## Plasticity, shape memory and strain accommodation

### December 30, 2010

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.

## High resolution electron microscopy of split patterns in Ni-base superalloys

### August 8, 2007

Title: Statistical analysis of $\gamma^{\prime}$ quartet split patterns in $\gamma-\gamma^{\prime}$ Ni alloys revealed by high resolution electron microscopy

Authors: H. A. Calderon; C. Kisielowski; T. Mori

Abstract: The frequencies of adjacent $\gamma^{\prime}$ pairs having in-phase and out-of-phase relationships in quartet configurations, determined by high resolution electron microscopy [Calderon et al., Phil. Mag. Lett. 85 51 (2005)], were examined in detail for $\gamma^{\prime}$ particles belonging to the same translational order domain. Consequently, there were always at least two out-of-phase adjacent pairs in any quartet. It is concluded that the quartet split patterns in $\gamma^{\prime}$ particles, but are produced by the migration of particles due to diffusion, these particles having been precipitated separately and independently prior to migration. An elasticity calculation is provided to show that two $\gamma^{\prime}$ particles migrate to align along <100> when their initial position deviates from this direction.

## Split patterns in ordered precipitates

### March 19, 2007

Do $L1_2$ ordered $Ni_3Al$ ($\gamma^{\prime}$) precipitates in the $Ni$-rich ($\gamma$) matrix undergo elastic stress driven splitting, or, is it particle coalescence which gives rise to split-looking patterns?

Luo et al, in a paper which is to appear in Acta Materialia, advance an altogether new mechanism, namely, nucleation of ordered particles at dislocations and the subsequent growth.

Even though the fact that ordered precipitates preferentially nucleate at dislocations in Ni-base alloys due to lattice mismatch is well known (See the 1966 classic paper of Ardell and Nicholson–with an appendix by Eshelby, for example), I have never come across any mention of the same in the context of particle splitting–though, from the paper, I understand that such a mechanism was discussed in the PhD thesis of Prof. Wang back in 1995.

Paper: Nucleation of ordered particles at dislocations and formation of split patterns

Authors: W Luo, C Shen and Y Wang

Abstract:

We investigated the effect of nucleation of ordered precipitates at dislocations and the subsequent growth of particle morphology through computer simulations using a phase-field model. The model treats simultaneously precipitates, dislocations and precipitate–dislocation interactions within a single algorithm. In particular, the model takes into account the structural discontinuity associated with a dislocation that leads to the formation of antiphase domains if the dislocation is within an ordered particle. Three long-range order parameters are used to describe the antiphase domains associated with L12 ordering and an additional set of non-conserved order parameters is introduced to characterize dislocations. We show that heterogeneous nucleation and subsequent growth of ordered precipitates at dislocations yield various “split” patterns, whose formation has been attributed to different mechanisms in literature.

Very interesting indeed!