Search results for "solution"
showing 10 items of 5638 documents
Stress induced grain boundary migration in very soluble brittle salt
1999
Abstract Grain boundary migration (GBM) was studied in-situ at room temperature, atmospheric pressure and an applied diffmfwerential stress of ∼9.5 MPa under the optical microscope, in a wet aggregate of an elastic-brittle salt (sodium chlorate). The aggregate was previously deformed predominantly by a combination of grain boundary sliding, pressure solution and cataclastic solution creep. After deformation, but when the sample was still under differential stress, undeformed, fracture-free grains were observed to grow at the cost of deformed, intensely fractured grains. GMB rates typically fell in the range 2--10 μm/day. GBM took place only as long as the sample was under stress. Boundaries…
The structure of reactive grain-boundaries under stress containing confined fluids
2006
We present numerical experiments on structure development in grain-boundaries during dissolution–precipitation creep. Two solids that are represented by an elastic spring configuration are pressed together with a compressible fluid in the grain-boundary. The solid can dissolve or precipitate depending on elastic and surface energy as well as fluid pressure and concentration of dissolved material in the fluid. We perform a number of numerical experiments with different starting configurations that represent a large-scale island-channel interface with solid–solid contacts across the islands, a rough grain-boundary interface with a fluid along the whole interface and a smooth thin-film interfa…
Effect of microcracking on pressure-solution strain rate: The Gratz grain-boundary model
1998
Different, but reasonable and well-accepted assumptions made about grain-boundary structure during pressure-solution (PS) creep may easily have an effect of more than 10 orders of magnitude on the calculated PS deformation rate. Understanding of grain-boundary structure during PS creep is therefore extremely important. Experimental evidence is presented in support of a grain-boundary model previously proposed by A. J. Gratz on the basis of observations on naturally deformed rocks. In this model, boundaries are assumed to have a static island-channel network structure. Channels are located where microcracks intersect the boundary. The rate of material transport is governed by thin-film diffu…
The effect of elastic strain on the microstructure of free surfaces of stressed minerals in contact with an aqueous solution
2001
The influence of gradients in bulk elastic strain energy on the dissolution and growth behaviour of minerals in rocks is commonly considered negligible. We experimentally observed, however, that regular arrays of macroscopically visible etch grooves may develop on the originally smooth free surfaces of soluble crystals held in an undersaturated aqueous solution if the crystals are only elastically stressed. These grooves are oriented perpendicular to the compressive stress. They disappear soon after the stress is taken off. The formation of the grooves is well explained by recent theories on the instability of the surface of stressed solids. Development of such instabilities could significa…
Crystallographic preferred orientation development by dissolution–precipitation creep
2000
Abstract Crystallographic preferred orientations (CPOs) in deformed rocks are commonly interpreted as resulting from crystal plastic deformation mechanisms, where deformation is achieved by the movement of dislocations. In this paper we investigate the possibility of CPO-development by dissolution–precipitation creep or pressure solution. A numerical model is presented, which simulates the development of a grain aggregate that deforms by reaction-controlled dissolution–precipitation creep. Grains are simulated as rectangular boxes that change their shape by growth, or dissolution of their surfaces, depending on the normal stresses acting on the individual surfaces. Grains can also rotate du…
Influence of data input in the evaluation of Stress Intensity Factors from Thermoelastic Stress Analysis
2021
Abstract Thermoelastic Stress Analysis (TSA) is applied to evaluate the Stress Intensity Factor (SIF), T-stress and J-Integral in a Single-Edge-Notched-Tension sample undergoing fatigue cycling. The Williams’ series stress formulation and a least-square fitting (LSF) procedure are used to obtain the SIF and the T-stress. The evaluation is carried out with the aim to investigate the influence of the input data in the system of equations solved with the LSF, and in particular: the number of coefficients used in the Williams’ series and the choice and position of the fitted experimental data points. Three algorithms for the determination of the crack tip position are also evaluated: a coarse g…
Stress fields in general composite laminates
1996
A direct approach is employed to obtain a general boundary integral formulation for the analysis of composite laminates subjected to uniform axial strain. The integral equations governing the problem are directly deduced from the reciprocity theorem, employing the generalized orthotropic elasticity fundamental solutions expressly inferred. The solution is achieved by the boundary element method, which gives, once the traction-free boundary conditions and the interfacial continuity conditions are enforced, a linear system of algebraic equations. The formulation does not present restrictions with regard to the laminate stacking sequence and it does not require any aprioristic assumption. The …
Purification of recovered phosphoric acid by extracting aluminium with di-2-ethylhexyl phosphoric acid
2021
AbstractThe extraction of aluminium from dilute phosphoric acid with di-2-ethylhexyl phosphoric acid (DEHPA) was optimized using response surface methodology. The optimization was based on the experimental three-level central composite face-centred design (CCF) and was conducted on real-life samples. The three variables included were pH, extractant concentration and aqueous to organic phase ratio (AO). Under the optimized conditions (pH 2.5, 0.6 M DEHPA and AO ratio 1:2), extraction efficiency of 99% for aluminium in four extraction stages is achieved. The purified phosphoric acid solution can then be utilized by the fertilizing industry. Stripping tests for organic phase loaded with alumin…
Nonlinear Nonhomogeneous Elliptic Problems
2019
We consider nonlinear elliptic equations driven by a nonhomogeneous differential operator plus an indefinite potential. The boundary condition is either Dirichlet or Robin (including as a special case the Neumann problem). First we present the corresponding regularity theory (up to the boundary). Then we develop the nonlinear maximum principle and present some important nonlinear strong comparison principles. Subsequently we see how these results together with variational methods, truncation and perturbation techniques, and Morse theory (critical groups) can be used to analyze different classes of elliptic equations. Special attention is given to (p, 2)-equations (these are equations driven…
THE MINIMIZING TOTAL VARIATION FLOW WITH MEASURE INITIAL CONDITIONS
2004
In this paper we obtain existence and uniqueness of solutions for the Cauchy problem for the minimizing total variation flow when the initial condition is a Radon measure in ℝN. We study limit solutions obtained by weakly approximating the initial measure μ by functions in L1(ℝN). We are able to characterize limit solutions when the initial condition μ=h+μs, where h∈L1(ℝN)∩L∞(ℝN), and μs=αℋk⌊ S,α≥0,k is an integer and S is a k-dimensional manifold with bounded curvatures. In case k<N-1 we prove that the singular part of the solution does not move, it remains equal to μs for all t≥0. In particular, u(t)=δ0 when u(0)=δ0. In case k=N-1 we prove that the singular part of the limit solution …