Landau-Type Theory of Planar Crystal Plasticity

Anomalous Softness in Amorphous Matter in the Reversible Plastic Regime

We study an elastoplastic model of an amorphous solid subject to athermal quasistatic cyclic shear strain. We focus on cycling amplitudes in the so-called reversible-plastic regime where, after a transient, the system locks into a hysteretic limit cycle and returns to the same microscopic configuration after one or more strain cycles. We show that the ground state energy of the terminal limit cycle decreases with increasing cycling amplitude. In analogy to an annealed alloy or an aged colloidal glass, one would expect the states with lower energy to be mechanically harder and to require larger stresses and strains to trigger microscopic rearrangements. However, we show the opposite result: the systems with lower energy cycled at higher strain amplitude are mechanically softer and begin to exhibit plastic rearrangements at smaller stresses and strains within the cycle. We explain this anomaly quantitatively in terms of Eshelby inclusion theory where an inclusion is subjected to a particular negative stress value after it undergoes a yielding event. These results point the way toward measurements to be conducted in experiments and particle-based computer simulations on cyclically sheared amorphous solids.

Coarse-Graining and Forecasting Atomic Material Simulations with Descriptors

Atomic simulations of materials require significant resources to generate, store, and analyze. Here, descriptor functions are proposed as a general, metric latent space for atomic structures, ideal for use in large-scale simulations. Descriptors can regress a broad range of properties, including character-dependent dislocation densities, stress states, or radial distribution functions. A vector autoregressive model can generate trajectories over yield points, resample from new initial conditions and forecast trajectory futures. A forecast confidence, essential for practical application, is derived by propagating forecasts through the Mahalanobis outlier distance, providing a powerful tool to assess coarse-grained models. Application to nanoparticles and yielding of nanoscale dislocation networks confirms low uncertainty forecasts are accurate and resampling allows for the propagation of smooth property distributions. Yielding is associated with a collapse in the intrinsic dimension of the descriptor manifold, which is discussed in relation to the yield surface.

Inelastic rotations and pseudoturbulent plastic avalanches in crystals

Plastic deformations in crystals produce microstructures with randomly oriented patches of unstressed lattice forming complex textures. We use a mesoscopic Landau-type tensorial model of crystal plasticity to show that in such textures rotations can originate from crystallographically exact microslips which self organize in the form of laminates of a pseudotwin type. The formation of such laminates can be viewed as an effective internal "wrinkling" of the crystal lattice. While such "wrinkling" disguises itself as an elastically neutral rotation, behind it is inherently dissipative, dislocation-mediated process. Our numerical experiments reveal pseudoturbulent effective rotations with power-law distributed spatial correlations which suggests that the process of dislocational self-organization is inherently unstable and points toward the necessity of a probabilistic description of crystal plasticity.

On the yielding of a point-defect-rich model crystal under shear: insights from molecular dynamics simulations

In real crystals and at finite temperatures point defects are inevitable. Under shear their dynamics severely influence the mechanical properties of these crystals, giving rise to non-linear effects, such as ductility. In an effort to elucidate the complex behavior of crystals under plastic deformation it is crucial to explore and to understand the interplay between the timescale related to the equilibrium point-defect diffusion and the shear-induced timescale. Based on extensive non-equilibrium molecular dynamics simulations we present a detailed investigation on the yielding behavior of cluster crystals, an archetypical model for a defect-rich crystal: in such a system clusters of overlapping particles occupy the lattice sites of a regular (FCC) structure. In equilibrium particles diffuse via site-to-site hopping while maintaining the crystalline structure intact. We investigate these cluster crystals at a fixed density and at different temperatures where the system remains in the FCC structure: temperature allows us to vary the diffusion timescale appropriately. We then expose the crystal to shear, thereby choosing shear rates which cover timescales that are both higher and lower than the equilibrium diffusion timescales. We investigate the macroscopic and microscopic response of our cluster crystal to shear and find that the yielding scenario of such a system does not rely on the diffusion of the particles - it is rather related to the plastic deformation of the underlying crystalline structure. The local bond order parameters and the measurement of local angles between neighboring clusters confirm the cooperative movement of the clusters close to the yield point. Performing complementary, related simulations for an FCC crystal formed by harshly repulsive particles reveals similarities in the yielding behavior between both systems. Still we find that the diffusion of particles does influence characteristic features in the cluster crystal, such as a less prominent increase of order parameters close to the yield point. Our simulations provide for the first time an insight into the role of the diffusion of defects in the yielding behavior of a defect-rich crystal under shear. These observations will thus be helpful in the development of theories for the plastic deformation of defect-rich crystals.

Yielding in an Integer Automaton Model for Amorphous Solids under Cyclic Shear

We present results on an automaton model of an amorphous solid under cyclic shear. After a transient, the steady state falls into one of three cases in order of increasing strain amplitude: (i) pure elastic behavior with no plastic activity, (ii) limit cycles where the state recurs after an integer period of strain cycles, and (iii) irreversible plasticity with longtime diffusion. The number of cycles N required for the system to reach a periodic orbit diverges as the amplitude approaches the yielding transition between regimes (ii) and (iii) from below, while the effective diffusivity D of the plastic strain field vanishes on approach from above. Both of these divergences can be described by a power law. We further show that the average period T of the limit cycles increases on approach to yielding.

Variety of scaling behaviors in nanocrystalline plasticity

We address the question of why larger, high-symmetry crystals are mostly weak, ductile, and statistically subcritical, while smaller crystals with the same symmetry are strong, brittle and supercritical. We link it to another question of why intermittent elasto-plastic deformation of submicron crystals features highly unusual size sensitivity of scaling exponents. We use a minimal integer-valued automaton model of crystal plasticity to show that with growing variance of quenched disorder, which can serve in this case as a proxy for increasing size, submicron crystals undergo a crossover from spin-glass marginality to criticality characterizing the second order brittle-to-ductile (BD) transition. We argue that this crossover is behind the nonuniversality of scaling exponents observed in physical and numerical experiments. The nonuniversality emerges only if the quenched disorder is elastically incompatible, and it disappears if the disorder is compatible.

Nucleation of Dislocations in 3.9 nm Nanocrystals at High Pressure

As circuitry approaches single nanometer length scales, it has become important to predict the stability of single nanometer-sized metals. The behavior of metals at larger scales can be predicted based on the behavior of dislocations, but it is unclear if dislocations can form and be sustained at single nanometer dimensions. Here, we report the formation of dislocations within individual 3.9 nm Au nanocrystals under nonhydrostatic pressure in a diamond anvil cell. We used a combination of x-ray diffraction, optical absorbance spectroscopy, and molecular dynamics simulation to characterize the defects that are formed, which were found to be surface-nucleated partial dislocations. These results indicate that dislocations are still active at single nanometer length scales and can lead to permanent plasticity.