Single Slip System Research Articles

Constitutive Relations for AA 5754 Based on Crystal Plasticity

Constitutive equations for the multiaxial stress-strain behavior of aluminum alloy 5754 sheets were developed, based on crystal plasticity. A Taylor-based polycrystal plasticity model, a tangent formulation of the self-consistent viscoplastic model (VPSC), and an N-site viscoplastic model based on the fast Fourier transform (VPFFT) were used to fit a single slip system hardening law to the available data for tension, plane strain, and biaxial stretching. The fitting procedure yields good agreement with the monotonic stress-strain data, with similar parameter values for each model. When simulating multiaxial tests using the developed hardening law, models that allow both stress and strain variations in grains give better predictions of the stress-strain curves. Furthermore, generally, the simulated texture evolution is too rapid when compared to the experiments. By incorporating a more detailed neighbor interaction effect, the VPFFT model predicts texture evolution in better agreement with experiments.

Anisotropic size effect in strength in coherent nanowires with tilted twins

When materials are deformed plastically via dislocations, a general finding is that samples with smaller dimensions exhibit higher strengths but with very limited amount of plasticity in tension. Here we report that one-dimensional coherent nanostructures with tilted internal twins exhibit anisotropic size effect: their strengths show no apparent change if only their thicknesses reduce, but become stronger as the sample sizes are reduced proportionally. Large-scale molecular dynamics simulations show that such nanowires deform primarily through twin migration mediated by partial dislocations in one active slip system, and a large amount of plasticity could be achieved in such nanowires via twin migration. The unique structure shown here is suitable to explore strengthening mechanisms in metals when plasticity is controlled by a single dislocation slip system. This study also suggests a novel approach to modulate strength and ductility in one-dimensional coherent nanostructures.

Study of evolution of dislocation structure with the deformation in Zirconium alloys

Evolution of dislocation structure as a function of deformation, in case of a two phase zirconium alloy, was characterized by transmission electron microscopy as well as X-ray line profile analysis. Dislocation structures up to a deformation of 10% show that deformation is mitigated by a single active slip system. Dislocation cellular structures were observed at a deformation of 27%. Two different X-ray based techniques of evaluation of dislocation density were used in the present study. The methods though differed in the absolute values of dislocation densities (ρ), agreed with each other in terms of trend in variation of ρ with the amount of plastic strain.

A Study on Tensile Deformation Features of Ni-Based Super-Alloy Prepared by EB-PVD

Large-scale Ni-based super-alloy sheet has been prepared by electron beam physical vapor deposition (EB-PVD). Microstructure and the dislocation structures in the γ-γ′ double phase alloy under different temperature after tensile strain are studied with Transmission electron microscopy (TEM). The results show that the dislocation glide in single slip system and shearing mechanics, the dislocation climb with part shearing, absolute dislocation climb and cross slip, dislocation round are a course of the interacting degree between dislocation and γ′ phase gradually weakened under the tensile temperature from room temperature to high temperature, so as to decrease materials strength and increase plasticity.

Grain boundary sliding during ambient-temperature creep in hexagonal close-packed metals

Even at ambient temperature or less, below their 0.2% proof stresses all hexagonal close-packed metals and alloys show creep behaviour because they have dislocation arrays lying on a single slip system with no tangled dislocation inside each grain. In this case, lattice dislocations move without obstacles and pile-up in front of a grain boundary. Then these dislocations must be accommodated at the grain boundary to continue creep deformation. Atomic force microscopy revealed the occurrence of grain boundary sliding (GBS) in the ambient-temperature creep region. Lattice rotation of 5° was observed near grain boundaries by electron backscatter diffraction pattern analyses. Because of an extra low apparent activation energy of 20 kJ/mol, conventional diffusion processes are not activated. To accommodate these piled-up dislocations without diffusion processes, lattice dislocations must be absorbed by grain boundaries through a slip-induced GBS mechanism.

