[1] Elastic properties of surfaces on nanoparticles

W G Wolfer

Lattice parameter changes in nanoparticles can be used to determine the surface stress of solids. In the past a Laplace–Young relationship has been employed to interpret the lattice parameter changes as a function of the particle size. In the meantime, however, atomistic calculations revealed a purely mechanical origin of the surface stress that is consistent with elasticity theory for solid surfaces as developed by Gurtin and Murdoch. In this theory the equilibrium distance for surface atoms may differ from that in the bulk solid, and the elastic properties of the surface layer may also deviate from bulk values. We apply this Gurtin–Murdoch theory to spherical nanoparticles and reanalyze past data as well as results from recent theoretical calculations on lattice parameter changes, thereby enabling us to determine surface properties commensurate with the mechanical interpretation of surface stress.

[2] Orientation dependence of twinning and strain hardening behaviour of a high manganese twinning induced plasticity steel with polycrystalline structure

H Beladi et al

The twinning induced plasticity steel 0.6 C–18 Mn–1.5 Al (wt.%) employed in this study exhibited a strength of about 1 GPa, combined with a large uniform elongation of over 60% at moderate strain rates. This excellent combination of tensile mechanical properties was shown to be a result of complex dynamic strain-induced microstructural reactions, including dislocation glide, dislocation dissociation, stacking fault formation, dynamic recovery, mechanical twinning and dynamic strain ageing. The contribution of each of these processes was discussed with respect to the strain hardening behaviour. An important observation was that the propensity for mechanical twinning in a particular grain strongly depends on its crystallographic orientation and is clearly correlated with the magnitude of the corresponding Taylor factor. The current results reveal that the development of partial dislocations and stacking faults at an early stage of straining and the consequent interaction of gliding dislocations with stacking fault interfaces enhances the strain hardening rate. Subsequent or concurrent initiation of mechanical twins also contributes to strain hardening through a dynamic Hall–Petch effect limiting the dislocation mean free path and consequently enhancing dislocation storage. Dynamic strain ageing (DSA) took place at a late stage of deformation, adding to strain hardening. DSA is a factor reducing ductility by promoting strain localization.

[3] A phase field study of strain energy effects on solute–grain boundary interactions

T W Heo et al

We have studied strain-induced solute segregation at a grain boundary and the solute drag effect on boundary migration using a phase field model integrating grain boundary segregation and grain structure evolution. The elastic strain energy of a solid solution due to the atomic size mismatch and the coherency elastic strain energy caused by the inhomogeneity of the composition distribution are obtained using Khachaturyan’s microelasticity theory. Strain-induced grain boundary segregation at a static planar boundary is studied numerically and the equilibrium segregation composition profiles are validated using analytical solutions. We then systematically studied the effect of misfit strain on grain boundary migration with solute drag. Our theoretical analysis based on Cahn’s analytical theory shows that enhancement of the drag force with increasing atomic size mismatch stems from both an increase in grain boundary segregation due to the strain energy reduction and misfit strain relaxation near the grain boundary. The results were analyzed based on a theoretical analysis in terms of elastic and chemical drag forces. The optimum condition for solute diffusivity to maximize the drag force under a given driving force was identified.

[4] Severe deformation twinning in pure copper by cryogenic wire drawing

A Kauffmann et al

The effect of low-temperature on the active deformation mechanism is studied in pure copper. For this purpose, cryogenic wire drawing at liquid nitrogen temperature (77 K) was performed using molybdenum disulfide lubrication. Microstructural investigation and texture analysis revealed severe twin formation in the cryogenically drawn copper, with a broad twin size distribution. The spacing of the observed deformation twins ranges from below 100 nm, as reported in previous investigations, up to several micrometers. The extent of twin formation, which is significantly higher when compared to other cryo-deformation techniques, is discussed with respect to the state of stress and the texture evolution during wire drawing.

