A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate

A novel multi-scale seamless model of brittle-crack propagation is proposed and applied to the simulation of fracture growth in a two-dimensional Ag plate with macroscopic dimensions. The model represents the crack propagation at the macroscopic scale as the drift-diffusion motion of the crack tip alone. The diffusive motion is associated with the crack-tip coordinates in the position space, and reflects the oscillations observed in the crack velocity following its critical value. The model couples the crack dynamics at the macroscales and nanoscales via an intermediate mesoscale continuum. The finite-element method is employed to make the transition from the macroscale to the nanoscale by computing the continuum-based displacements of the atoms at the boundary of an atomic lattice embedded within the plate and surrounding the tip. Molecular dynamics (MD) simulation then drives the crack tip forward, producing the tip critical velocity and its diffusion constant. These are then used in the Ito stochastic calculus to make the reverse transition from the nanoscale back to the macroscale. The MD-level modelling is based on the use of a many-body potential. The model successfully reproduces the crack-velocity oscillations, roughening transitions of the crack surfaces, as well as the macroscopic crack trajectory. The implications for a 3-D modelling are discussed.

Multiscale numerical modelling of crack propagation in two-dimensional metal plate

A novel multiscale model of brittle crack propagation in an Ag plate with macroscopic dimensions has been developed. The model represents crack propagation as stochastic drift-diffusion motion of the crack tip atom through the material, and couples the dynamics across three different length scales. It integrates the nanomechanics of bond rupture at the crack tip with the displacement and stress field equations of continuum based fracture theories. The finite element method is employed to obtain the continuum based displacement and stress fields over the macroscopic plate, and these are then used to drive the crack tip forward at the atomic level using the molecular dynamics simulation method based on many-body interatomic potentials. The linkage from the nanoscopic scale back to the macroscopic scale is established via the Ito stochastic calculus, the stochastic differential equation of which advances the tip to a new position on the macroscopic scale using the crack velocity and diffusion constant obtained on the nanoscale. Well known crack characteristics, such as the roughening transitions of the crack surfaces, crack velocity oscillations, as well as the macroscopic crack trajectories, are obtained.

A multi-scale numerical modelling of crack propagation in a 2D metallic plate

A new multi-scale model of brittle fracture growth in an Ag plate with macroscopic dimensions is proposed in which the crack propagation is identified with the stochastic drift-diffusion motion of the crack-tip atom through the material. The model couples molecular dynamics simulations, based on many-body interatomic potentials, with the continuum-based theories of fracture mechanics. The Ito stochastic differential equation is used to advance the tip position on a macroscopic scale before each nano-scale simulation is performed. Well-known crack characteristics, such as the roughening transitions of the crack surfaces, as well as the macroscopic crack trajectories are obtained.

Computer simulation of crack propagation in power electronics module solder joints

A numerical modelling method for the analysis of solder joint damage and crack propagation has been described in this paper. The method is based on the disturbed state concept. Under cyclic thermal-mechanical loading conditions, the level of damage that occurs in solder joints is assumed to be a simple monotonic scalar function of the accumulated equivalent plastic strain. The increase of damage leads to crack initiation and propagation. By tracking the evolution of the damage level in solder joints, crack propagation path and rate can be simulated using Finite Element Analysis method. The discussions are focused on issues in the implementation of the method. The technique of speeding up the simulation and the mesh dependency issues are analysed. As an example of the application of this method, crack propagation in solder joints of power electronics modules under cyclic thermal-mechanical loading conditions has been analyzed and the predicted cracked area size after 3000 loading cycles is consistent with experimental results.

The role of space charge formation in the generation of thermally stimulated current (TSC) spectroscopy data for a model amorphous drug system

Thermally stimulated current (TSC) spectroscopy is attracting increasing attention as a means of materials characterization, particularly in terms of measuring slow relaxation processes in solid samples. However, wider use of the technique within the pharmaceutical field has been inhibited by difficulties associated with the interpretation of TSC data, particularly in terms of deconvoluting dipolar relaxation processes from charge distribution phenomena. Here, we present evidence that space charge and electrode contact effects may play a significant role in the generation of peaks that have thus far proved difficult to interpret. We also introduce the use of a stabilization temperature in order to control the space charge magnitude. We have studied amorphous indometacin as a model drug compound and have varied the measurement parameters (stabilization and polarization temperatures), interpreting the changes in spectral composition in terms of charge redistribution processes. More specifically, we suggested that charge drift and diffusion processes, charge injection from the electrodes and high activation energy charge redistribution processes may all contribute to the appearance of shoulders and 'spurious' peaks. We present recommendations for eliminating or reducing these effects that may allow more confident interpretation of TSC data.

A regional chemostratigraphically-defined correlation framework for the late Triassic TAG-I Formation in Blocks 402 and 405a, Algeria

The Triassic Argilo-Gréseux Inférieur Formation (TAG-I) is one of the principal hydrocarbon reservoirs in the Berkine Basin of Algeria. Sedimentological studies have shown that it exhibits marked spatial and temporal facies variations on both a local field scale and a regional basinal scale. This variability, combined with a lack of diagnostic flora and fauna, makes regional correlation within the unit difficult. In turn, the lack of a consistent regional stratigraphic framework hampers the comparison of the various correlation schemes devised by operators in the basin. Contrasting the TAG-I in Blocks 402 and 405a exemplifies the problems encountered when attempting regionally to define a correlation framework for the interval. Between these two blocks, a distance of approximately 200 km, there are marked changes in the style of deposition from sand-dominated, proximal fluvial systems in the SW (Block 405a, MLN, MLC, KMD and MLNW fields) to a more distal, more clay-prone system in the NE (Block 402, ROD/BRSE/BSFN, SFNE and BSF fields). A chemostratigraphic study of the TAG-I in these two blocks has allowed a four-fold correlation framework to be defined, where each chemostratigraphic package has distinctive geochemical features. Chemostratigraphic Package 10, the oldest unit, lies above the Hercynian Unconformity, but beneath a geochemically identifiable hiatal surface. Chemostratigraphic Package 20 lies above the hiatal surface but is separated from the overlying packages by a mineralogical change identifiable in both claystone and sandstone geochemistry. Chemostratigraphic Packages 30 and 40 are chemically somewhat similar, but are separated by a regional event interpreted as a period of dolocrete and lacustrine development. By combining the geochemical differentiation of the units and recognition of their stratal boundaries, it is possible to define a correlation for the TAG-I between Blocks 402 and 405a. The proposed correlation between the two blocks suggests that the northern parts of Block 405a may have been occupied by a spur or subsidiary channel from the main SW–NE-trending fluvial system, resulting in one of the chemically defined packages being demonstrably absent in the MLNW, MLN, KMD and MLC fields when compared with the other areas of the study.

Finite volume modelling of shrinkage porosity formation in metal casting

Abstract not available