Curt A. Bronkhorst

Dislocation subgrain structures and modeling the plastic hardening of metallic single crystals

A single crystal plasticity theory for insertion into finite element simulation is formulated using sequential laminates to model subgrain dislocation structures. It is known that local models do not adequately account for latent hardening, as latent hardening is not only a material property, but a nonlocal property (e.g. grain size and shape). The addition of the nonlocal energy from the formation of subgrain structure dislocation walls and the boundary layer misfits provide both latent and self-hardening of a crystal slip. Latent hardening occurs as the formation of new dislocation walls limits motion of new mobile dislocations, thus hardening future slip systems. Self-hardening is accomplished by an evolution of the subgrain structure length scale. The substructure length scale is computed by minimizing the nonlocal energy. The minimization of the nonlocal energy is a competition between the dislocation wall energy and the boundary layer energies. The nonlocal terms are also directly minimized within the subgrain model as they affect deformation response. The geometrical relationship between the dislocation walls and slip planes affecting the dislocation mean free path is taken into account, giving a first-order approximation to shape effects. A coplanar slip model is developed due to requirements while modeling the subgrain structure. This subgrain structure plasticity model is noteworthy as all material parameters are experimentally determined rather than fit. The model also has an inherit path dependence due to the formation of the subgrain structures. Validation is accomplished by comparison with single crystal tension test results.

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.

Response and representation of ductile damage under varying shock loading conditions in tantalum

The response of polycrystalline metals, which possess adequate mechanisms for plastic deformation under extreme loading conditions, is often accompanied by the formation of pores within the structure of the material. This large deformation process is broadly identified as progressive with nucleation, growth, coalescence, and failure the physical path taken over very short periods of time. These are well known to be complex processes strongly influenced by microstructure, loading path, and the loading profile, which remains a significant challenge to represent and predict numerically. In the current study, the influence of loading path on the damage evolution in high-purity tantalum is presented. Tantalum samples were shock loaded to three different peak shock stresses using both symmetric impact, and two different composite flyer plate configurations such that upon unloading the three samples displayed nearly identical “pull-back” signals as measured via rear-surface velocimetry. While the “pull-back” sig...

The Influence of Grain Interactions on the Plastic Stability of Heterophase Interfaces

Two-phase bimetal composites contain both grain boundaries and bi-phase interfaces between dissimilar crystals. In this work, we use a crystal plasticity finite element framework to explore the effects of grain boundary interactions on the plastic stability of bi-phase interfaces. We show that neighboring grain interactions do not significantly alter interface plastic stability during plane strain compression. The important implications are that stable orientations at bimetal interfaces can be different than those within the bulk layers. This finding provides insight into bi-phase microstructural development and suggests a pathway for tuning interface properties via severe plastic deformation.

Evaluating the effects of loading parameters on single-crystal slip in tantalum using molecular mechanics

This study is aimed at developing a physics-based crystal plasticity finite element model for body-centred cubic (BCC) metals, through the introduction of atomic-level deformation information from molecular dynamics (MD) investigations of dislocation motion at the onset of plastic flow. In this study, three critical variables governing crystal plasticity mediated by dislocation motion are considered. MD simulations are first performed across a range of finite temperatures up to 600K to quantify the temperature dependence of critical stress required for slip initiation. An important feature of slip in BCC metals is that it is not solely dependent on the Schmid law measure of resolved shear stress, commonly employed in crystal plasticity models. The configuration of a screw dislocation and its subsequent motion is studied under different load orientations to quantify these non-Schmid effects. Finally, the influence of strain rates on thermal activation is studied by inducing higher stresses during activation at higher applied strain rates. Functional dependence of the critical resolved shear stress on temperature, loading orientation and strain rate is determined from the MD simulation results. The functional forms are derived from the thermal activation mechanisms that govern the plastic behaviour and quantification of relevant deformation variables. The resulting physics-based rate-dependent crystal plasticity model is implemented in a crystal plasticity finite element code. Uniaxial simulations reveal orientation-dependent tension–compression asymmetry of yield that more accurately represents single-crystal experimental results than standard models.

