Time-resolved shear transformations in the transient plastic regime of sheared amorphous silicon.

The accumulation of shear transformations (STs) in space and time is responsible for plastic deformation in amorphous solids. Here we study the effect of finite strain rates on STs during simulations of athermal shear deformation in an atomistic model of amorphous silicon. We present a time-resolved analysis of STs by mapping the plastic events identified in the atomistic simulations on a collection of Eshelby inclusions, which are characterized in terms of number, effective volume, lifetime, and orientation. Our analysis led us to distinguish between small and large events. We find that the main effect of a lower strain rate is to allow for a larger number of small events, roughly identified by an effective volume γ_{0}V_{0}<20 Å^{3}, while the number and characteristics of larger events are surprisingly independent of the strain rate. We show that at low strains, the decrease of the stress observed at lower strain rates is mainly due to the excess of small events, while at larger strains, when the glass approaches the yield point where a shear band forms, larger events start to play a role and organize due to their elastic interactions. This phenomenology is compared with the predictions of mesoscale elastoplastic models. The technique developed here can be used as a systematic tool to analyze plasticity during molecular dynamics simulations. It can also give valuable information to develop physically grounded mesoscale models of plasticity, providing quantitative predictions of the mechanical properties of amorphous materials.

Nonaffine lattice dynamics with the Ewald method reveals strongly nonaffine elasticity of α-quartz.

A lattice dynamical formalism based on nonaffine response theory is derived for noncentrosymmetric crystals, accounting for long-range interatomic interactions using the Ewald method. The framework takes equilibrated static configurations as input to compute the elastic constants in excellent agreement with both experimental data and calculations under strain. Besides this methodological improvement, which enables faster evaluation of elastic constants without the need of explicitly simulating the deformation process, the framework provides insights into the nonaffine contribution to the elastic constants of α-quartz. It turns out that, due to the noncentrosymmetric lattice structure, the nonaffine (softening) correction to the elastic constants is very large, such that the overall elastic constants are at least 3-4 times smaller than the affine Born-Huang estimate.

Cellulose crystals plastify by localized shear.

Cellulose microfibrils are the principal structural building blocks of wood and plants. Their crystalline domains provide outstanding mechanical properties. Cellulose microfibrils have thus a remarkable potential as eco-friendly fibrous reinforcements for structural engineered materials. However, the elastoplastic properties of cellulose crystals remain poorly understood. Here, we use atomistic simulations to determine the plastic shear resistance of cellulose crystals and analyze the underpinning atomic deformation mechanisms. In particular, we demonstrate how the complex and adaptable atomic structure of crystalline cellulose controls its anisotropic elastoplastic behavior. For perfect crystals, we show that shear occurs through localized bands along with noticeable dilatancy. Depending on the shear direction, not only noncovalent interactions between cellulose chains but also local deformations, translations, and rotations of the cellulose macromolecules contribute to the response of the crystal. We also reveal the marked effect of crystalline defects like dislocations, which decrease both the yield strength and the dilatancy, in a way analogous to that of metallic crystals.

Plastic anisotropy and dislocation trajectory in BCC metals.

Plasticity in body-centred cubic (BCC) metals at low temperatures is atypical, marked in particular by an anisotropic elastic limit in clear violation of the famous Schmid law applicable to most other metals. This effect is known to originate from the behaviour of the screw dislocations; however, the underlying physics has so far remained insufficiently understood to predict plastic anisotropy without adjustable parameters. Here we show that deviations from the Schmid law can be quantified from the deviations of the screw dislocation trajectory away from a straight path between equilibrium configurations, a consequence of the asymmetrical and metal-dependent potential energy landscape of the dislocation. We propose a modified parameter-free Schmid law, based on a projection of the applied stress on the curved trajectory, which compares well with experimental variations and first-principles calculations of the dislocation Peierls stress as a function of crystal orientation.

Reversible dilatancy in entangled single-wire materials.

Designing structures that dilate rapidly in both tension and compression would benefit devices such as smart filters, actuators or fasteners. This property however requires an unusual Poisson ratio, or Poisson function at finite strains, which has to vary with applied strain and exceed the familiar bounds: less than 0 in tension and above 1/2 in compression. Here, by combining mechanical tests and discrete element simulations, we show that a simple three-dimensional architected material, made of a self-entangled single long coiled wire, behaves in between discrete and continuum media, with a large and reversible dilatancy in both tension and compression. This unusual behaviour arises from an interplay between the elongation of the coiled wire and rearrangements due to steric effects, which, unlike in traditional discrete media, are hysteretically reversible when the architecture is made of an elastic fibre.

Orientational anisotropy in simulated vapor-deposited molecular glasses.

Enhanced kinetic stability of vapor-deposited glasses has been established for a variety of glass organic formers. Several recent reports indicate that vapor-deposited glasses can be orientationally anisotropic. In this work, we present results of extensive molecular simulations that mimic a number of features of the experimental vapor deposition process. The simulations are performed on a generic coarse-grained model and an all-atom representation of N,N'-bis(3-methylphenyl)-N,N'-diphenylbenzidine (TPD), a small organic molecule whose vapor-deposited glasses exhibit considerable orientational anisotropy. The coarse-grained model adopted here is found to reproduce several key aspects reported in experiments. In particular, the molecular orientation of vapor-deposited glasses is observed to depend on substrate temperature during deposition. For a fixed deposition rate, the molecular orientation in the glasses changes from isotropic, at the glass transition temperature, Tg, to slightly normal to the substrate at temperatures just below Tg. Well below Tg, molecular orientation becomes predominantly parallel to the substrate. The all-atom model is used to confirm some of the equilibrium structural features of TPD interfaces that arise above the glass transition temperature. We discuss a mechanism based on distinct orientations observed at equilibrium near the surface of the film, which get trapped within the film during the non-equilibrium process of vapor deposition.