The initiation of strain localisation in plagioclase-rich rocks: Insights from detailed microstructural analyses

In order to shed light on the cause for onset of strain localisation in plagioclase-rich rocks we have performed detailed microstructural analyses on a sheared anorthosite–leucogabbro using optical microscopy, electron backscatter diffraction (EBSD) and chemical analyses. The analysed sample is from an Archaean unit, SW Greenland, deformed at lower to mid crustal conditions ( T = 675–700 °C and moderate pressure). The initial deformation occurred dominantly by dislocation creep and the grain size was reduced primarily by subgrain rotation recrystallisation. Recrystallised plagioclase grains (average size 80 μm) are dominantly found in (i) clusters, (ii) lenses and (iii) continuous bands subparallel to shear zone boundaries. Recrystallised grains in clusters and lenses display inherited crystallographic orientations. Their bulk crystallographic preferred orientation (CPO) is random; however, crystallographic characteristics show that parent and daughter grains have the same misorientation axes and possibly the same active slip systems. Recrystallised grains in continuous bands show a CPO with a single dominant active slip system, (001)<110>, aligned with the structural (XYZ) framework. For these parent and daughter grains, misorientation axes are random and the dominant slip system is different. Grain rotations of recrystallised grains are traceable back to the orientation of the adjacent porphyroclast. We infer that the cause for strain localisation is recrystallisation and development of a CPO in continuous recrystallised bands. Microstructures in combination with misorientation and slip system analyses indicate a possible change from dislocation creep in clusters and lenses to dislocation-accommodated grain boundary sliding (DisGBS) in continuous bands. This inferred shift in dominant deformation mechanism would lower the strength of the shear zone.

Grain Boundary Sliding Below Ambient Temperature in H.C.P. Metals

Hexagonal close-packed metals and alloys show significant creep behavior with extremely low activation energies at and below ambient temperature even below their 0.2% proof stresses. It is caused by straightly-aligned dislocation arrays in a single slip system without any dislocation cuttings. These dislocation arrays should, then, pile up at grain boundary (GB) because of violation of von Mises' condition in H.C.P. structure. The piled-up dislocations have to be accommodated by GB sliding. Electron back scatter diffraction (EBSD) analyses and atomic force microscope (AFM) observations were performed to reveal the mechanism of GB sliding below ambient temperature in H.C.P. metals as an accommodation mechanism of ambient temperature creep. EBSD analyses revealed that crystal lattice rotated near GB, which indicates the pile up of lattice dislocations at GB. AFM observation showed a step caused by GB sliding. GB sliding below ambient temperature in H.C.P. metals are considered to compensate the incompatibility between neighboring grains by dislocation slip, which is called slip induced GB sliding.

Grain boundary sliding induced by lattice dislocation activity during ambient temperature creep in h.c.p. metals

Hexagonal close-packed metals and alloys show significant creep behavior at ambient temperature, even below their 0.2% proof stresses. That creep behavior arises from straightly aligned dislocation arrays in a single slip system without any dislocation cuttings. These dislocation arrays pile up at grain boundary (GB) because of violation of von Mises' condition. Therefore, GB sliding must accommodate the piled-up dislocations. In this study, electron back scatter diffraction (EBSD) analyses and atomic force microscope (AFM) observations revealed an accommodation mechanism in ambient temperature creep region. Lattice rotation occurred near GB during creep, as revealed by EBSD analyses, indicating the pile up of lattice dislocations there. GB sliding during creep was revealed by AFM observations.