[1] Migration of grain boundaries in free-standing nanocrystalline thin films

Dynkin and Gutkin

Theoretical models are suggested which describe stress-coupled migration of grain boundaries in free-standing nanocrystalline films under external loading. The critical stresses for the start of migration and the transition from stable to unstable migration are calculated and analyzed in dependence on the grain size, grain boundary misorientation angle, film thickness, distance from the closest free surface, and migration direction. It is shown that the least stable are low-angle grain boundaries of larger length which emerge on surfaces of thinnest films.

[2] Insight into the phase transformations between Ice Ih and Ice II from electron backscatter diffraction data

D J Prior et al

Electron backscatter diffraction data from polycrystalline water ice, cycled three times through the 1h to II phase transformation, show that an area equivalent to the original grain-size (∼450μm) now comprises equant 10μm grains with a non-random crystallographic preferred orientation (CPO). Pole figures show small-circle ring and fence patterns characteristic of CPO development controlled by an orientation relationship during phase transformation. Misorientation analysis shows that one of two orientation relationships can explain the data: 1h/II, {10-10}1h/{0001}II or 1h/II, {10-10}1h/{0001}II .

[3] Comment on ”Simulation of damage evolution in composites: A phase-field model”

Emmerich and Pilipenko

Here we reassess the results of [S.B. Biner, S.Y. Hu Acta Matt. 57(2009) 2088-2097] on phase-field simulations of damage evolution in composite materials. In particular we discuss the validity of the results presented therein in the framework of linear elasticity theory.

Update: Reply to “comment on simulation of damage evolution In composites: a phase-field model by H. Emmerich and D. Pilipenko ”

Biner and Yu

Migration of Σ7 tilt grain boundary in Al under an applied external stress

Molodov et al

Stress driven migration of symmetrical tilt grain boundaries with misorientations close to 38.2°, 73.4° and 135.6° rotations related to the same special Σ7{132} CSL boundary was measured by in-situ observations in a scanning electron microscope. Contrary to expectations and theoretical predictions, the investigated boundaries moved under an applied stress, but their motion did not produce shear. The three crystallographically equivalent Σ7 boundaries were found to behave different with respect to migration rate and its temperature dependence.

Crystal plasticity finite-element analysis versus experimental results of pyramidal indentation into (0 0 1) fcc single crystal

B Eidel

Pyramidal microindentation into the (0 0 1) surface of an face-centered cubic (fcc) single crystal made of a Ni-base superalloy is analyzed in experiment and crystal plasticity finite-element simulations. The resultant material pile-up at the surface reflects the material’s symmetry and turns out to be insensitive to different loading scenarios as induced by (i) different azimuthal orientations of the pyramidal indenter, (ii) different indenter shapes (sphere or pyramid) and (iii) the elastic anisotropy. Experiments and simulations are in agreement and suggest that pile-up deformation patterns merely depend on the geometry of discrete slip systems but are invariant to different anisotropic stress distributions as induced by (i)–(iii). The local adaption of pile-up to the pyramidal indenter leads to convex or concave indent shapes corresponding to the indenter orientation. We contrast the present findings for curved indent shapes of fcc single crystals to similar, well-known observations for quasi-isotropic polycrystals. Although phenomenologically similar in kind, the driving mechanisms are different: for the single crystal it is the discrete and anisotropic nature of plastic glide in certain slip systems; for isotropic polycrystals it is the rate of strain-hardening caused by the cumulative response of dislocations.

Phase transformation in free-standing SMA nanowires

F R Phillips et al

The primary focus of this work is on determining if the phase transformation of shape memory alloy (SMA) nanowires exhibits a critical size below which the phase transformation is inhibited. The SMA nanowires are fabricated through the use of the mechanical pressure injection method. The mechanical pressure injection method is a template-assisted nanowire fabrication method in which an anodized aluminum oxide (AAO) template is impregnated with liquid metal. The fabrication of SMA nanowires with different diameters is accomplished through the fabrication of AAO templates of varying diameters. The phase transformation behavior of the fabricated SMA nanowires is characterized using transmission electron microscopy. By analysis of the fabricated SMA nanowires, it is found that the phase transformation of SMA nanowires is not affected for nanowires ranging in diameter from 650 to 10 nm.