Dislocation locking versus easy glide in titanium and zirconium.

The ease of a metal to deform plastically in selected crystallographic planes depends on the core structure of its dislocations. As the latter is controlled by electronic interactions, metals with the same valence electron configuration usually exhibit a similar plastic behaviour. For this reason, titanium and zirconium, two transition metals of technological importance from the same column of the periodic table, have so far been assumed to deform in a similar fashion. However, we show here, using in situ transmission electron microscopy straining experiments, that plasticity proceeds very differently in these two metals, being intermittent in Ti and continuous in Zr. This observation is rationalized using first-principles calculations, which reveal that, in both metals, dislocations may adopt the same set of different cores that are either glissile or sessile. An inversion of stability of these cores between Zr and Ti is shown to be at the origin of the profoundly different plastic behaviours.

Signature of dislocations and stacking faults of face-centred cubic nanocrystals in coherent X-ray diffraction patterns: a numerical study.

Crystal defects induce strong distortions in diffraction patterns. A single defect alone can yield strong and fine features that are observed in high-resolution diffraction experiments such as coherent X-ray diffraction. The case of face-centred cubic nanocrystals is studied numerically and the signatures of typical defects close to Bragg positions are identified. Crystals of a few tens of nanometres are modelled with realistic atomic potentials and 'relaxed' after introduction of well defined defects such as pure screw or edge dislocations, or Frank or prismatic loops. Diffraction patterns calculated in the kinematic approximation reveal various signatures of the defects depending on the Miller indices. They are strongly modified by the dissociation of the dislocations. Selection rules on the Miller indices are provided, to observe the maximum effect of given crystal defects in the initial and relaxed configurations. The effect of several physical and geometrical parameters such as stacking fault energy, crystal shape and defect position are discussed. The method is illustrated on a complex structure resulting from the simulated nanoindentation of a gold nanocrystal.

First-principles study of secondary slip in zirconium.

Although the favored glide planes in hexagonal close-packed Zr are prismatic, screw dislocations can escape their habit plane to glide in either pyramidal or basal planes. Using ab initio calculations within the nudged elastic band method, we show that, surprisingly, both events share the same thermally activated process with an unusual conservative motion of the prismatic stacking fault perpendicularly to itself. Halfway through the migration, the screw dislocation adopts a nonplanar metastable configuration with stacking faults in adjacent prismatic planes joined by a two-layer pyramidal twin.

Quantum effect on thermally activated glide of dislocations.

Crystal plasticity involves the motion of dislocations under stress. So far, atomistic simulations of this process have predicted Peierls stresses, the stress needed to overcome the crystal resistance in the absence of thermal fluctuations, of more than twice the experimental values, a discrepancy best-known in body-centred cubic crystals. Here we show that a large contribution arises from the crystal zero-point vibrations, which ease dislocation motion below typically half the Debye temperature. Using Wigner's quantum transition state theory in atomistic models of crystals, we found a large decrease of the kink-pair formation enthalpy due to the quantization of the crystal vibrational modes. Consequently, the flow stress predicted by Orowan's law is strongly reduced when compared with its classical approximation and in much closer agreement with experiments. This work advocates that quantum mechanics should be accounted for in simulations of materials and not only at very low temperatures or in light-atom systems.

Predicting dislocation climb and creep from explicit atomistic details.

Here we report kinetic Monte Carlo simulations of dislocation climb in heavily deformed, body-centered cubic iron comprising a supersaturation of vacancies. This approach explicitly incorporates the effect of nonlinear vacancy-dislocation interaction on vacancy migration barriers as determined from atomistic calculations, and enables observations of diffusivity and climb over time scales and temperatures relevant to power-law creep. By capturing the underlying microscopic physics, the calculated stress exponents for steady-state creep rates agree quantitatively with the experimentally measured range, and qualitatively with the stress dependence of creep activation energies.

Role of friction in the mechanics of nonbonded fibrous materials.

Discrete element simulations are employed to study the influence of static friction on the mechanical response of assemblies of nonbonded semiflexible fibers during cycles of isostatic compressions and releases. Hysteresis is evidenced during the cycles and is related to the sensitivity of the frictional contacts on normal forces. Nonzero frictions are shown to decrease both the packing density and caging number but do not affect the critical exponents that characterize the pressure and bulk and shear moduli. Assemblies of frictionless fibers are found fragile in the sense that they resist isostatic compressions but have a zero shear modulus at all densities.

Distribution of thermally activated plastic events in a flowing glass.

The potential energy landscape of a flowing metallic glass is revealed using the activation-relaxation technique. For a two-dimensional Lennard-Jones system initially deformed into a steady-state condition through quasistatic shear, the distribution of activation energies is shown to contain a large fraction of low-energy barriers, consistent with a highly nonequilibrium flow state. The distribution of plastic strains has a fundamentally different shape than that obtained during quasistatic simulations, exhibiting a peak at finite strain and, after elastic unloading, a nonzero mean plastic strain that evidences a polarization of the flow state. No significant correlation is found between the activation energy of a plastic event and its associated plastic strain.

Discrete modeling of the mechanics of entangled materials.

We employ a discrete computational model to study the entanglement transition of non-cross-linked semiflexible fibers during isostatic compressions. We determine, as a function of the fiber aspect ratio, packing densities and caging numbers, i.e., the density and number of contacts per fiber at the entanglement transition. The caging number is found to be 8 for short fibers and to drop down to 4 for longer fibers. Compressions beyond the entanglement transition allow us to determine, for these networks that deform primarily by bending, the scaling exponents of the pressure and of the bulk modulus (=3), as well as of the number of contacts per fiber (=1).