Nathan R. Barton

A multiscale strength model for extreme loading conditions

We present a multiscale strength model in which strength depends on pressure, strain rate, temperature, and evolving dislocation density. Model construction employs an information passing paradigm to span from the atomistic level to the continuum level. Simulation methods in the overall hierarchy include density functional theory, molecular statics, molecular dynamics, dislocation dynamics, and continuum based approaches. Given the nature of the subcontinuum simulations upon which the strength model is based, the model is particularly appropriate to strain rates in excess of 104 s−1. Strength model parameters are obtained entirely from the hierarchy of simulation methods to obtain a full strength model in a range of loading conditions that so far has been inaccessible to direct measurement of material strength. Model predictions compare favorably with relevant high energy density physics (HEDP) experiments that have bearing on material strength. The model is used to provide insight into HEDP experimental ...

Defect evolution and pore collapse in crystalline energetic materials

This work examines the use of crystal based continuum mechanics in the context of dynamic loading. In particular, we examine model forms and simulations which are relevant to pore collapse in crystalline energetic materials. Strain localization and the associated generation of heat are important for the initiation of chemical reactions in this context. The crystal mechanics based model serves as a convenient testbed for the interactions among wave motion, slip kinetics, defect generation kinetics and physical length scale. After calibration to available molecular dynamics and single crystal gas gun data for HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine), the model is used to predict behaviors for the collapse of pores under various conditions. Implications for experimental observations are discussed.

Direct numerical simulation of shear localization and decomposition reactions in shock-loaded HMX crystal

A numerical model is developed to study the shock wave ignition of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) crystal. The model accounts for the coupling between crystal thermal/mechanical responses and chemical reactions that are driven by the temperature field. This allows for the direct numerical simulation of decomposition reactions in the hot spots formed by mechanical loading. The model is used to simulate intragranular pore collapse under shock wave loading. In a reference case: (i) shear-enabled micro-jetting is responsible for a modest extent of reaction in the pore collapse region, and (ii) shear banding is found to be an important mode of localization. The shear bands, which are filled with molten HMX, grow out of the pore collapse region and serve as potential ignition sites. The model predictions of shear banding and reactivity are found to be quite sensitive to the respective flow strengths of the solid and liquid phases. In this regard, it is shown that reasonable assumptions o...

Strong stabilization of the Rayleigh-Taylor instability by material strength at megabar pressures

Experimental results showing significant reductions from classical in the Rayleigh–Taylor (RT) instability growth rate due to high pressure effective lattice viscosity in metal foils are presented. Stabilization of RT instability (RTI) by ablation and density gradients has been studied for decades. The regime of stabilized RTI due to material strength at high pressure is new. On the Omega Laser in the Laboratory for Laser Energetics, University of Rochester, target samples of polycrystalline vanadium are compressed and accelerated quasi-isentropically at ∼1 Mbar pressures, while maintaining the samples in the solid-state. Provided strong shocks are avoided, the higher the applied peak pressure, the higher the predicted foil strength, and hence, the higher the degree of strength stabilization of RTI. Several experiments were conducted where the amount of RT growth is measured by face-on radiography. The vanadium samples are probed by a laser driven He-α x-ray backlighter which produced 5.2 keV radiation. C...

Crystal level continuum modelling of phase transformations: the α ↔ epsilon transformation in iron

We present a crystal level model for thermo-mechanical deformation with phase transformation capabilities. The model is formulated to allow for large pressures (on the order of the elastic moduli) and makes use of a multiplicative decomposition of the deformation gradient. Elastic and thermal lattice distortions are combined into a single lattice stretch to allow the model to be used in conjunction with general equation of state relationships. Phase transformations change the mass fractions of the material constituents. The driving force for phase transformations includes terms arising from mechanical work, the temperature dependent chemical free energy change on transformation, and the interaction energy among the constituents. Deformation results from both these phase transformations and elasto-viscoplastic deformation of the constituents themselves. Simulation results are given for the α to phase transformation in iron. Results include simulations of shock-induced transformation in single crystals and of compression of polycrystals. Results are compared with available experimental data.