The role of strain accommodation during the variant selection of primary twins in magnesium

J J Jonas et al

Samples of magnesium alloys AM30 and AZ31 were deformed in tension at room temperature and a strain rate of 0.1 s−1 to strains of 0.08 and 0.15. Of the numerous contraction twins that formed, the orientations of 977 were determined by electron backscatter diffraction techniques. The orientations of their host grains were also measured, so that the Schmid factors (SFs) applicable to each of the six contraction twins that could potentially form in each grain could also be calculated. About half of the observed twins were of the “high SF” (0.3–0.5) type, while nearly half had “low” SFs (0.15–0.30). Furthermore, 5% of the observed twins had associated Schmid factors of only 0.03–0.15, i.e. these were of the “very low SF” type. Of particular interest is the observation that many potential “high Schmid factor” twins did not form. The presence of the low and very low SF twins and the absence of many potential high SF twins are explained in terms of the accommodation strains that are or would be required to permit their formation. These were calculated by rotating the twinning shear displacement gradient tensor into the crystallographic reference frame of the neighboring grain. It is shown that the very high plastic anisotropy of Mg grains permits the “easy” accommodations to take place but conversely prevents accommodation of the potential twinning shears when these are “difficult” (when these involve high critical resolved shear stresses). The twins that appear require little or no “difficult” accommodation.

[1] In situ study of nucleation and growth of the irregular α-Al/β-Al5FeSi eutectic by 3-D synchrotron X-ray microtomography

S Terzi et al

In order to better understand the formation of β-Al5FeSi intermetallic plates during solidification of Al–Si casting alloys, an Al–8% Si–4% Cu–0.8% Fe alloy has been studied by in situ microtomography using high-energy X-rays in the synchrotron. After formation of the aluminium dendrites, the β phase forms as an irregular eutectic together with eutectic α-Al. Only four plates were nucleated in the sample, and all nucleated in the very early stage of the eutectic reaction and subsequently developed into complex connected three-dimensional plates. The plates display very rapid lateral growth and slow thickening, which, together with the observation of imprints of dendrites and ridges in the plates, suggest a very weakly coupled eutectic.

[2] Deformation of hierarchically twinned martensite

P Muellner and A H King

Shape-memory alloys deform via the reorganization of a hierarchically twinned microstructure. Twin boundaries themselves present obstacles for twin boundary motion. In spite of a high density of obstacles, twinning stresses of Ni–Mn–Ga Heusler alloys are very low. Neither atomistic nor dislocation-based models account for such low yield stresses. Twinning mechanisms are studied here on a mesoscopic length scale making use of the disclination theory. In a first approach, a strictly periodic twin pattern containing periodic disclination walls with optimally screened stress fields is considered. Strict periodicity implies that the twin microstructure reorganizes homogeneously. In a second approach, a discontinuity of the fraction of secondary twins is introduced and modeled as a disclination dipole. The stress required for nucleation of this discontinuity is larger than the stress required for homogeneous reorganization. However, once the dipole is formed, it can move under a much smaller stress in agreement with experimental findings.

[3] New Interpretation of the Haasen Plot for Solute-strengthened Alloys

W A Curtin

The Haasen plot (inverse activation area 1/Δa versus offset flow stress σ-σs) for solute-strengthened alloys is usually assumed additive, 1/Δa=1/Δas+1/Δaf, with 1/Δafnot, vert, similarβ(σ-σs) due to forest interactions. Experiments often show a slope < β. Here, a model for the dislocation activation enthalpy is proposed that predicts a slope 1/(Δasσs) determined only by solute parameters Δas and σs and not directly connected to forest hardening. This parameter-free prediction agrees well with a wide range of experiments on Al-X alloys at T=78K.

