David H. Lassila

Multi-scale modeling of polycrystal plasticity: a workshop report

Abstract The workshop on multi-scale modeling of polycrystal plasticity was held on April 9–11, 1997 at the Institute for Mechanics and Materials at the University of California, San Diego in La Jolla, CA. This workshop addressed length-scale issues associated with developing a predictive capability in the modeling of the plastic deformation of polycrystals by the incorporation of more physically based information in the models. The goals of the workshop were to: (1) establish a model system that is well suited to the multi-scale modeling methodology; (2) explore a set of discrete simulation methods at the continuum-scale, meso-scale, micro-scale, and atomic-scale; and (3) identify critical links connecting the length scales which will allow information to be passed among scales and allow the end goal of predictive models at the continuum scale. This paper presents the technical summary of the topics covered by the speakers at the workshop and a discussion of critical issues at each length scale.

Observation of dislocation dynamics in the electron microscope

Abstract Deformation experiments performed in situ in the transmission electron microscope have led to an increased understanding of dislocation dynamics. To illustrate the capability of this technique two examples will be presented. In the first example, the processes of work hardening in Mo at room temperature will be presented. These studies have improved our understanding of dislocation mobility, dislocation generation, and dislocation–obstacle interactions. In the second example, the interaction of matrix dislocations with grain boundaries will be described. From such studies predictive criteria for slip transfer through grain boundaries have been developed.

Shock-Induced Omega Phase in Tantalum

The deformation substructure developed within polycrystalline tantalum under a high shock pressure (45 GPa) with a 1.8 {micro}s duration has been examined using transmission electron microscopy. A shock-induced {beta} (bcc) {yields} {omega} (hexagonal) displacive transformation is observed for the first time within tantalum. Needle- or plate-like {omega} phase is found to form accompanied with the {l_brace}112{r_brace} type deformation twins within shock-recovered tantalum. The orientation relationships between the shock-induced {omega} and parent {beta} phases are determined to be {l_brace}10{bar 1}0{r_brace}{sub {omega}} {parallel} {l_brace}211{r_brace}{sub {beta}}, [0001]{sub {omega}} {parallel} {sub {beta}} and {sub {omega}} {parallel} [0{bar 1}1]{sub {beta}}. The lattice parameters of {omega} phase are a{sub {omega}} = ({radical}2a{sub {beta}}) = 0.468 nm and c{sub {omega}} = ({radical}3/2) a{sub {beta}} = 0.286 nm (c/a = 0.611). Both deformation twins and shock-induced {omega} phase are primarily formed along the {l_brace}211{r_brace}{sub {beta}} slip planes with high resolved shear stresses, and have a common habit plane [i.e. the {l_brace}211{r_brace} plane] with the parent {beta} matrix. It is suggested that shear deformation on the {l_brace}211{r_brace} planes is the major cause for the formation of shock-induced {omega} phase within tantalum.

The effects of tungsten addition on the microtexture and mechanical behavior of tantalum plate

Abstract Microtexture variations in annealed tantalum and tantalum–tungsten alloy plate materials have been studied by orientation imaging microscopy (OIM) and correlated with the mechanical behavior over a strain rate range of 10 −3 s −1 to 3000 s −1 . Plates of nominally pure Ta and Ta–W alloys (2.5, 5 and 10 wt% W), ≈6 mm thick were mechanically tested quasistatically in compression and tension and dynamically via a split Hopkinson pressure bar and punch through shear tests. The results indicate that the unalloyed Ta exhibits anomalous mechanical responses such as inverse barreling or hourglassing in compression and multiple necks in tension, whereas the tungsten containing alloys deform homogeneously. OIM indicates severe texture banding in the pure Ta such that the fraction of grains with near 〈111〉 normals is very high near the centerline of the plate and decreases toward the surfaces. Large deviations from this generic description occur from specimen to specimen. Microtexture analyses of the Ta–W alloys reveals no significant texture gradients but rather a change in overall texture from a 〈111〉 fiber to a 〈100〉 cube texture with the addition of 2.5 wt% tungsten. The evidence suggests that the addition of tungsten results in a more uniform texture and thus homogeneous mechanical response.

