Logarithmic Rate Dependence Research Articles

Thermally activated intermittent flow in amorphous solids.

Using mean field theory and a mesoscale elastoplastic model, we analyze the steady state shear rheology of thermally activated amorphous solids. At sufficiently high temperature and driving rates, flow is continuous and described by well-established rheological flow laws such as Herschel-Bulkley and logarithmic rate dependence. However, we find that these flow laws change in the regime of intermittent flow, where collective events no longer overlap and serrated flow becomes pronounced. In this regime, we identify a thermal activation stress scale, xa(T,), that wholly captures the effect of driving rate  and temperature T on average flow stress, stress drop (avalanche) size and correlation lengths. Different rheological regimes are summarized in a dynamic phase diagram for the amorphous yielding transition. Theoretical predictions call for a need to re-examine the rheology of very slowly sheared amorphous matter much below the glass transition.

Finite Element Technique for Predicting Stress Distribution in Milling TC4 Titanium Alloy

Cutting forces modeling is the basis to understand, simulate milling process and further to control milling process parameters for obtaining higher precision workpieces. With the development of engineering technology, FEM can be used to simulate metal machining process and gain better understanding of material flow within dies, so as to optimize tooling to eliminate tears, laps and other forging defects. In this paper, the calculated cutting force increases approximately logarithmically with the cutting speed, as should be expected from the logarithmic rate dependence.

A two‐scale model for sheared fault gouge: Competition between macroscopic disorder and local viscoplasticity

AbstractWe develop a model for sheared gouge layers that accounts for the local increase in temperature at the grain contacts during sliding. We use the shear transformation zone theory, a statistical thermodynamic theory, to describe irreversible macroscopic plastic deformations due to local rearrangements of the gouge particles. We track the temperature evolution at the grain contacts using a one‐dimensional heat diffusion equation. At low temperatures, the strength of the asperities is limited by the flow strength, as predicted by dislocation creep models. At high temperatures, some of the constituents of the grains may melt leading to the degradation of the asperity strength. Our model predicts a logarithmic rate dependence of the steady state shear stress in the quasistatic regime. In the dense flow regime the frictional strength decreases rapidly with increasing slip rate due to thermal softening at the granular interfaces. The transient response following a step in strain rate includes a direct effect and a following evolution effect, both of which depend on the magnitude and direction of the velocity step. In addition to frictional heat, the energy budget includes an additional energy sink representing the fraction of external work consumed in increasing local disorder. The model links low‐speed and high‐speed frictional response of gouge layers and provides an essential ingredient for multiscale modeling of earthquake ruptures with enhanced coseismic weakening.

Numerical Simulation and Prediction of Cutting Force in Turning of Titanium Alloy

Though titanium alloys are being increasingly sought in a wide variety of engineering and biomedical applications, their manufacturability, especially machining and grinding imposes lot of constraints. With the development of engineering technology, FEM can be used to simulate metal machining process and gain better understanding of material flow within dies, so as to optimize tooling to eliminate tears, laps and other forging defects. In this paper, numerical simulation was conducted by using FEM software on the whole cutting process for TC4 alloy mounting parts in an effort to investigate the metal flow behavior. The calculated cutting force increases approximately logarithmically with the cutting speed, as should be expected from the logarithmic rate dependence.

Surface characterization of oxide growth on porous germanium films oxidized in air

A time iterative surface analytical study of as-deposited and chlorinated nanoporous germanium (PGe) films oxidized in Class 1000 cleanroom air at room temperature is reported. Deconvolution of X-ray photoelectron spectroscopy (XPS) Ge 3d core level spectra for as-deposited films showed stable levels of Ge2O, GeO, and Ge2O3 with air exposure duration, while growth of GeO2 was observed with logarithmic rate dependence, characteristic of low temperature oxide growth on fully dense Ge films. In contrast, chlorinated PGe showed an initially reduced surface and growth of all GeOx phases for up to 10h of air exposure, after which only GeO2 was observed to grow with similar kinetics to that observed on the as-deposited films. Deconvolution of the XPS Cl 2p core level spectra showed continual loss of chlorine for up to ~10h of air exposure after which no ClGe components could be resolved. The results reported herein reveal logarithmic growth of each of the GeOx phases on chlorinated PGe during displacement of chlorine with oxygen. Once chlorine is removed from the surface, the percentages of Ge2O, GeO, and Ge2O3 suboxides remain constant with only GeO2 growth with further air exposure. These results offer insight into the early stages of oxide growth on porous germanium indicating the formation of a suboxide transition layer onto which GeO2 grows.

Logarithmic rate dependence of force networks in sheared granular materials.

Many models of slow, dense granular flows assume that the internal stresses are independent of the shearing rate. In contrast, logarithmic rate dependence is found in solid-on-solid friction, geological settings and elsewhere. Here we investigate the rate dependence of stress in a slowly sheared two-dimensional system of photoelastic disks, in which we are able to determine forces on the granular scale. We find that the mean (time-averaged) stress displays a logarithmic dependence on the shear rate for plastic (irreversible) deformations. However, there is no perceivable dependence on the driving rate for elastic (reversible) deformations, such as those that occur under moderate repetitive compression. Increasing the shearing rate leads to an increase in the strength of the force network and stress fluctuations. Qualitatively, this behaviour resembles the changes associated with an increase in density. Increases in the shearing rate also lead to qualitative changes in the distributions of stress build-up and relaxation events. If shearing is suddenly stopped, stress relaxations occur with a logarithmic functional form over long timescales. This slow collective relaxation of the stress network provides a mechanism for rate-dependent strengthening.

Kinetics in Highly Viscous Liquid Phase Realized under High Pressure.

Effect of pressure on the rate of relatively slow thermal Z to E isomerizations was studied in viscous organic liquids. The results clearly demonstrated that the reactions were transferred from the activation limited to the solvent-fluctuation limited regime by an increase in the solvent viscosity. The viscosity dependence of the observed rate could be analyzed by assuming a two-step mechanism based on the two-dimensional reaction coordinate model proposed by one of the present authors. A recent Biswas-Bagchi prediction of an inverse logarithmic dependence of rate was not born out by our experimental results. A single case of a multi exponential decay is also reported.