The influence of peak shock stress on the high pressure phase transformation in Zr

At high pressures zirconium is known to undergo a phase transformation from the hexagonal close packed (HCP) alpha phase to the simple hexagonal omega phase. Under conditions of shock loading, a significant volume fraction of high-pressure omega phase is retained upon release. However, the hysteresis in this transformation is not well represented by equilibrium phase diagrams and the multi-phase plasticity under shock conditions is not well understood. For these reasons, the influence of peak shock stress and temperature on the retention of omega phase in Zr has been explored. VISAR and PDV measurements along with post-mortem metallographic and neutron diffraction characterization of soft recovered specimens have been utilized to quantify the volume fraction of retained omega phase and qualitatively understand the kinetics of this transformation. In turn, soft recovered specimens with varying volume fractions of retained omega phase have been utilized to understand the contribution of omega and alpha phases to strength in shock loaded Zr.

Influence of shock loading kinetics on the spall response of copper

A suite of plate-impact experiments was designed and conducted to examine the influence of loading kinetics on the spall response of high purity copper samples. The peak compressive stresses (1.5 GPa) and the density of grain boundaries dynamically loaded were held constant for all experiments. The kinetics of the tensile pulses were designed using a hydrodynamic, shock-wave propagation code and experimentally achieved by controlling the geometry of copper impactors and targets. Examination of damage fields shows that the total fraction of damage (voids) increases as the tensile rates decrease. In addition, an accompanying larger plastic dissipation, in the form of grain misorientation measured by means of electron backscatter diffraction, is present in the samples deformed at lower tensile rates. These results suggest a time dependent behaviour of the processes the plastic processes for void growth.

Effects of grain boundary structure and distribution on the spall response of copper

Plate impact experiments have been carried out to examine the influence of grain boundary characteristics, i.e density and structure, on the spall response of Cu samples with grain sizes of 30-, 60-, 100- and 200-µm. The peak compressive stress is ~1.50 GPa for all experiments, low enough to cause an early stage of incipient spall damage. A clear effect of the grain size is observed in the free surface velocity behavior after the pull-back minima, when re-acceleration occurs. The post-impact metallographic analyses show that for the materials with intermediate grain sizes (60 µm), the damage behavior is dominated by the growth of isolated voids and plastic dissipation. Whereas in the 30- and 200-µm samples, void coalescence is observed to dominate the damage behavior. Electron backscatter diffraction (EBSD) observations show that special boundaries corresponding to Σ3-type (~ 60° misorientation) are more resistant to void formation.

Local Mechanical Property Evolution During High Strain-Rate Deformation of Tantalum

Damage within ductile metals is often linked to local heterogeneities. In ductile metals, damage typically occurs after plastic deformation, which evolves the microstructure and its properties in ways that are not easily measured in situ. This is particularly true for materials subject to dynamic loading. Here, we use a combination of spherical nanoindentation testing and electron microscopy to quantify changes in local dislocation slip resistance as a function of grain orientation in polycrystalline tantalum subjected to high strain-rate deformation. A nanoindentation data analysis technique is used to convert spherical nanoindentation data into stress–strain curves. This technique works with microstructural characterization at the indentation site and involves two steps: (1) determination of the functional dependence of the indentation yield strength (Yind) on the crystal orientation in the undeformed condition, and (2) use of nanoindentation and EBSD measurements on the deformed samples to determine changes in the local slip resistance. In this work, undeformed Ta had indentation yield values that varied by as much as 40% depending on the crystal orientation. The dynamically deformed Ta displayed a large variance in the strain hardening rates as a function of grain orientation. Soft grains (those with low Taylor Factor) were found to harden significantly more as compared to hard grains (those with a high Taylor Factor). These data are discussed in terms of grain interactions where the hard grains impose additional work on neighboring soft grains due to constraint at the boundaries.

Controlled shock loading conditions for micrstructural correlation of dynamic damage behavior

Materials performance is recognized as being central to many emergent technologies. Future technologies will place increasing demands on materials performance with respect to extremes in stress, strain, temperature, and pressure. In this study, the dynamic ductile damage evolution of OFHC Cu is explored as a test bed to understand the role of spatial effects due to loading profile and defect density. Well-characterized OFHC Cu samples of 30 μm, 60 μm, 100 μm, and 200 μm grain sizes were subjected to plate impact uniaxial strain loading at 1.5 GPa. This spall geometry produced early stage (incipient) damage in the Cu samples that could be correlated to microstructural features in metallographic analysis. The recovered damaged microstructure was examined using traditional 2D metallographic techniques (optical and electron microscopy) as well as 3D x-ray microtomography. Calculated spall strength from the free surface velocimetry (VISAR) showed no change with respect to changes in grain size, however, the ma...