Evolution of plasticity in notched Ni-base superalloy single crystals

Numerical and experimental investigations of evolution of slip fields in notched Ni-base superalloy single crystal tensile specimens are presented as functions of load and secondary (notch) orientation. Three crystallographic orientations were investigated with the primary (load) orientation fixed along the [0 0 1] direction while the notch directions are parallel to [ 1 ¯ 10 ] / [ 1 1 ¯ 0 ] , [ 0 1 0 ] / [ 0 1 ¯ 0 ] , and [ 3 ¯ 1 0 ] / [ 3 1 ¯ 0 ] , respectively. A three-dimensional elastic anisotropic finite element analysis (FEA) was used to compute the triaxial stress fields in the neighborhood of the notch. The elastic solution is successful in identifying which slip systems are activated initially. Interestingly this procedure was found to be also successful in predicting slip evolution at higher loads, because of slip localization in the superalloy tested. Based on this analysis, the concept of “dominant slip system” is introduced and defined as the single slip system that experiences the highest resolved shear stress (RSS) at a given point near the notch. The dominant slip systems are seen to persist with increasing load and inhibit the activation of new slip systems, which implies that when plasticity is initiated in the dominant slip systems, either softening takes place and/or the rate of increase in RSS on the other slip systems is reduced significantly. The distribution of dominant slip systems in the neighborhood of the notch and on the surface is used to accurately predict the evolution of activated slip sectors and sector boundaries observed experimentally. The activated stress fields are shown to vary strongly through the specimen thickness. Elastic anisotropy governs the development of the elastic stress field and controls which slip systems become initially dominant/activated. Therefore inclusion of elastic anisotropy was found to be important for the prediction of stress field evolution as functions of load and crystal orientation.

Relaxation of a class of variational models in crystal plasticity

We investigated the effect of spontaneous formation of microstructures on the macroscopic material behaviour in a class of models in finite single-crystal plasticity without hardening. In particular, we show that, even in the presence of a single active slip system, the formation of slip bands leads to a very soft behaviour of the sample in response to a large class of applied loads. This contrasts with results obtained under the assumption of rigid elasticity.

Plane constrained shear of single crystal strip with one and two active slip systems

AbstractThe plane constrained shear problems of a single crystal strip with one and two active slip systems are considered within the continuum dislocation theory. Analytical solutions are found for single slip and symmetric double slip systems which exhibit the energetic and dissipative thresholds for dislocation nucleation, the Bauschinger translational work hardening and the size effect. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Size Dependence of Dislocation‐Mediated Plasticity in Ni Single Crystals: Molecular Dynamics Simulations

We investigate the compressive yielding of Ni single crystals by performing atomistic simulations with the sample diameters in the range of 5 nm ∼ 40 nm. Remarkable effects of sample sizes on the yield strength are observed in the nanopillars with two different orientations. The deformation mechanisms are characterized by massive dislocation activities within a single slip system and a nanoscale deformation twining in an octal slip system. A dislocation dynamics‐based model is proposed to interpret the size and temperature effects in single slip‐oriented nanopillars by considering the nucleation of incipient dislocations.

Statistical approach to dislocation dynamics: From dislocation correlations to a multiple-slip continuum theory of plasticity

Due to recent successes of a statistical-based nonlocal continuum crystal plasticity theory for single-glide in explaining various aspects such as dislocation patterning and size-dependent plasticity, several attempts have been made to extend the theory to describe crystals with multiple-slip systems using ad hoc assumptions. We present here a mesoscale continuum theory of plasticity for multiple-slip systems of parallel edge dislocations. We begin by constructing the Bogolyubov-Bom-Green-Yvon-Kirkwood integral equations relating different orders of dislocation correlation functions in a grand canonical ensemble. Approximate pair correlation functions are obtained for single-slip systems with two types of dislocations and, subsequently, for general multiple-slip systems of both charges. The effect of the correlations manifests itself in the form of an entropic force in addition to the external stress and the self-consistent internal stress. Comparisons with a previous multiple-slip theory based on phenomenological considerations shall be discussed.