Uniaxial Stress Deformation Experiment for Validation of 3-D Dislocation Dynamics Simulations

An apparatus has been developed for performing compression deformation experiments on oriented metallic single crystals to provide data for validation of 3-D dislocation dynamics simulations. The experiment is performed under conditions that allow unconstrained motion of the upper and lower compression platen, and thus a relatively uniform state of axial stress is maintained during the deformation. Experiments have been performed on high-purity Mo single crystal and polycrystalline Cu. Various aspects of the experimental procedures and results are presented. Possible usages of the experimental data for the validation of 3-D dislocation dynamics simulations are discussed.

Shock-induced displacive transformations in tantalum and tantalum-tungsten alloys

A recent investigation on the deformation substructure of shocked tantalum by transmission electron microscopy (TEM) has for the first-time revealed that a displacive omega transformation can also take place in tantalum (a group V transition metal) under a high shock peak pressure (45 GPa). Plate- or lath-like {omega} phase ({omega}{prime} hereafter) has been observed within shocked tantalum, which is considered to be unusual since tantalum has a bcc structure and exhibits no equilibrium phase transformation up to its melting temperature at ambient pressure. The occurrence of displacive omega transformation within shocked tantalum is of great interest because it provides not only an effective strengthening mechanism for tantalum and tantalum alloys but also an opportunity to study and understand the mechanisms of displacive {beta} {yields} {omega}{prime} transition induced by high strain-rate deformation. Results from the investigation of displacive omega transformation in tantalum and tantalum-tungsten alloy are reported and discussed here.

Calculation of the Slip System Activity in Deformed Zinc Single Crystals Using Digital 3-D Image Correlation Data

A 3-D image correlation system, which measures the full-field displacements in three dimensions, has been used to experimentally determine the full deformation gradient matrix for two zinc single crystals. Based on the image correlation data, slip system activity for the two crystals has been calculated. The results of the calculation show that, for one crystal, only the primary slip system is active, which is consistent with traditional theory. The other crystal, however, shows appreciable deformation on slip systems other than the primary. An analysis was conducted verifying the experimental observation that the net result from slip on the secondary slip systems is approximately one third the magnitude and directly orthogonal to the primary system.

Dislocation multiplication in bcc molybdenum: A dislocation dynamics simulation

Plastic deformation of Mo single crystals is examined by direct simulation of dislocation dynamics under stress. Initial dislocation populations are made to mimic real dislocation microstructures observed in transmission electron microscopy cross-sections of pure annealed Mo single crystals. No a priori sources for dislocation multiplication are introduced, and yet multiplication takes place through a sequence involving aggregation of grown-in superjogs, bowing of screw dislocation segments and fast lateral motion of edge segments, producing a large number of elongated loops and a characteristic cross-grid pattern of screw dislocations.

The effect of tungsten on the mechanical properties of tantalum

This paper reports a study of the mechanical behavior of Ta and Ta-W alloys. The results show that tungsten additions increase the yield strength and the rate of work hardening of tantalum. These additions also cause a change in the deformed microstructure from one that is primarily cellular to one that consists mostly of dislocation tangles. It is proposed that the increase in yield strength arises from solid solution hardening and that the increase in the work hardening can be correlated with an increase in the density and arrangement of dislocations present in the material.

The mechanical behavior of pre-shocked copper at strain rates of 10-3-104s-1 and temperatures of 25-400°C

Abstract We report the results of our study of the mechanical behavior of pre-shock-loaded oxygen-free electronic (OFE) grade copper. From quasi-static data for samples of 30 μm grain size shocked to 10 GPa for 1 μs, we derive a value of the thermal component of the mechanical threshold stress (MTS) characteristic of this material that is in good agreement with values in the literature. Using the MTS model for the flow stress of OFE copper, we show that our value of the threshold stress provides an excellent description of split Hopkinson pressure bar data for strain rate of 2700 s −1 . We then calculate the stress-strain behavior of electromagnetically launched expanding rings of 10 μm OFE copper previously shocked to 11.5 GPa for 1.6 μs, and we find excellent agreement with experimental observations, despite the large strain rate and temperature excursions characteristic of these experiments. We consider the possible influence of differences in the shock pressure and duration between the 10 and 30 μm materials on the value of the thermal component of the MTS, and we suggest that experimental scatter implied in the literature is too large to resolve any such differences. The effects of temperature and the limits of plastic flow are discussed briefly within the context of the MTS model.