Dynamically strained ferroelastics: Statistical behavior in elastic and plastic regimes

Abstract

The dynamic evolution in ferroelastic crystals under external shear is explored by computer simulation of a twodimensional model. The characteristic geometrical patterns obtained during shear deformation include dynamic tweed in the elastic regime as well as interpenetrating needle domains in the plastic regime. As a result, the statistics of jerk energy differ in the elastic and plastic regimes. In the elastic regime the distributions of jerk energy are sensitive to temperature and initial configurations. However, in the plastic regime the jerk distributions are rather robust and do not depend much on the details of the configurations, although the geometrical pattern formed after yield is strongly influenced by the elastic constants of the materials and the configurations we used. Specifically, for all geometrical configurations we studied, the energy distribution of jerks shows a power-law noise pattern P (E) ∼ E −(γ −1) (γ − 1 = 1.3 − 2) at low temperatures and a Vogel-Fulcher distribution P (E) ∼ exp-(E/E 0) at high temperatures. More complex behavior occurs at the crossover between these two regimes where our simulated jerk distributions are very well described by a generalized Poisson distributions P (E) ∼ E −(γ −1) exp-(E/E 0) n with n = 0.4-0.5 and γ − 1 ≈ 0 (Kohlrausch law). The geometrical mechanisms for the evolution of the ferroelastic microstructure under strain deformation remain similar in all thermal regimes, whereas their thermodynamic behavior differs dramatically: on heating, from power-law statistics via the Kohlrausch law to a Vogel-Fulcher law. There is hence no simple way to predict the local evolution of the twin microstructure from just the observed statistical behavior of a ferroelastic crystal. It is shown that the Poisson distribution is a convenient way to describe the crossover behavior contained in all the experimental data without recourse to specific scaling functions or temperature-dependent cutoff lengths.

Isothermal annealing of shocked zirconium: Stability of the two-phase α/ω microstructure

“…In that work the evolution of ω fraction is fit to a modified Kohlrausch-Williams-Watts equation [42]or stretched exponential of the form η(t) ∝ t −α · exp − t τ (T ) β , there η is the ω fraction, t −α is an pre-factor that accounts for non-thermally activated events, T is the ab-solute temperature, and τ is the relaxation time or time for ≈37% of the transformation to take place. The produced fits show that the α was close to zero indicating that that the thermal contribution to the kinetics was small and the exponent β ≈ 0.5 indicating that the kinetics are analogous to other "glassy" or "frustrated" systems and not consistent with JohnsonMehl-Avrami-Kolmogorov nucleation and growth [43,44]. The predicted kinetics of the ω → α transformation in Ti with a simulated shocked microstructure via molecular dynamics was qualitatively consistent with the experimental results for Zr.…”

Strain rate dependence of twinning avalanches at high speed impact

“…1(a)), with values similar to results from previous quasistatic simulations. [7][8][9][10] Increasing the strain rate decreases the yield energy from 4 meV/atom at 5 Â 10 À6 s À1 , to 0.5 meV/atom at 5 Â 10 À5 s À1 (Fig. 1(b)), and to values smaller than 0.01 meV/atom at 10 À4 s À1 (Fig.…”

“…The details of properties obtained by this potential are described in our previous work. [7][8][9][10] The equilibrium unit cell is in shape of parallelogram with the shear angle of 4 . We set the equilibrium lattice constant a ¼ 1 Å and atomic mass to M ¼ 100 amu.…”

“…[7][8][9] This twin pattern is highly complex with a multitude of intersecting twin boundaries, the formation of needle domains and kinks inside twin walls. [7][8][9] The dynamics of the formation of the pattern near the yield point is dominated by a high number of energy jerks related to the nucleation and extension of twin patterns. Many of these pattern changes occur in avalanches so that the energy jerks scale the avalanche energies.…”

“…The yield process was shown previously to follow power law dynamics. [7][8][9][10] The avalanche dynamics of twinning has been investigated experimentally at low strain rates [11][12][13] while little is known for high strain rates. Two questions are tantamount: does the yield process remain scale invariant and if so, does the energy exponent of the power law distribution of the avalanche formation 14 change?…”