A Quasicontinuum study of nanovoid collapse under uniaxial loading in Ta

The mechanisms underlying the deformation of nanovoids in Ta single crystals are analyzed when they are subjected to cyclic uniaxial deformation using numerical simulations. Boundary and cell-size effects have been mitigated by means of the Quasicontinuum (QC) method. We have considered ≈1 billion-atom systems containing 10.9 nm voids. Two kinds of simulations have been performed, each characterized by a different boundary condition. First, we compress the material along the nominal [0 0 1] direction, resulting in a highly symmetric configuration that results in high stresses. Second, we load the material along the high-index [ 4 ¯ 8 19 ] direction to confine plasticity to a single slip system and break the symmetry. We find that the plastic response under these two conditions is strikingly different, the former governed by dislocation loop emission and dipole formation, while the latter is dominated by twinning. We calculate the irreversible plastic work budget derived from a loading–unloading cycle and identify the most relevant yield points. These calculations represent the first fully three-dimensional, fully non-local simulations of any body-centered cubic metal using QC.

Plastic deformation of orthoenstatite and the ortho- to high-pressure clinoenstatite transition: a metadynamics simulation study

Atomic-scale mechanisms of plastic deformation in orthoenstatite, MgSiO3 are studied by computer simulation methods. The combined use of metadynamics and molecular dynamics allows a direct observation of the structural changes during the creation of stacking faults in the (100) plane. A sequence of slip deformations in two different (100) planes at P = 15 GPa and T = 1,000 K reveals a probable transformation mechanism for the ortho- to high-pressure clinopyroxene transition. Each of the observed slips consists of at least four partial deformations crossing high-energy intermediate structures. In agreement with experimental studies, both (100)[010] and (100)[001] slip systems are activated in the deformation process. The observation of a dominant (100)[001] single slip system in pyroxenes may be related to the fact that high-energy intermediate dislocations with (100)[010] component are not stable on geological or experimental timescales.

Petrofabrics and seismic properties of garnet peridotite from the UHP Sulu terrane (China): Implications for olivine deformation mechanism in a cold and dry subducting continental slab

Lattice-preferred orientations (LPO) of olivine, diopside, enstatite and garnet from the Zhimafang garnet peridotite body in the Sulu ultrahigh-pressure (UHP) metamorphic terrane (China) were measured using the electron backscatter diffraction (EBSD) technique. The peridotite was captured from a mantle wedge immediately adjacent the subducted Yangtze slab and then experienced the UHP metamorphism at 750–950 °C and 4–7 GPa. The olivine LPO is characterized by the [001] axis close to the stretching lineation and the (100) plane subparallel to the foliation, indicating the prevailing of (100) [001] slip. Enstatite LPO displays the dominance of (100) [001] slip. Diopside developed complex LPO patterns that are difficult to explain using a single slip system of (100) [001]. Garnet is almost randomly oriented due to its low volume fractions, cubic symmetry and the presence of numerous slip systems. Calculated seismic properties of the peridotite yield a maximum P-wave velocity normal to the foliation and a minimum along the foliation, with anisotropy up to 8% in strongly sheared samples. The S-wave velocity pattern is complex but the fast polarization plane generally normal to the foliation. The inferred shear sense from the olivine LPO is top-to-SE, in contrary to exhumation-induced top-to-NW thrusting recorded in the quartz LPO, implying that the olivine LPO formed at early UHP metamorphic conditions. The olivine crystals have relatively low water contents (141–475 H/10 6 Si), indicating a fluid-deficient environment for the LPO formation. The present study suggests that a combination of low temperature and UHP plays a much more important role than the water content to promote the activation of (100) [001] slip in olivine.

Studies of scale dependent crystal viscoplasticity models

A scale dependent crystal viscoplasticity model with a second strain gradient effect is introduced, as a simple extension of the conventional crystal plasticity theory. We confine attention to a single crystal undergoing slip on a single slip system under small strain conditions. Connections between this model and other existing theories are investigated in some detail. Furthermore, some basic predictions of the model, due to the second gradients and the material viscosity, are illustrated, using a constrained simple shear problem for a thin strip bounded by two rigid walls. The effect of viscosity on evolution of the boundary layer is examined, as well as the behavior of the thin strip undergoing reverse/cyclic shear loading, and the ability to predict plastic flow localization.