Yield Strength Asymmetry Predictions From Polycrystal Elastoplasticity

Since the 1960s, it has been known that elastoplastic polycrystal models predict asymmetries in the yield strength for polycrystals that have been prestrained. After prestraining in tension, a model polycrystal exhibits Bauschinger-like behavior in that it yields in compression at a lower stress magnitude than in tension. Furthermore, the knee of the reloading stress-strain curve is more gradual for compression than for tension. The origins of these behaviors reside in the assumption that links the macroscopic deformation to the deformations in individual crystals. More precisely, the reloading response is biased by the residual stress field which is induced with plastic straining by the anisotropy of the single crystal yield surface. While the earlier work pointed to the polycrystalline origins of the asymmetry, it did not resolve the degree to which the particular linking assumption affects the amount of asymmetry. However, due to the strong influence of the linking assumption on the crystal stresses, the sensitivity of the asymmetry to the linking assumption is expected to be appreciable. In this paper we examine the influence of the linking assumption on the magnitude of the computed yield strength asymmetry of prestrained polycrystals. Elastoplastic polycrystal simulations based on upper bound (Taylor) and lower bound (equilibrium-based) linking assumptions are compared to finite element computations in which elements constitute individual crystals. The finite element model maintains compatibility while satisfying equilibrium in a weak sense and treats the influence of neighboring crystals explicitly. The strength of the predicted Bauschinger effect does depend on the linking assumption, with ‘compatibility first’ models developing stronger yield strength asymmetries.

Precision of lattice strain and orientation measurements using high-energy monochromatic X-ray diffraction

A systematic framework for estimating the uncertainty associated with measurements of finite stretch and orientation of a crystalline lattice using monochromatic X-ray diffraction is presented. A hierarchical method is implemented, in which uncertainties in the locations of diffraction peaks are communicated to the lattice stretch and rotation parameters by using the classical method of weighted least squares. This enables the uncertainty of the lattice stretch and rotation parameters to be estimated from a single full rotation scan. This method is applied to diffraction data obtained from a ruby single crystal as an idealized case for validation, and an example application is demonstrated by analyzing a strained and plastically deformed polycrystalline titanium alloy, β21S. For the ruby single crystal, it was possible to attain average uncertainties for lattice orientation and strain that were found to be comparable to standard statistical analysis of repeated measurements. For the titanium alloy, a single grain was analyzed, and a precision of 0.03° for lattice orientation and 100–250 × 10−6 for lattice strain components was obtained. The basic framework of the uncertainty analysis is generally applicable, although specific results are unique to monochromatic X-ray diffraction experiments.

Analysis of deformation twinning in tantalum single crystals under shock loading conditions

The competition between dislocation slip and twinning in tantalum single crystals has been investigated utilizing a crystal level twinning model and the results from gas gun recovery experiments conducted at peak normal stresses of 25 and 55 GPa. The recovered samples were characterized using electron back scattered diffraction, and the observed twinning fractions were compared with the model. The experimental results show very low twin fractions in all orientations at 25 GPa, and that among (100), (110), (111), and (123) crystals, the (110) crystals had the largest amount of twinning at 55 GPa. The analysis shows that the general trends observed in the experimental data can be reproduced by the model when an orientation dependent dislocation evolution is used. This analysis gives insight into the possible influence of the dislocation density and its evolution on the observed twinning behavior.

Pole Figure Inversion Using Finite Elements Over Rodrigues Space

Using finite elements over Rodrigues space, methods are developed for the formation and inversion of pole figures. The methods take advantage of the properties of Rodrigues space, particularly the fact that geodesics corresponding to pole figure projection paths are straight lines. Both discrete and continuous pole figure data may be inverted to obtain orientation distribution functions (ODFs) in Rodrigues space, and we include sample applications for both types of data.

A method for intragranular orientation and lattice strain distribution determination

A novel approach to quantifying intragranular distributions is developed and applied to the α → ∊ phase transition in iron. The approach captures both the distribution of lattice orientation within a grain and the orientation dependence of the lattice strain. Use of a finite element discretization over a ball in Rodrigues space allows for the efficient use of degrees of freedom in the numerical approach and provides a convenient framework for gradient-based regularization of the inverse problem. Application to the α → ∊ phase transition in iron demonstrates the utility of the method in that intragranular orientation and lattice strain distributions in the α phase are related to the observed ∊ orientations. Measurement of the lattice strain distribution enables quantitative analysis of the driving forces for ∊ variant selection. The measurement and analysis together indicate quantitatively that the Burgers mechanism is operative under the experimental conditions examined here.