electron microscopy of deformed Ti–6Al–4 V micro-cantilevers

Single α–β colony micro-cantilevers were machined from a polycrystalline commercial Ti–6Al–4 V sample using a focussed ion beam. Each cantilever contained several alpha lamellae separated by thin fillets of beta. A nanoindenter was used to perform micro-bending tests. The a3 prismatic slip system was selectively activated in the cantilevers by controlling the crystal orientation along the micro-cantilever. Specimens for transmission electron microscopy (TEM) were prepared using a dual-beam focussed ion beam from a series of micro-cantilevers deformed to various extents. Bright field scanning transmission electron microscopy (BF-STEM) was used to investigate the processes of slip nucleation, propagation and transmission through the α/β interface. The cantilevers had an equilateral triangular cross-section with the bar at the top and the apex at the bottom. The compressive stresses developed near the apex were thus twice the tensile stresses near the top. Dislocations initiate first from the bottom and then from the top and move toward the neutral line. Even in the sample with a small deflection, i.e. 0.5 µm, dislocations were observed at the bottom of the cantilever, but dislocations were not observed at the top until the deflection reached 3 µm. Pile-ups pushed the dislocations past the neutral line when the micro-cantilevers were deflected to more than 4 µm.

Optimal microstructures for martensitic steels

Abstract

Slip transfer and plastic strain accumulation across grain boundaries in Hastelloy X

In this study, high resolution ex situ digital image correlation (DIC) was used to measure plastic strain accumulation with sub-grain level spatial resolution in uniaxial tension of a nickel-based superalloy, Hastelloy X. In addition, the underlying microstructure was characterized with similar spatial resolution using electron backscatter diffraction (EBSD). With this combination of crystallographic orientation data and plastic strain measurements, the resolved shear strains on individual slip systems were spatially calculated across a substantial region of interest, i.e., we determined the local slip system activity in an aggregate of ∼600 grains and annealing twins. The full-field DIC measurements show a high level of heterogeneity in the plastic response with large variations in strain magnitudes within grains and across grain boundaries (GBs). We used the experimental results to study these variations in strain, focusing in particular on the role of slip transmission across GBs in the development of strain heterogeneities. For every GB in the polycrystalline aggregate, we have established the most likely dislocation reaction and used that information to calculate the residual Burgers vector and plastic strain magnitudes due to slip transmission across each interface. We have also used molecular dynamics simulations (MD) to establish the energy barriers to slip transmission for selected cases yielding different magnitudes of the residual Burgers vector. From our analysis, we show an inverse relation between the magnitudes of the residual Burgers vector and the plastic strains across GBs. Also, the MD simulations reveal a higher energy barrier for slip transmission at high magnitudes of the residual Burgers vector. We therefore emphasize the importance of considering the magnitude of the residual Burgers vector to obtain a better description of the GB resistance to slip transmission, which in turn influences the local plastic strains in the vicinity of grain boundaries.

Energetics of residual dislocations associated with slip–twin and slip–GBs interactions

Abstract During direct slip transmission of a dislocation through a twin or grain boundary, typically a residual dislocation remains in the boundary plane. Through atomistic simulations, we show systematic cases of slip transmission through various types of 〈1 1 0〉 tilts and 〈1 1 1〉 twists grain boundaries (GBs). Additionally, one specific type of GB, the coherent twin boundary (CTB), is viewed to investigate the effects of orientation and dislocation type on the slip transmission process. In every case, we measure the residual Burgers vector within the boundary and energy barrier for slip to transmit through the CTB or GB. There exists a direct correlation between the magnitude of the residual Burgers vector and the energy barrier for slip transmission. Hence, in cases of easy slip transmission (i.e. low energy barrier), a small residual dislocation is left in the GB; meanwhile in cases where it is difficult for slip to transmit past the CTB or GB (i.e. high energy barrier), a large residual Burgers vector remains within the boundary.

Early stage dynamic damage and the role of grain boundary type

The role of grain boundary type in the early stages of dynamic damage evolution in copper has been investigated. Through a combination of polycrystalline and large-grained specimens, it has been shown that Σ3 and low-angle boundaries are resistant to void nucleation during shock loading to peak compressive stresses between 1.5 and 2.5 GPa. It is postulated that these boundaries promote slip transmission or secondary slip activation and thereby relieve the stress concentrations necessary for void nucleation at a boundary.

Slip transmission across fcc/bcc interfaces with varying interface shear strengths

Interfaces with relatively low shear strengths can be strong barriers to slip transmission because of core spreading of the dislocation within the interface. Using atomistic modeling and elasticity-based calculations we have studied the influence of interface shear strength on the slip transmission of a single dislocation across fcc/bcc interfaces. “Tunable” interatomic potentials were employed to vary the interface shear strength for the same interface crystallography. The results show that the slip transmission barrier increases with decreasing shear strength of the interface. The results reveal a mechanism for the variations in ultra-high strengths observed in nanoscale fcc/bcc multilayers.

Atomic-level study of twin nucleation from face-centered-cubic/body-centered-cubic interfaces in nanolamellar composites

We report deformation twinning in Cu within accumulative roll-bonded Cu-Nb nanolamellar composites. Twins appear connected to the Nb{112}//Cu{112} interface with the Kurdjumov-Sachs orientation relationship, which we show to be ordered and faceted. The interface adopts a different faceted structure after twinning. Our analysis suggests that deformation twinning involves facet dissociation and slip-transfer from the Nb layer to the Cu layer due to a geometrically favorable slip transmission pathway.

The Role of Slip Transmission on Plastic Strain accumulationacross Grain Boundaries

In the present study our aim is to develop a deeper understanding of strain accumulation in the vicinity of grain boundaries (GBs) within a polycrystalline aggregate. We focus on the role of slip transmission in the uniaxial plastic deformation of a nickel-based superalloy,Hastelloy-X. Utilizing high resolution ex-situ digital image correlation (DIC) and electron backscatter diffraction (EBSD), we establish the most likely dislocation reactions due to slip transmission and use this information to calculate the residual Burgers vector and plastic strain magnitudes across each interface. From our analysis, we quantitatively show an influence of the magnitude of the residual Burgers vector on plastic strains across GBs.