Molecular dynamics study of solute strengthening in Al/Mg alloys

The strengthening of Al by Mg solute atoms is investigated using molecular dynamics (MD) studies of single dislocations moving through a field of randomly placed solutes. The MD method permits explicit treatment of “core” effects, dislocation pinning and deceleration, and dislocation unpinning by thermal activation, all under an applied load. Choice of an appropriate MD simulation cell size is assessed using analytic concepts developed by Labusch. The interaction energy of a single Mg atom with straight edge and screw dislocations is computed and compared with continuum models. Using the single Mg energies, a one-dimensional energy landscape for the motion of a straight edge dislocation through a random field of Mg solutes is computed. The minima in this landscape match well with those found in the MD simulations at zero temperature. The stress to unpin a straight edge dislocation trapped in a local energy minimum generated by the solutes is then predicted semi-analytically using the energy landscape, and good agreement is obtained with the MD results. At temperatures of 300 and 500 K, the thermally activated rate of unpinning vs. stress and temperature is calculated semi-analytically, and agreement with the full MD results is again obtained with the fitting of a single attempt frequency in a transition state model. The agreement of the semi-analytical models provides a basis for calculating yield stress vs. strain rate and temperature, resulting from statistical pinning, for the case of non-interacting dislocations on a single slip system, and for extending the analysis to study dynamic strain aging effects resulting from diffusion of Mg atoms around a pinned dislocation.

Simulation of Short Crack Propagation ‐ Transition from Stage I to Stage II

AbstractThe life‐time of cyclically loaded components with smooth surfaces is mainly determined by the initiation and propagation of microstructurally short fatigue cracks. The phase of short crack propagation can be subdivided into crack growth along single slip bands (stage I, in the direction of maximum shear stress in front of the crack tip) and the growth along alternating slip bands (stage II, perpendicular to the direction of maximum normal stress). Hence, the propagation starts in a single grain and continues through several grains in stage I. Then, additional slip bands are activated and the crack grows on alternating glide planes perpendicular to the direction of maximum normal stress. During the whole propagation process of the still relatively short crack, the plastic deformation on slip bands is blocked by grain boundaries. Due to the strong interaction with the microstructure, a description of the short crack propagation based on linear elastic fracture mechanics is not possible. Thus, an extended two‐dimensional yield‐strip model [1] based on the ideas of Navarro and de los Rios [2] has been developed. The boundary‐element method is used to calculate the displacements along the crack, treating the plastic zones in front of the crack tip as yield strips. Each boundary element consists of a mathematical dislocation at its beginning and its end, describing a constant normal and tangential displacement in the element. Geometrical crack closure can be considered by constraints allowing only positive normal displacements within the crack elements. The model is extended to the transition of stage I crack growth on single slip systems to crack propagation on multiple slip systems, which is presented here. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Plasticity size effects in tension and compression of single crystals

The effect of size and loading conditions on the tension and compression stress–strain response of micron-sized planar crystals is investigated using discrete dislocation plasticity. The crystals are taken to have a single active slip system and both small-strain and finite-strain analyses are carried out. When rotation of the tensile axis is constrained, the build-up of geometrically necessary dislocations results in a weak size dependence but a strong Bauschinger effect. On the other hand, when rotation of the tensile axis is unconstrained, there is a strong size dependence, with the flow strength increasing with decreasing specimen size, and a negligible Bauschinger effect. Below a certain specimen size, the flow strength of the crystals is set by the nucleation strength of the initially present Frank–Read sources. The main features of the size dependence are the same for the small-strain and finite-strain analyses. However, the predicted hardening rates differ and the finite-strain analyses give rise to some tension–compression asymmetry.