Energy Density Of Configuration Research Articles

Discrete dislocation modelling of δ hydrides in Zr: towards an understanding of the importance of interfacial stresses for crack initiation

We carried out discrete dislocation plasticity (DDP) simulations in the infinite-matrix approximation of δ Zr micro-hydrides – including their elastic field - first precipitating in Zr and then subjected to an external stress. We calculate and present the dislocation density, maximum principal shear and stresses, configurational energy density and plastic displacement. It was found that even hydrides as thin as 20 nm have a large impact on dislocation density, plastic deformation and stress build-up, and that this effect increases for increasing hydride thickness. It also appears that the critical location for crack nucleation is at the Zr/hydride interface. In fact, slip bands that develop on one side of the interface, and are stopped by it, are accompanied by the formation of high stresses. The observation that the interfacial stress is the only way in which hydrides are represented in the simulations, with no point obstacles or change in the slip systems at the interface, combined with the observed strong influence of the hydrides on the results, suggests a possible mechanistic explanation for the embrittlement caused by the precipitation of intragranular hydrides. The mechanism is rooted in the volumetric expansion upon precipitation and naturally includes a thickness dependence that is also experimentally observed.

First-principles calculation of the configurational energy density of states for a solid-state ion conductor with a variant of the Wang and Landau algorithm.

In this work, a variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is proposed. The algorithm was developed for the purpose of using first-principles simulations, such as density functional theory, to calculate the partition function of disordered sublattices in crystal materials. The expensive calculations of first-principles methods make a parallel algorithm necessary for a practical computation of the configurational energy density of states within a supercell approximation of a solid-state material. The algorithm developed in this work is tested with the two-dimensional (2d) Ising model to bench mark the algorithm and to help provide insight for implementation to a materials science application. Tests with the 2d Ising model revealed that the algorithm has good performance compared to the original Wang and Landau algorithm and the 1/t algorithm, in particular the short iteration performance. A proof of convergence is presented within an adiabatic assumption, and the analysis is able to correctly predict the time dependence of the modification factor to the density of states. The algorithm was then applied to the lithium and lanthanum sublattice of the solid-state lithium ion conductor Li_{0.5}La_{0.5}TiO_{3}. This was done to help understand the disordered nature of the lithium and lanthanum. The results find, overall, that the algorithm performs very well for the 2d Ising model and that the results for Li_{0.5}La_{0.5}TiO_{3} are consistent with experiment while providing additional insight into the lithium and lanthanum ordering in the material. The primary result is that the lithium and lanthanum become more mixed between layers along the c axis for increasing temperature. In part, the simulation of the disordered Li_{0.5}La_{0.5}TiO_{3} system serves as a benchmark for what size systems are currently and in the near future practical to calculate with density functional theory methods.

Discrete dislocation, crystal plasticity and experimental studies of fatigue crack nucleation in single-crystal nickel

Dislocation configurational energy and stored energy densities are determined in discrete dislocation and crystal plasticity modelling respectively and assessed with respect to experiments on single crystal nickel fatigue crack nucleation. Direct comparisons between the three techniques are provided for two crystal orientation fatigue tests. These provide confirmation that both quantities correctly identify the sites of fatigue crack nucleation and that stored energy density is a reasonable approximation to the more rigorous dislocation configurational energy. GND density is shown to be important in locating crack nucleation sites because of its role in the local configurational energy density.

Effects of Grain Size, Orientation, and Source Density on Dislocation Configurational Energy Density

The effects of grain size, source density, and misorientations on the dislocation configurational energy area density are investigated using two-dimensional discrete dislocation plasticity. Grain boundaries are modeled as impenetrable to dislocations. The considered grain size ranges from $$ 0.4\;\upmu{\text{m}}^{2} $$ to $$ 8.0\;\upmu{\text{m}}^{2} $$ . The configurational energy area density displays a strong size dependence, similar to the stress response. Two sets of materials are considered, with low and high source/obstacle density. The high-source-density specimens exhibit negative configurational energy, implying that the dislocation structure is more stable than for isolated dislocations . The contribution of misorientation to the configurational energy density is analyzed using specimens with a single orientation or a checkerboard arrangement. The configurational energy density is found not only to depend on the dislocation spacing but also to be related to the local stress states. Low source densities lead to higher (positive) configurational energy densities.

The dislocation configurational energy density in discrete dislocation plasticity

Dislocation configurational energy is the term assigned to describe the elastically-stored energy associated with the interaction of dislocations and their structures. It is the energy which is over and above that from the summation of the dislocation line energies when considered isolated and non-interacting. It is therefore different to the free energy and the stored energy. This paper presents a formulation for its determination utilising discrete dislocation plasticity. The total geometrically necessary (GND) and statistically stored dislocation density mean free distance allows the configurational energy density to be determined, thus providing a length scale over which the configurational energy is stored. This quantity is assessed in polycrystals undergoing fatigue loading showing that clear microstructural locations, often associated with high GND density, become established at which the progressive, cyclic, increasing configurational energy occurs. A higher length scale crystal plasticity stored energy density has recently been introduced which attempts to capture local dislocation configurational energy density as an indicator of fatigue crack nucleation and growth. The former is compared and assessed against the dislocation configurational energy density in this paper.

Abinitio Micromagnetic Calculations in Steel with Ferromagnetic Behavior

The numerical magnetization modeling in magnetic materials is achieved by computing methods which determine the specific characteristics of each material by region and boundary conditions. Finite element method is presented, in comparison with other methods. Furthermore, there is presented the mathematical formula used, based on the minimization of the total energy density of configuration of magnetization.