[1] Dislocation dynamics simulations of dislocation interactions and stresses in thin films

R S Fertig III and S P Baker

The dislocation interactions that stop threading dislocations (threads) during relaxation at increasing applied strains in single-crystal thin films are investigated using large-scale three-dimensional dislocation dynamics simulations. Threads were observed to stop via interactions with both threads and misfit dislocations (misfits). Both types of interactions were shown to depend on stress inhomogeneity. Low-stress regions enabled threads to stop in weak thread–misfit interactions even at high average film stresses. Threads were also concentrated in low-stress regions, which facilitated their interaction with other threads. Threads accumulated in thread–thread interactions, and stopped only temporarily in thread–misfit interactions. The mean free path for dislocation motion is shown to be accurately predicted from details of the inhomogeneous stress state arising from the applied strain and the misfit structure. These behaviors are analyzed to present a more complete picture of film strength, strain hardening and relaxation.

[2] Comparing grain boundary energies in face centered cubic metals: Al, Au, Cu and Ni

E A Holm et al

The energy of 388 grain boundaries in Al, Au, Cu and Ni were calculated using atomistic simulations. Grain boundary energies in different elements are strongly correlated. Consistent with a dislocation model for grain boundary structure, the boundary energy scales with the shear modulus. Boundaries with substantial stacking fault character scale with the stacking fault energy. There is more scatter in the data for Al, which has a high stacking fault energy, than for the low stacking fault energy elements.

[1] Influence of interface energies on solute partitioning mechanisms in doped aluminas

S J Dillon et al

The experiments described in this paper have been designed to understand how particular dopants in alumina (Ca, Mg, Si, and Y) affect microstructural development through the energetics of their associated precipitates. Specifically, the role of the interphase boundary energy and precThe experiments described in this paper have been designed to understand how particular dopants in alumina (Ca, Mg, Si, and Y) affect microstructural development through the energetics of their associated precipitates. Specifically, the role of the interphase boundary energy and precipitation activation energy are considered to be in competition with grain boundary complexion (disorder) transitions for partitioning excess solute. The results reveal a relationship between the relative precipitation activation energy and the temperature at which grain boundary complexion transitions occur. The large differences in activation energy primarily derive from the interphase boundary energy. Precipitates that form lower interphase boundary energies tend to suppress complexion transitions, while systems that contain precipitates with high interphase boundary energies are more susceptible. Based on the findings, a new criterion for additive selection to control complexion transitions and abnormal grain growth is proposed that is based on interfacial energies between the host and precipitate.ipitation activation energy are considered to be in competition with grain boundary complexion (disorder) transitions for partitioning excess solute. The results reveal a relationship between the relative precipitation activation energy and the temperature at which grain boundary complexion transitions occur. The large differences in activation energy primarily derive from the interphase boundary energy. Precipitates that form lower interphase boundary energies tend to suppress complexion transitions, while systems that contain precipitates with high interphase boundary energies are more susceptible. Based on the findings, a new criterion for additive selection to control complexion transitions and abnormal grain growth is proposed that is based on interfacial energies between the host and precipitate.

[2] Effect of particles in promoting twin nucleation in a Mg–5 wt% Zn alloy

J D Robson et al

The number of 10View the MathML source2 twins formed in a compressed Mg–5wt% Zn alloy increased when precipitate particles were present, reaching a maximum in the peak aged condition. Particles were observed to promote twin nucleation, but inhibit twin growth. A simple model has been developed to show that in peak and over–aged condition the increase in twin number is well predicted by assuming the additional stress driving twin nucleation equates to the Orowan stress inhibiting twin growth.

[3] Nucleation of paired twins at grain boundaries in titanium

L Wang et al

An experimental study of deformation twins in a polycrystalline α-Ti bend specimen was performed. In some grain pairs, mechanical twins in adjacent grains were coincident at a grain boundary (T+T). Based on the identified T+T pairs, factors including twin system alignment, twinning Schmid factor, disorientation of the parent grains, and parent grain size were assessed. An indicative combination of geometric conditions was identified that can account for the formation of most of the observed T+T pairs.