Pracownicy

Streszczenie:
The effect of a crack on the structural response of a nanobeam is commonly modeled by introducing a discontinuity in the slope at the cracked cross-section, with the magnitude proportional to the bending moment transmitted through the section. The proportionality factor (i.e., the crack compliance) is typically derived from closed-form solutions based on classical linear elastic fracture mechanics, whose validity at micro- and nanoscale dimensions is not well established. This study reveals size effects in the crack compliance of silicon nanobeams by integrating large-scale molecular dynamics (MD) simulations involving >2.3 million atoms with beam formulations derived from a local/nonlocal stress-driven gradient elasticity theory. Size-dependent bending and free transverse vibration responses of intact nanobeams are obtained through MD simulations and used to calibrate the nonlocal parameters of the continuum models. The calibrated models are then employed to study cracked nanobeams. Comparisons between MD predictions and theoretical results reveal pronounced size effects: classical formulas substantially underestimate crack-induced flexibility in nanobeams, while the discrepancy decreases with increasing beam length. We demonstrate that this size-dependent crack compliance is influenced by both the crystallographic orientation and the imposed boundary conditions. An atomic strain analysis reveals that the near-tip strain distribution in short nanobeams deviates from the classical singular form; however, for sufficiently long nanobeams (e.g., L ≈ 180 nm for a fixed–guided nanobeam under bending), discrete atomic effects become negligible, and strain distribution and crack compliance converge toward classical predictions.

Słowa kluczowe:
Molecular dynamics, Nonlocal elasticity theory, Nanobeams, Crack compliance, Size effect, Silicon

Streszczenie:
Classical continuum theories neglect surface-dominated effects that govern the mechanical response of nanostructures at high surface-to-volume ratios (SVR). Using molecular dynamics simulations, this work examines the size-dependent free transverse vibration of solid and hollow silicon nanobeams and shows that hollow geometries exhibit a non-monotonic dependence of natural frequency on cavity size, in contrast to the monotonic surface-induced softening displayed by solid nanobeams. For small cavities, geometric stiffening from the redistribution of material away from the neutral axis outweighs surface softening, increasing the frequency despite a rising SVR; as the cavity enlarges and the walls thin, the negative surface elastic constants of silicon dominate, producing a pronounced frequency drop. This competition is shown to be quantitatively consistent with an extension of the Miller–Shenoy surface-elasticity framework to hollow cross-sections, and is distilled into a minimal two-term dimensionless scaling law that balances a geometric stiffening term against a surface-softening term governed by the ratio of an intrinsic material length scale to the beam's outer dimension. The scaling law predicts the cavity ratio at which the stiffening-to-softening transition occurs, and the molecular dynamics results show this transition at a smaller cavity ratio than the continuum prediction, pointing to an additional, cross-section-dependent atomistic contribution to surface softening not captured by the linear continuum model. These results clarify the competing mechanisms governing the vibrational response of hollow nanobeams and provide a predictive, extensible framework connecting molecular-scale surface elasticity to continuum-level nanoscale design.

Słowa kluczowe:
Hollow nanobeams, Non-monotonic vibration, Surface-to-volume ratio, Size-dependent effects, Molecular dynamics

Streszczenie:
A two-dimensional constitutive model was developed to simulate grain boundary motion in polycrystalline titanium exposed simultaneously to magnetic field and elastic strain based on the thermodynamic laws. The multi-scale coupled finite element and multi-phase-field simulations were used to investigate the simultaneous effects of the driving forces arising from the magnetic field and elastic strain energy on microstructure evolution of titanium bicrystalline and polycrystalline samples. The multi-phase-field approach was employed to implement the kinetic relations of grain boundary migration at the mesoscale level. On the other hand, the equilibrium equations were implemented on a macroscale level by the finite element method. Based on the simulation results, the magnetically induced driving force overrides the elastic strain driving force and causes texture evolution toward orientations that contain less magnetic stored energy when the microstructure is exposed to a magnetic field of sufficient strength. Additionally, applying an elastic strain before annealing reduces the time required for magnetic field annealing by accelerating the microstructure evolution. The mean grain size and desired texture grow rapidly when the magnetic field strength and elastic strain are simultaneously increased.

Słowa kluczowe:
Multi-phase-field model, Grain growth, Magnetic field, Stressed grain growth

Streszczenie:
The influence of magnetic field-driven grain growth in a polycrystalline microstructure is studied via the multi-phase-field approach with the assumptions of isotropic and anisotropic grain boundary (GB) energy. Simulations are carried out using a two-dimensional representative volume element of titanium polycrystalline with the hexagonal crystal structure. The GB energy is a function of the misorientation angle by Read-Shockley equation and is independent of the GB inclination. The simulation results illustrate that the grain growth kinetics and final texture influentially depend on the initial texture when considering the misorientation-dependent anisotropy of GB energy. If the Euler angle is randomly distributed for all of the grains, the simulation results are similar for isotropic and anisotropic GB energies. Whereas the simulation results for anisotropic GB energy are significantly different from the isotropic case by considering for all grains. The elongation of grains, the aggregation of grains with analogous orientations, and deceleration of texture evolution and grain growth kinetics are its most important features. Also, the impact of magnetic field intensity is examined and, it is illustrated that the difference in simulation results for isotropic and anisotropic GB energies decreases with increasing the magnetic field intensity.

Słowa kluczowe:
Misorientation-dependent anisotropy, Magnetic field, Multi-phase-field model, Grain growth